Question

Find the kinetic energy K of a satellite with mass m in a circular orbit with radius R. Express your answer in terms of m, M, G, and R.

Answer 1

Answer:

$K=\frac{GmM}{2R}$

Explanation:

The kinetic energy is defined as:

$K=\frac{mv^2}{2}(1)$

Here, m is the object's mass and v its speed. In this case the speed of the satellite is the orbital speed, which is given by:

$v_{orb}=\sqrt\frac{GM}{R}(2)$

Here, G is the gravitational constant, M is the mass of the object that the satellite is orbiting and R is the radius of its circular orbit. Replacing (2) in (1):

$K=\frac{mv_{orb}^2}{2}\\K=\frac{m(\sqrt\frac{GM}{R})^2}{2}\\K=\frac{GmM}{2R}$