A satellite X of mass m is in a concentric circular orbit of radius R about a planet of mass M - AQA - A-Level Physics - Question 14 - 2017 - Paper 2

Since the satellite is in a circular orbit, the gravitational force provides the necessary centripetal force to keep the satellite in orbit. Thus,

$F = \frac{mv^2}{R}$

Equating the gravitational force to the centripetal force gives:

$\frac{GMm}{R^2} = \frac{mv^2}{R}$.

Rearranging the equation gives:

$v^2 = \frac{GM}{R}$.

Taking the square root,

$$v = \sqrt{\frac{GM}{R}}.$

The kinetic energy (KE) of the satellite can be calculated using the formula:

$KE = \frac{1}{2}mv^2.$

Substituting the value of v from the previous step:

$$KE = \frac{1}{2}m\left(\frac{GM}{R}\right) = \frac{GMm}{2R}.$

According to the above calculation, the correct answer for the kinetic energy of satellite X is:

A) ( \frac{GMm}{2R} ).