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

In a circular orbit, the gravitational force provides the necessary centripetal force. Thus, we set the centripetal force equal to the gravitational force: $\frac{mv^2}{R} = \frac{GMm}{R^2}$ Simplifying this gives: v^2 = \frac{GM}{R} Therefore, the speed (v) of the satellite is: v = \sqrt{\frac{GM}{R}}.

Kinetic energy (KE) is given by the formula: $KE = \frac{1}{2}mv^2$ Substituting the expression for v: $KE = \frac{1}{2}m\left(\frac{GM}{R}\right)$ This simplifies to: $KE = \frac{GMm}{2R}.$