Escape Velocity: Difference between revisions
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:<math>v_e = \sqrt{\frac{2GM}{r}},</math> | :<math>v_e = \sqrt{\frac{2GM}{r}},</math> | ||
where ''G'' is the universal [[gravitational constant]] (''G'' = 6.67×10<sup>−11</sup> m<sup>3</sup> kg<sup>−1</sup> s<sup>−2</sup>), ''M'' the mass of the body to be escaped, and ''r'' the distance from the [[center of mass]] of the mass ''M'' to the object.<ref group="nb"> | where ''G'' is the universal [[gravitational constant]] (''G'' = 6.67×10<sup>−11</sup> m<sup>3</sup> kg<sup>−1</sup> s<sup>−2</sup>), ''M'' is the mass of the large body to be escaped, and ''r'' the distance from the [[center of mass]] of the mass ''M'' to the object.<ref group="nb"> This equation assumes there is no atmospheric friction and is an ideal scenario with sending an object on a trajectory. In fact, the escape velocity stated here should actually be called escape speed due to the fact that the quantity to be calculated is completely independent of direction. Notice that the equation does not include the mass of the object escaping a large body as escape velocity is only dependent on gravitational force. We also assume that an object is escaping from a uniform body. | ||
===A Mathematical Model=== | ===A Mathematical Model=== | ||
Revision as of 15:50, 5 December 2015
created by Varun Rajagopal
Escape velocity is defined as the minimum velocity required for an object to escape the gravitational force of a large object. The sum of an object's kinetic energy and its Gravitational potential energy is equal to zero. The gravitational potential energy is negative due to the fact that kinetic energy is always positive. The velocity of the object will be be zero at infinite distance from the centre of gravity. There is no net force on an object as it escapes and zero acceleration is perceived.
The Main Idea
The formula for escape velocity at a certain distance from a body is calculated by the formula Template:Cite book
- [math]\displaystyle{ v_e = \sqrt{\frac{2GM}{r}}, }[/math]
where G is the universal gravitational constant (G = 6.67×10−11 m3 kg−1 s−2), M is the mass of the large body to be escaped, and r the distance from the center of mass of the mass M to the object.<ref group="nb"> This equation assumes there is no atmospheric friction and is an ideal scenario with sending an object on a trajectory. In fact, the escape velocity stated here should actually be called escape speed due to the fact that the quantity to be calculated is completely independent of direction. Notice that the equation does not include the mass of the object escaping a large body as escape velocity is only dependent on gravitational force. We also assume that an object is escaping from a uniform body.
A Mathematical Model
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
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Examples
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