State Newton’s law of gravitation.
A satellite with mass $m$ moves in a circular orbit of radius $r$ around a planet of mass $M$. For this planet, the value of $GM$ is $4.00 \times 10^{14} \text{N m}^2\text{ kg}^{-1}$, where $G$ is the gravitational constant. You may assume that the planet is isolated in space.
Using the gravitational force on the satellite together with the centripetal force, show that the kinetic energy $E_{K}$ of the satellite is given by $E_{K} = \frac{GMm}{2r}$.
The satellite’s mass is $620\ \text{kg}$ and it starts in a circular orbit of radius $7.34 \times 10^{6}\ \text{m}$, as shown in Fig. 1.1.
Use your answers in (ii) to explain whether the linear speed of the satellite increases, decreases or stays the same when the radius of the orbit decreases.