derive escape velocity...
Answers
Answer:
In order to overcome the gravitational pull of a planet, moon or sun, an object must be accelerated to the gravitational escape velocity for that celestial body at a given altitude above the body's surface.
You can derive the equation for the gravitational escape velocity by considering the initial gravitational potential energy at the given altitude and the initial kinetic energy of the object. By comparing this total initial energy with the sum of the potential and kinetic energies at an infinite separation, you can determine the escape velocity equation.
Questions you may have include:
two objects at some separation is:
ject and is thus negative:
ve = − √(2GM/Ri)
Note: Although convention-wise, the negative version of the equation is correct, most textbooks will give the positive version of the equation. You should be aware of this fact.
Altitude factor
The equation can also be written considering the initial altitude of the escaping object:
ve = − √[2GM/(r + h)]
where
r is the radius of the celestial body in km
h is the altitude or separation from the surface of the body in km
The altitude factor is necessary since the escaping object must accelerate over some displacement to reach the escape velocity.
Summary
The derivation of the gravitational escape velocity of an object from a much larger mass is achieved by comparing the potential and kinetic energy values at some given point with the values at infinity, applying the Law of Conservation of Energy.
The equation for the gravitational escape velocity is:
tational Potential Energy - HyperPhysics
Escape Velocity - From Wikipedia
Gravitation Resources