http://www.physicsbook.gatech.edu/api.php?action=feedcontributions&feedformat=atom&user=Dchiodo3Physics Book - User contributions [en]2026-05-06T17:42:28ZUser contributionsMediaWiki 1.42.7http://www.physicsbook.gatech.edu/index.php?title=File:652px-Topological_insulator_band_structure.svg.png&diff=22636File:652px-Topological insulator band structure.svg.png2016-04-17T23:30:13Z<p>Dchiodo3: </p>
<hr />
<div></div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=22233Gravitational waves2016-04-17T17:45:01Z<p>Dchiodo3: </p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. They have now been directly observed. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
In order to understand this theory, think about a two-dimensional field, such as the ocean's surface. As a small speedboat travels across the water, it distorts the surface, causing ripples to travel perpendicular to its momentum. A larger ship would produce stronger waves, which would carry more energy. Gravitational waves are the three-dimensional counterpart to this analogy. The speedboat represents a planet, and the ship represents a star. The object of greater mass produces stronger gravitational waves. If the propulsion of the ship suddenly shut down, the ship would gradually slow down until its velocity was zero, due to the energy transfer from the movement of the ship to the water. As a planet or star moves through space, it too is slowing down due to the energy transfer to space-time in the form of gravitational waves.<br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves. Observations made included the rate of change in the orbits of the two stars as they underwent orbital decay.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, named LISA, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
==Mathematics==<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are one and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects.<br />
<br />
== See also ==<br />
<br />
<br />
===Further reading===<br />
<br />
<br />
[http://www.nature.com/news/all-you-need-to-know-about-gravitational-waves-1.14886 "All You Need to Know About Gravitational Waves : Nature News & Comment." Nature News & Comment. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
[http://m.esa.int/Our_Activities/Space_Science/LISA_Pathfinder_en_route_to_gravitational_wave_demonstration "LISA Pathfinder En Route to Gravitational Wave Demonstration / Space Science / Our Activities / ESA Mobile." European Space Agency. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
===Also on PhysicsBook===<br />
<br />
[http://www.physicsbook.gatech.edu/Einstein%27s_Theory_of_General_Relativity Einstein's Theory of General Relativity]<br />
<br />
[http://www.physicsbook.gatech.edu/Albert_Einstein Albert Einstein]<br />
<br />
[http://www.physicsbook.gatech.edu/Gravitational_Potential_Energy Gravitational Potential Energy]<br />
<br />
==References==<br />
<br />
DISCLAIMER: ALL IMAGES AND GIFS WERE TAKEN FROM THE PUBLIC DOMAIN FOR THIS PAGE. I DO NOT OWN ANY OF THE CONTENT.<br />
<br />
<br />
All You Need to Know About Gravitational Waves : Nature News & Comment. (n.d.). Retrieved December 5, 2015,<br />
<br />
Gravitational waves and where to find them | symmetry magazine. (n.d.). Retrieved from [http://www.symmetrymagazine.org/article/gravitational-waves-and-where-to-find-them]<br />
<br />
<br />
Gravitational Waves in General Relativity. VII. Waves from Axi-Symmetric Isolated Systems | Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. (n.d.). Retrieved from [http://rspa.royalsocietypublishing.org/content/269/1336/21.short]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=22232Gravitational waves2016-04-17T17:44:32Z<p>Dchiodo3: </p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. They have no been directly observed. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
In order to understand this theory, think about a two-dimensional field, such as the ocean's surface. As a small speedboat travels across the water, it distorts the surface, causing ripples to travel perpendicular to its momentum. A larger ship would produce stronger waves, which would carry more energy. Gravitational waves are the three-dimensional counterpart to this analogy. The speedboat represents a planet, and the ship represents a star. The object of greater mass produces stronger gravitational waves. If the propulsion of the ship suddenly shut down, the ship would gradually slow down until its velocity was zero, due to the energy transfer from the movement of the ship to the water. As a planet or star moves through space, it too is slowing down due to the energy transfer to space-time in the form of gravitational waves.<br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves. Observations made included the rate of change in the orbits of the two stars as they underwent orbital decay.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, named LISA, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
==Mathematics==<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are one and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects.<br />
<br />
== See also ==<br />
<br />
<br />
===Further reading===<br />
<br />
<br />
[http://www.nature.com/news/all-you-need-to-know-about-gravitational-waves-1.14886 "All You Need to Know About Gravitational Waves : Nature News & Comment." Nature News & Comment. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
[http://m.esa.int/Our_Activities/Space_Science/LISA_Pathfinder_en_route_to_gravitational_wave_demonstration "LISA Pathfinder En Route to Gravitational Wave Demonstration / Space Science / Our Activities / ESA Mobile." European Space Agency. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
===Also on PhysicsBook===<br />
<br />
[http://www.physicsbook.gatech.edu/Einstein%27s_Theory_of_General_Relativity Einstein's Theory of General Relativity]<br />
<br />
[http://www.physicsbook.gatech.edu/Albert_Einstein Albert Einstein]<br />
<br />
[http://www.physicsbook.gatech.edu/Gravitational_Potential_Energy Gravitational Potential Energy]<br />
<br />
==References==<br />
<br />
DISCLAIMER: ALL IMAGES AND GIFS WERE TAKEN FROM THE PUBLIC DOMAIN FOR THIS PAGE. I DO NOT OWN ANY OF THE CONTENT.<br />
<br />
<br />
All You Need to Know About Gravitational Waves : Nature News & Comment. (n.d.). Retrieved December 5, 2015,<br />
<br />
