- 2017: The kinetic energy of the satellite is given by:
$$ K = \frac{1}{2}mv^2 $$
where m is the mass of the satellite and v is its velocity. The gravitational force between the satellite and the earth is given by:
$$ F = \frac{GMm}{r^2} $$
where G is the gravitational constant, M is the mass of the earth, and r is the distance between the satellite and the earth.
The kinetic energy of the satellite is related to the gravitational force by:
$$ F = \frac{ma}{r} $$
where a is the acceleration of the satellite.
Substituting this into the equation for kinetic energy, we get:
$$ K = \frac{1}{2}mv^2 = \frac{1}{2}m\left(\frac{GMm}{r^2}\right) = \frac{GMm^2}{2r^2} $$
Therefore, the kinetic energy of the satellite is:
$$ K = \frac{GMm^2}{2r^2}
