State the law of gravitation proposed by Newton.
A satellite of mass $m$ moves in a circular orbit of radius $r$ around a planet of mass $M$. For this planet, the product $GM$ is $4.00 \times 10^{14}\,\text{N m}^2\,\text{kg}^{-1}$, where $G$ denotes the gravitational constant. The planet may be taken as isolated in space.
Show, by considering the gravitational force on the satellite together with the centripetal force, that the kinetic energy $E_K$ of the satellite is given by $E_K = \frac{GMm}{2r}$.
The satellite has mass $620\,\text{kg}$ and begins 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 orbital radius decreases.