Gravitational waves and where to find them | symmetry magazine. (n.d.). Retrieved from [http://www.symmetrymagazine.org/article/gravitational-waves-and-where-to-find-them]<br />
<br />
<br />
Gravitational Waves in General Relativity. VII. Waves from Axi-Symmetric Isolated Systems | Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. (n.d.). Retrieved from [http://rspa.royalsocietypublishing.org/content/269/1336/21.short]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=File:Pylon.detail.arp.750pix.jpg&diff=22122File:Pylon.detail.arp.750pix.jpg2016-04-17T16:25:01Z<p>Dchiodo3: </p>
<hr />
<div></div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=18428Gravitational waves2015-12-06T02:27:09Z<p>Dchiodo3: /* Orbital Decay */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
In order to understand this theory, think about a two-dimensional field, such as the ocean's surface. As a small speedboat travels across the water, it distorts the surface, causing ripples to travel perpendicular to its momentum. A larger ship would produce stronger waves, which would carry more energy. Gravitational waves are the three-dimensional counterpart to this analogy. The speedboat represents a planet, and the ship represents a star. The object of greater mass produces stronger gravitational waves. If the propulsion of the ship suddenly shut down, the ship would gradually slow down until its velocity was zero, due to the energy transfer from the movement of the ship to the water. As a planet or star moves through space, it too is slowing down due to the energy transfer to space-time in the form of gravitational waves.<br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves. Observations made included the rate of change in the orbits of the two stars as they underwent orbital decay.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, named LISA, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
==Mathematics==<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are one and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects.<br />
<br />
== See also ==<br />
<br />
<br />
===Further reading===<br />
<br />
<br />
[http://www.nature.com/news/all-you-need-to-know-about-gravitational-waves-1.14886 "All You Need to Know About Gravitational Waves : Nature News & Comment." Nature News & Comment. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
[http://m.esa.int/Our_Activities/Space_Science/LISA_Pathfinder_en_route_to_gravitational_wave_demonstration "LISA Pathfinder En Route to Gravitational Wave Demonstration / Space Science / Our Activities / ESA Mobile." European Space Agency. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
===Also on PhysicsBook===<br />
<br />
[http://www.physicsbook.gatech.edu/Einstein%27s_Theory_of_General_Relativity Einstein's Theory of General Relativity]<br />
<br />
[http://www.physicsbook.gatech.edu/Albert_Einstein Albert Einstein]<br />
<br />
[http://www.physicsbook.gatech.edu/Gravitational_Potential_Energy Gravitational Potential Energy]<br />
<br />
==References==<br />
<br />
DISCLAIMER: ALL IMAGES AND GIFS WERE TAKEN FROM THE PUBLIC DOMAIN FOR THIS PAGE. I DO NOT OWN ANY OF THE CONTENT.<br />
<br />
<br />
All You Need to Know About Gravitational Waves : Nature News & Comment. (n.d.). Retrieved December 5, 2015,<br />
<br />
Gravitational waves and where to find them | symmetry magazine. (n.d.). Retrieved from [http://www.symmetrymagazine.org/article/gravitational-waves-and-where-to-find-them]<br />
<br />
<br />
Gravitational Waves in General Relativity. VII. Waves from Axi-Symmetric Isolated Systems | Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. (n.d.). Retrieved from [http://rspa.royalsocietypublishing.org/content/269/1336/21.short]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=18421Gravitational waves2015-12-06T02:26:01Z<p>Dchiodo3: /* Connectedness */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
In order to understand this theory, think about a two-dimensional field, such as the ocean's surface. As a small speedboat travels across the water, it distorts the surface, causing ripples to travel perpendicular to its momentum. A larger ship would produce stronger waves, which would carry more energy. Gravitational waves are the three-dimensional counterpart to this analogy. The speedboat represents a planet, and the ship represents a star. The object of greater mass produces stronger gravitational waves. If the propulsion of the ship suddenly shut down, the ship would gradually slow down until its velocity was zero, due to the energy transfer from the movement of the ship to the water. As a planet or star moves through space, it too is slowing down due to the energy transfer to space-time in the form of gravitational waves.<br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves. Observations made included the rate of change in the orbits of the two stars as they underwent orbital decay.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, named LISA, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
==Mathematics==<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects.<br />
<br />
== See also ==<br />
<br />
<br />
===Further reading===<br />
<br />
<br />
[http://www.nature.com/news/all-you-need-to-know-about-gravitational-waves-1.14886 "All You Need to Know About Gravitational Waves : Nature News & Comment." Nature News & Comment. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
[http://m.esa.int/Our_Activities/Space_Science/LISA_Pathfinder_en_route_to_gravitational_wave_demonstration "LISA Pathfinder En Route to Gravitational Wave Demonstration / Space Science / Our Activities / ESA Mobile." European Space Agency. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
===Also on PhysicsBook===<br />
<br />
[http://www.physicsbook.gatech.edu/Einstein%27s_Theory_of_General_Relativity Einstein's Theory of General Relativity]<br />
<br />
[http://www.physicsbook.gatech.edu/Albert_Einstein Albert Einstein]<br />
<br />
[http://www.physicsbook.gatech.edu/Gravitational_Potential_Energy Gravitational Potential Energy]<br />
<br />
==References==<br />
<br />
DISCLAIMER: ALL IMAGES AND GIFS WERE TAKEN FROM THE PUBLIC DOMAIN FOR THIS PAGE. I DO NOT OWN ANY OF THE CONTENT.<br />
<br />
<br />
All You Need to Know About Gravitational Waves : Nature News & Comment. (n.d.). Retrieved December 5, 2015,<br />
<br />
