Law of Gravitation: Difference between revisions

Revision as of 01:14, 4 December 2015

Every two objects in nature attract each other. The magnitude of the attraction force is proportional to the product of the masses of these two objects, and inverse proportional to the square of the distance between these two objects. This page is about Kepler's Three Laws and Law of Gravitation.

Kepler's Three Laws

The areas the line swipes are the same during the same period of time. This shows that the line speed of a planet is changing during circulation movement.

(1) Kepler's First Law

Kepler's First Law which is also called ellipse orbital law. This law talks about that all the planets that rotate around the sun has a orbital shape of ellipse. Sun is at one focal point of all the ellipse orbitals.

(2) Kepler's Second Law

Kepler's Second Law which is also called area law talks about that the line connected the planet and the sun will swipe the same area at the same period of time.

(3) Kepler's Third Law

Kepler's Third Law which is also called period law talks about that the ratio of cube of half of the length of the major axis to the square of the orbital period for every planet around the sun is the same. [math]\displaystyle{ \frac{R^3}{T^2}=k \text{ or }\frac{R1^3}{T1^2}=\frac{R2^3}{R2^2} }[/math] Note that Kepler's Third Law does not only work for planet but also work for satellite. The constant k is only related to the central celestial body.

Law of Gravitation

Every two objects in nature attract each other. The magnitude of the attraction force is proportional to the product of the masses of these two objects, and inverse proportional to the square of the distance between these two objects. If using m1 and m2 to represent the mass of two objects, and using r to represent the distance between these two objects, then the equation of Law of Gravitation is [math]\displaystyle{ F=G \frac{m1*m2}{r^2} }[/math] In this equation, the unit of mass is kg, the unit of distance is m, and the unit of force is N. G is a constant, which can be used for another objects. The magnitude of G is equal to the gravitational force between two 1 kg objects when they are separated by 1 m. The standard value of G is around 6.67259e-11 N*m^2/kg^2. Usually using 6.67e-11.

Two Mathematical Model

At any position inside a uniform shell, the gravitational force on an object is ZERO

What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\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.

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Simple

Middling

Difficult

Connectedness

How is this topic connected to something that you are interested in?
How is it connected to your major?
Is there an interesting industrial application?

History

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

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 In this equation, the unit of mass is kg, the unit of distance is m, and the unit of force is N. G is a constant, which can be used for another objects. The magnitude of G is equal to the gravitational force between two 1 kg objects when they are separated by 1 m. The standard value of G is around 6.67259e-11 N*m^2/kg^2. Usually using 6.67e-11.
-===A Mathematical Model===
+==Two Mathematical Model==
+===At any position inside a uniform shell, the gravitational force on an object is ZERO===
 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.