Gravitational waves and where to find them | symmetry magazine. (n.d.). Retrieved from [http://www.symmetrymagazine.org/article/gravitational-waves-and-where-to-find-them]<br />
<br />
<br />
Gravitational Waves in General Relativity. VII. Waves from Axi-Symmetric Isolated Systems | Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. (n.d.). Retrieved from [http://rspa.royalsocietypublishing.org/content/269/1336/21.short]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=18420Gravitational waves2015-12-06T02:25:30Z<p>Dchiodo3: /* History */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
In order to understand this theory, think about a two-dimensional field, such as the ocean's surface. As a small speedboat travels across the water, it distorts the surface, causing ripples to travel perpendicular to its momentum. A larger ship would produce stronger waves, which would carry more energy. Gravitational waves are the three-dimensional counterpart to this analogy. The speedboat represents a planet, and the ship represents a star. The object of greater mass produces stronger gravitational waves. If the propulsion of the ship suddenly shut down, the ship would gradually slow down until its velocity was zero, due to the energy transfer from the movement of the ship to the water. As a planet or star moves through space, it too is slowing down due to the energy transfer to space-time in the form of gravitational waves.<br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves. Observations made included the rate of change in the orbits of the two stars as they underwent orbital decay.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, named LISA, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
==Mathematics==<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, and we could learn how to harness their power into future engineering projects.<br />
<br />
== See also ==<br />
<br />
<br />
===Further reading===<br />
<br />
<br />
[http://www.nature.com/news/all-you-need-to-know-about-gravitational-waves-1.14886 "All You Need to Know About Gravitational Waves : Nature News & Comment." Nature News & Comment. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
[http://m.esa.int/Our_Activities/Space_Science/LISA_Pathfinder_en_route_to_gravitational_wave_demonstration "LISA Pathfinder En Route to Gravitational Wave Demonstration / Space Science / Our Activities / ESA Mobile." European Space Agency. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
===Also on PhysicsBook===<br />
<br />
[http://www.physicsbook.gatech.edu/Einstein%27s_Theory_of_General_Relativity Einstein's Theory of General Relativity]<br />
<br />
[http://www.physicsbook.gatech.edu/Albert_Einstein Albert Einstein]<br />
<br />
[http://www.physicsbook.gatech.edu/Gravitational_Potential_Energy Gravitational Potential Energy]<br />
<br />
==References==<br />
<br />
DISCLAIMER: ALL IMAGES AND GIFS WERE TAKEN FROM THE PUBLIC DOMAIN FOR THIS PAGE. I DO NOT OWN ANY OF THE CONTENT.<br />
<br />
<br />
All You Need to Know About Gravitational Waves : Nature News & Comment. (n.d.). Retrieved December 5, 2015,<br />
<br />
Gravitational waves and where to find them | symmetry magazine. (n.d.). Retrieved from [http://www.symmetrymagazine.org/article/gravitational-waves-and-where-to-find-them]<br />
<br />
<br />
Gravitational Waves in General Relativity. VII. Waves from Axi-Symmetric Isolated Systems | Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. (n.d.). Retrieved from [http://rspa.royalsocietypublishing.org/content/269/1336/21.short]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=18412Gravitational waves2015-12-06T02:24:39Z<p>Dchiodo3: </p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
In order to understand this theory, think about a two-dimensional field, such as the ocean's surface. As a small speedboat travels across the water, it distorts the surface, causing ripples to travel perpendicular to its momentum. A larger ship would produce stronger waves, which would carry more energy. Gravitational waves are the three-dimensional counterpart to this analogy. The speedboat represents a planet, and the ship represents a star. The object of greater mass produces stronger gravitational waves. If the propulsion of the ship suddenly shut down, the ship would gradually slow down until its velocity was zero, due to the energy transfer from the movement of the ship to the water. As a planet or star moves through space, it too is slowing down due to the energy transfer to space-time in the form of gravitational waves.<br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, named LISA, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
==Mathematics==<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, and we could learn how to harness their power into future engineering projects.<br />
<br />
== See also ==<br />
<br />
<br />
===Further reading===<br />
<br />
<br />
[http://www.nature.com/news/all-you-need-to-know-about-gravitational-waves-1.14886 "All You Need to Know About Gravitational Waves : Nature News & Comment." Nature News & Comment. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
[http://m.esa.int/Our_Activities/Space_Science/LISA_Pathfinder_en_route_to_gravitational_wave_demonstration "LISA Pathfinder En Route to Gravitational Wave Demonstration / Space Science / Our Activities / ESA Mobile." European Space Agency. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
===Also on PhysicsBook===<br />
<br />
[http://www.physicsbook.gatech.edu/Einstein%27s_Theory_of_General_Relativity Einstein's Theory of General Relativity]<br />
<br />
[http://www.physicsbook.gatech.edu/Albert_Einstein Albert Einstein]<br />
<br />
[http://www.physicsbook.gatech.edu/Gravitational_Potential_Energy Gravitational Potential Energy]<br />
<br />
==References==<br />
<br />
DISCLAIMER: ALL IMAGES AND GIFS WERE TAKEN FROM THE PUBLIC DOMAIN FOR THIS PAGE. I DO NOT OWN ANY OF THE CONTENT.<br />
<br />
<br />
All You Need to Know About Gravitational Waves : Nature News & Comment. (n.d.). Retrieved December 5, 2015,<br />
<br />
Gravitational waves and where to find them | symmetry magazine. (n.d.). Retrieved from [http://www.symmetrymagazine.org/article/gravitational-waves-and-where-to-find-them]<br />
<br />
<br />
Gravitational Waves in General Relativity. VII. Waves from Axi-Symmetric Isolated Systems | Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. (n.d.). Retrieved from [http://rspa.royalsocietypublishing.org/content/269/1336/21.short]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=18352Gravitational waves2015-12-06T02:16:37Z<p>Dchiodo3: /* References */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, named LISA, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
==Mathematics==<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, and we could learn how to harness their power into future engineering projects.<br />
<br />
== See also ==<br />
<br />
<br />
===Further reading===<br />
<br />
<br />
[http://www.nature.com/news/all-you-need-to-know-about-gravitational-waves-1.14886 "All You Need to Know About Gravitational Waves : Nature News & Comment." Nature News & Comment. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
[http://m.esa.int/Our_Activities/Space_Science/LISA_Pathfinder_en_route_to_gravitational_wave_demonstration "LISA Pathfinder En Route to Gravitational Wave Demonstration / Space Science / Our Activities / ESA Mobile." European Space Agency. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
===Also on PhysicsBook===<br />
<br />
[http://www.physicsbook.gatech.edu/Einstein%27s_Theory_of_General_Relativity Einstein's Theory of General Relativity]<br />
<br />
[http://www.physicsbook.gatech.edu/Albert_Einstein Albert Einstein]<br />
<br />
[http://www.physicsbook.gatech.edu/Gravitational_Potential_Energy Gravitational Potential Energy]<br />
<br />
==References==<br />
<br />
DISCLAIMER: ALL IMAGES AND GIFS WERE TAKEN FROM THE PUBLIC DOMAIN FOR THIS PAGE. I DO NOT OWN ANY OF THE CONTENT.<br />
<br />
<br />
All You Need to Know About Gravitational Waves : Nature News & Comment. (n.d.). Retrieved December 5, 2015,<br />
<br />
Gravitational waves and where to find them | symmetry magazine. (n.d.). Retrieved from [http://www.symmetrymagazine.org/article/gravitational-waves-and-where-to-find-them]<br />
<br />
<br />
Gravitational Waves in General Relativity. VII. Waves from Axi-Symmetric Isolated Systems | Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. (n.d.). Retrieved from [http://rspa.royalsocietypublishing.org/content/269/1336/21.short]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=18327Gravitational waves2015-12-06T02:13:34Z<p>Dchiodo3: /* References */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, named LISA, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
==Mathematics==<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, and we could learn how to harness their power into future engineering projects.<br />
<br />
== See also ==<br />
<br />
<br />
===Further reading===<br />
<br />
<br />
[http://www.nature.com/news/all-you-need-to-know-about-gravitational-waves-1.14886 "All You Need to Know About Gravitational Waves : Nature News & Comment." Nature News & Comment. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
[http://m.esa.int/Our_Activities/Space_Science/LISA_Pathfinder_en_route_to_gravitational_wave_demonstration "LISA Pathfinder En Route to Gravitational Wave Demonstration / Space Science / Our Activities / ESA Mobile." European Space Agency. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
===Also on PhysicsBook===<br />
<br />
[http://www.physicsbook.gatech.edu/Einstein%27s_Theory_of_General_Relativity Einstein's Theory of General Relativity]<br />
<br />
[http://www.physicsbook.gatech.edu/Albert_Einstein Albert Einstein]<br />
<br />
[http://www.physicsbook.gatech.edu/Gravitational_Potential_Energy Gravitational Potential Energy]<br />
<br />
==References==<br />
<br />
DISCLAIMER: ALL IMAGES AND GIFS WERE TAKEN FROM THE PUBLIC DOMAIN FOR THIS PAGE. I DO NOT OWN ANY OF THE CONTENT.<br />
<br />
<br />
<br />
Thorne, Kip S. (1995). "Gravitational Waves". arXiv:gr-qc/9506086<br />
<br />
Clavin, Whitney (30 January 2015). "Gravitational Waves from Early Universe Remain Elusive". NASA</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17920Gravitational waves2015-12-06T01:26:05Z<p>Dchiodo3: /* External links */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, named LISA, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
==Mathematics==<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, and we could learn how to harness their power into future engineering projects.<br />
<br />
== See also ==<br />
<br />
<br />
===Further reading===<br />
<br />
<br />
[http://www.nature.com/news/all-you-need-to-know-about-gravitational-waves-1.14886 "All You Need to Know About Gravitational Waves : Nature News & Comment." Nature News & Comment. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
[http://m.esa.int/Our_Activities/Space_Science/LISA_Pathfinder_en_route_to_gravitational_wave_demonstration "LISA Pathfinder En Route to Gravitational Wave Demonstration / Space Science / Our Activities / ESA Mobile." European Space Agency. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
===Also on PhysicsBook===<br />
<br />
[http://www.physicsbook.gatech.edu/Einstein%27s_Theory_of_General_Relativity Einstein's Theory of General Relativity]<br />
<br />
[http://www.physicsbook.gatech.edu/Albert_Einstein Albert Einstein]<br />
<br />
[http://www.physicsbook.gatech.edu/Gravitational_Potential_Energy Gravitational Potential Energy]<br />
<br />
==References==<br />
<br />
DISCLAIMER: ALL IMAGES AND GIFS WERE TAKEN FROM THE PUBLIC DOMAIN FOR THIS PAGE. I DO NOT OWN ANY OF THE CONTENT.<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17904Gravitational waves2015-12-06T01:24:03Z<p>Dchiodo3: /* External links */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, named LISA, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
==Mathematics==<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, and we could learn how to harness their power into future engineering projects.<br />
<br />
== See also ==<br />
<br />
<br />
===Further reading===<br />
<br />
<br />
[http://www.nature.com/news/all-you-need-to-know-about-gravitational-waves-1.14886 "All You Need to Know About Gravitational Waves : Nature News & Comment." Nature News & Comment. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
[http://m.esa.int/Our_Activities/Space_Science/LISA_Pathfinder_en_route_to_gravitational_wave_demonstration "LISA Pathfinder En Route to Gravitational Wave Demonstration / Space Science / Our Activities / ESA Mobile." European Space Agency. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
===External links===<br />
<br />
[http://www.physicsbook.gatech.edu/Einstein%27s_Theory_of_General_Relativity Einstein's Theory of General Relativity]<br />
<br />
[http://www.physicsbook.gatech.edu/Albert_Einstein Albert Einstein]<br />
<br />
==References==<br />
<br />
DISCLAIMER: ALL IMAGES AND GIFS WERE TAKEN FROM THE PUBLIC DOMAIN FOR THIS PAGE. I DO NOT OWN ANY OF THE CONTENT.<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17899Gravitational waves2015-12-06T01:23:32Z<p>Dchiodo3: /* External links */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, named LISA, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
==Mathematics==<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, and we could learn how to harness their power into future engineering projects.<br />
<br />
== See also ==<br />
<br />
<br />
===Further reading===<br />
<br />
<br />
[http://www.nature.com/news/all-you-need-to-know-about-gravitational-waves-1.14886 "All You Need to Know About Gravitational Waves : Nature News & Comment." Nature News & Comment. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
[http://m.esa.int/Our_Activities/Space_Science/LISA_Pathfinder_en_route_to_gravitational_wave_demonstration "LISA Pathfinder En Route to Gravitational Wave Demonstration / Space Science / Our Activities / ESA Mobile." European Space Agency. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
===External links===<br />
<br />
[http://www.physicsbook.gatech.edu/Einstein%27s_Theory_of_General_Relativity Einstein's Theory of General Relativity]<br />
<br />
==References==<br />
<br />
DISCLAIMER: ALL IMAGES AND GIFS WERE TAKEN FROM THE PUBLIC DOMAIN FOR THIS PAGE. I DO NOT OWN ANY OF THE CONTENT.<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17888Gravitational waves2015-12-06T01:22:08Z<p>Dchiodo3: /* Radiated Power */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, named LISA, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
==Mathematics==<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, and we could learn how to harness their power into future engineering projects.<br />
<br />
== See also ==<br />
<br />
<br />
===Further reading===<br />
<br />
<br />
[http://www.nature.com/news/all-you-need-to-know-about-gravitational-waves-1.14886 "All You Need to Know About Gravitational Waves : Nature News & Comment." Nature News & Comment. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
[http://m.esa.int/Our_Activities/Space_Science/LISA_Pathfinder_en_route_to_gravitational_wave_demonstration "LISA Pathfinder En Route to Gravitational Wave Demonstration / Space Science / Our Activities / ESA Mobile." European Space Agency. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
DISCLAIMER: ALL IMAGES AND GIFS WERE TAKEN FROM THE PUBLIC DOMAIN FOR THIS PAGE. I DO NOT OWN ANY OF THE CONTENT.<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17884Gravitational waves2015-12-06T01:21:37Z<p>Dchiodo3: /* Connectedness */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, named LISA, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, and we could learn how to harness their power into future engineering projects.<br />
<br />
== See also ==<br />
<br />
<br />
===Further reading===<br />
<br />
<br />
[http://www.nature.com/news/all-you-need-to-know-about-gravitational-waves-1.14886 "All You Need to Know About Gravitational Waves : Nature News & Comment." Nature News & Comment. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
[http://m.esa.int/Our_Activities/Space_Science/LISA_Pathfinder_en_route_to_gravitational_wave_demonstration "LISA Pathfinder En Route to Gravitational Wave Demonstration / Space Science / Our Activities / ESA Mobile." European Space Agency. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
DISCLAIMER: ALL IMAGES AND GIFS WERE TAKEN FROM THE PUBLIC DOMAIN FOR THIS PAGE. I DO NOT OWN ANY OF THE CONTENT.<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17877Gravitational waves2015-12-06T01:21:03Z<p>Dchiodo3: /* Further reading */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, named LISA, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
<br />
<br />
== See also ==<br />
<br />
<br />
===Further reading===<br />
<br />
<br />
[http://www.nature.com/news/all-you-need-to-know-about-gravitational-waves-1.14886 "All You Need to Know About Gravitational Waves : Nature News & Comment." Nature News & Comment. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
[http://m.esa.int/Our_Activities/Space_Science/LISA_Pathfinder_en_route_to_gravitational_wave_demonstration "LISA Pathfinder En Route to Gravitational Wave Demonstration / Space Science / Our Activities / ESA Mobile." European Space Agency. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
DISCLAIMER: ALL IMAGES AND GIFS WERE TAKEN FROM THE PUBLIC DOMAIN FOR THIS PAGE. I DO NOT OWN ANY OF THE CONTENT.<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17868Gravitational waves2015-12-06T01:19:57Z<p>Dchiodo3: /* See also */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, named LISA, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
<br />
<br />
== See also ==<br />
<br />
<br />
===Further reading===<br />
<br />
<br />
[http://www.nature.com/news/all-you-need-to-know-about-gravitational-waves-1.14886 "All You Need to Know About Gravitational Waves : Nature News & Comment." Nature News & Comment. N.p., n.d. Web. 5 Dec. 2015.]<br />
<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
DISCLAIMER: ALL IMAGES AND GIFS WERE TAKEN FROM THE PUBLIC DOMAIN FOR THIS PAGE. I DO NOT OWN ANY OF THE CONTENT.<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17846Gravitational waves2015-12-06T01:16:55Z<p>Dchiodo3: </p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, named LISA, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
DISCLAIMER: ALL IMAGES AND GIFS WERE TAKEN FROM THE PUBLIC DOMAIN FOR THIS PAGE. I DO NOT OWN ANY OF THE CONTENT.<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17841Gravitational waves2015-12-06T01:16:16Z<p>Dchiodo3: /* Examples */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
DISCLAIMER: ALL IMAGES AND GIFS WERE TAKEN FROM THE PUBLIC DOMAIN FOR THIS PAGE. I DO NOT OWN ANY OF THE CONTENT.<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17836Gravitational waves2015-12-06T01:15:51Z<p>Dchiodo3: /* References */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
DISCLAIMER: ALL IMAGES AND GIFS WERE TAKEN FROM THE PUBLIC DOMAIN FOR THIS PAGE. I DO NOT OWN ANY OF THE CONTENT.<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17822Gravitational waves2015-12-06T01:14:49Z<p>Dchiodo3: /* Orbital Decay */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17819Gravitational waves2015-12-06T01:14:36Z<p>Dchiodo3: /* A Computational Model */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17816Gravitational waves2015-12-06T01:14:24Z<p>Dchiodo3: /* A Computational Model */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
[[Image:orbit5.gif|thumb|200px|Two stars start out in highly elliptical orbits.]]<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17810Gravitational waves2015-12-06T01:13:38Z<p>Dchiodo3: /* Orbital Decay */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17805Gravitational waves2015-12-06T01:13:11Z<p>Dchiodo3: /* A Computational Model */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
===A Computational Model===<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17802Gravitational waves2015-12-06T01:12:51Z<p>Dchiodo3: /* Orbital Decay */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
===A Computational Model===<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
<br />
[[Image:orbit5.gif|thumb|200px|The two stars start in very elliptical orbits around their common center of mass. ]]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17797Gravitational waves2015-12-06T01:12:34Z<p>Dchiodo3: /* Orbital Decay */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
<br />
[[Image:orbit1.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass.]]<br />
<br />
===A Computational Model===<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
<br />
[[Image:orbit5.gif|thumb|200px|The two stars start in very elliptical orbits around their common center of mass. ]]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17796Gravitational waves2015-12-06T01:12:26Z<p>Dchiodo3: /* A Computational Model */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
<br />
[[Image:orbit5.gif|thumb|200px|The two stars start in very elliptical orbits around their common center of mass. ]]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17787Gravitational waves2015-12-06T01:11:34Z<p>Dchiodo3: /* A Computational Model */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
Here we see the same system of two stars in a binary star system. Both start out in elliptical orbits around their commend center of mass. After quite a bit of time, their orbits will decay and circularize. After even more time, the two stars will eventually merge at the center of mass.<br />
<br />
[[Image:orbit1.gif|thumb|200px|The two stars start in very elliptical orbits around their common center of mass.]]<br />
<br />
[[Image:orbit5.gif|thumb|200px|The two stars' orbits now have decayed to the point where they are on and the same around their common center of mass. ]]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=File:Orbit1.gif&diff=17755File:Orbit1.gif2015-12-06T01:08:22Z<p>Dchiodo3: </p>
<hr />
<div></div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=File:Orbit5.gif&diff=17735File:Orbit5.gif2015-12-06T01:07:03Z<p>Dchiodo3: </p>
<hr />
<div></div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=File:Orbit2.gif&diff=17726File:Orbit2.gif2015-12-06T01:06:37Z<p>Dchiodo3: </p>
<hr />
<div></div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17696Gravitational waves2015-12-06T01:04:28Z<p>Dchiodo3: /* Orbital Decay */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math>,<br />
<br />
with the variables representing the same values as the previous equation.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17690Gravitational waves2015-12-06T01:03:58Z<p>Dchiodo3: /* Radiated Power */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math>,<br />
<br />
where E stands for Energy, and r represents the distance between the two objects.<br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17673Gravitational waves2015-12-06T01:02:56Z<p>Dchiodo3: /* Orbital Decay */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math><br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===Orbital Decay===<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17664Gravitational waves2015-12-06T01:02:23Z<p>Dchiodo3: /* Radiated Power */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math><br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
==Orbital Decay==<br />
<br />
As mentioned earlier, graviational radiation in the form of waves causes a system of two orbiting bodies to lose some energy, leading to orbital decay. For example, the system of a comet in a highly elliptical orbit and the Sun has some angular momentum, L. As gravitational waves are emanating from the center of mass from this system, the total energy of the system decreases, leading to a loss of angular momentum. Over time, this loss of energy causes the orbit of the comet to circularize, or become less elliptical. <br />
<br />
This orbital decay is also dependent on the mass of the two systems. The equation used to find the rate of change of the distance between two object due to the result of emanating gravitational waves is the following: <br />
<br />
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17600Gravitational waves2015-12-06T00:56:40Z<p>Dchiodo3: /* Overview */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time in its sphere of influence. The gravitational waves radiate outward from the gravity well, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a gravitational wave passes an observer, it slightly alters the distance between the observer and the mass of origin by a factor of billionths of a millimeter.<br />
<br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math><br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17575Gravitational waves2015-12-06T00:54:54Z<p>Dchiodo3: /* History */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time around its sphere of influence. The gravitational waves radiate outward from a mass that is in motion, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a graviational wave passes an observer, it slightly alters the distance between the observer and the mass of origin. <br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math><br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Albert Einstein first theorized about gravitational waves in his Theory of General Relativity. He hypthesized that as a gravity well moves through space-time, it would emit a "wake," of energy much like a boat leaves a wake behind it in the water.<br />
<br />
In 1993, the Nobel Prize in Physics was awarded for the observations of the Hulse-Taylor star system, which provided some concrete evidence for the existence of gravitational waves.<br />
<br />
On December 3, 2015, the European Space Agency launched a test probe, designed to orbit at the L1 Lagrange Point and measure gravitational waves by measuring the relative positions of released gold-platinum cubes with high precision lasers. If gravitational waves do exist, then the the positions of the cubes should be several billionths of a millimeter off from free fall.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=17494Gravitational waves2015-12-06T00:48:25Z<p>Dchiodo3: /* Overview */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time around its sphere of influence. The gravitational waves radiate outward from a mass that is in motion, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a graviational wave passes an observer, it slightly alters the distance between the observer and the mass of origin. <br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math><br />
<br />
This radiated energy helps explain orbital decay, which is when two the orbit of one mass around another circularizes and the distance between them slowly begins to decrease. Earth is currently undergoing this phenomenon with the Sun, as it looses about 200 joules of total energy in its orbit every second. However, that only causes a decay of the orbit of only about 1E-15 meters per day. At that rate, it would take about 1E10 times the current age of the universe to fall into the Sun.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=11741Gravitational waves2015-12-04T06:29:14Z<p>Dchiodo3: /* Radiated Power */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time around its sphere of influence. The gravitational waves radiate outward from a mass that is in motion, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a graviational wave passes an observer, it slightly alters the distance between the observer and the mass of origin. <br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=11740Gravitational waves2015-12-04T06:29:01Z<p>Dchiodo3: /* Radiated Power */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time around its sphere of influence. The gravitational waves radiate outward from a mass that is in motion, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a graviational wave passes an observer, it slightly alters the distance between the observer and the mass of origin. <br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
:<math>P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}</math> ,<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=11729Gravitational waves2015-12-04T06:26:22Z<p>Dchiodo3: /* A Mathematical Model */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time around its sphere of influence. The gravitational waves radiate outward from a mass that is in motion, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a graviational wave passes an observer, it slightly alters the distance between the observer and the mass of origin. <br />
<br />
===Radiated Power===<br />
<br />
The loss in energy from a system due to the radiation of gravitational waves can be predicted by using the following equation:<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=11724Gravitational waves2015-12-04T06:22:21Z<p>Dchiodo3: /* The Main Idea */</p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==Overview==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time around its sphere of influence. The gravitational waves radiate outward from a mass that is in motion, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a graviational wave passes an observer, it slightly alters the distance between the observer and the mass of origin. <br />
<br />
===A Mathematical Model===<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=11722Gravitational waves2015-12-04T06:22:00Z<p>Dchiodo3: </p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. <br />
<br />
[[File:Graviational waves.jpg|thumb|While gravitational waves emit no light, here they can be visualized traveling through space-time.]]<br />
<br />
==The Main Idea==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time around its sphere of influence. The gravitational waves radiate outward from a mass that is in motion, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a graviational wave passes an observer, it slightly alters the distance between the observer and the mass of origin. <br />
<br />
===A Mathematical Model===<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=File:Graviational_waves.jpg&diff=11719File:Graviational waves.jpg2015-12-04T06:21:17Z<p>Dchiodo3: </p>
<hr />
<div></div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=11703Gravitational waves2015-12-04T06:13:26Z<p>Dchiodo3: </p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves. [[File:bh_gws.png]]<br />
<br />
==The Main Idea==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time around its sphere of influence. The gravitational waves radiate outward from a mass that is in motion, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a graviational wave passes an observer, it slightly alters the distance between the observer and the mass of origin. <br />
<br />
===A Mathematical Model===<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
<br />
How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
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== See also ==<br />
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===Further reading===<br />
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==References==<br />
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This section contains the the references you used while writing this page<br />
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[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=11695Gravitational waves2015-12-04T06:10:43Z<p>Dchiodo3: </p>
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<div><br />
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Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves.<br />
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==The Main Idea==<br />
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Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time around its sphere of influence. The gravitational waves radiate outward from a mass that is in motion, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a graviational wave passes an observer, it slightly alters the distance between the observer and the mass of origin. <br />
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===A Mathematical Model===<br />
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What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
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===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
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==Examples==<br />
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Be sure to show all steps in your solution and include diagrams whenever possible<br />
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===Simple===<br />
===Middling===<br />
===Difficult===<br />
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==Connectedness==<br />
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How objects move through space has always fascinated me, especially due to the scale and the speed of celestial objects. As an Aerospace Engineering Major, I am much more interested in how we can learn about propulsion and energy just by observing the interactions of objects in the cosmos. By learning more about space-time, we could potentially develop methods of propelling our machines deeper into space than we previously thought possible. NASA and the ESA have already put extensive resources into studying gravitational waves in hopes that by unlocking their secrets, we could learn how to harness their power into future engineering projects. <br />
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==History==<br />
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Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
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== See also ==<br />
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Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
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===Further reading===<br />
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Books, Articles or other print media on this topic<br />
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===External links===<br />
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Internet resources on this topic<br />
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==References==<br />
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This section contains the the references you used while writing this page<br />
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[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=11669Gravitational waves2015-12-04T05:57:43Z<p>Dchiodo3: </p>
<hr />
<div><br />
<br />
Gravitational waves are waves in the curvature of space-time believed to be emanating from gravity wells. While they have not been ''directly'' observed, they can be indirectly observed as the loss in energy of binary system, such as a star orbiting a planet or another star. The gradual decay in angular momentum over the course of time in a orbital system can be attributed to the emission of gravitational waves.<br />
<br />
==The Main Idea==<br />
<br />
Albert Einstein explained gravity in his theory of general relativity as a phenomenon resulting from the curvature of space-time. This curvature is caused by a mass distorting and bending the space-time around its sphere of influence. The gravitational waves radiate outward from a mass that is in motion, and travel at the speed of light. These waves occur through the fabric of space-time much like mechanical waves travel through a fluid. As a graviational wave passes an observer, it slightly alters the distance between the observer and the mass of origin. <br />
<br />
===A Mathematical Model===<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
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===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
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==History==<br />
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Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
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== See also ==<br />
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Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
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===Further reading===<br />
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Books, Articles or other print media on this topic<br />
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===External links===<br />
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Internet resources on this topic<br />
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==References==<br />
<br />
This section contains the the references you used while writing this page<br />
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[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=8498Gravitational waves2015-12-02T22:08:20Z<p>Dchiodo3: </p>
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<div><br />
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Short Description of Topic<br />
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==The Main Idea==<br />
<br />
Claimed by Dylan Chiodo<br />
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===A Mathematical Model===<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
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== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3http://www.physicsbook.gatech.edu/index.php?title=Gravitational_waves&diff=6826Gravitational waves2015-12-01T22:49:49Z<p>Dchiodo3: Created page with "PLEASE DO NOT EDIT THIS PAGE. COPY THIS TEMPLATE AND PASTE IT INTO A NEW PAGE FOR YOUR TOPIC. Short Description of Topic ==The Main Idea== State, in your own words, the mai..."</p>
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<div>PLEASE DO NOT EDIT THIS PAGE. COPY THIS TEMPLATE AND PASTE IT INTO A NEW PAGE FOR YOUR TOPIC.<br />
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Short Description of Topic<br />
<br />
==The Main Idea==<br />
<br />
State, in your own words, the main idea for this topic<br />
Electric Field of Capacitor<br />
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===A Mathematical Model===<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Dchiodo3