(a)[2]
State Newton’s law of gravitation for two point masses.
(b)
A planet can be treated as a uniform sphere. A satellite moves in a circular orbit of period $T$ around the planet at height $h$ above its surface. The orbit height can be changed by the satellite’s rocket engines. Fig. 1.1 shows how $T^2$ varies with $h$.
(b(i))[2]
By referring to the forces involved, explain why the satellite’s orbit is circular.
(b(ii))[3]
Use Newton’s law of gravitation to demonstrate that $h$ and $T$ satisfy $(h + B)^3 = \frac{GA}{4\pi^2} T^2$, where $G$ is the gravitational constant and $A$ and $B$ are constants depending on the planet’s properties.
(b(iii))[5]
Use the gradient and intercept of the line in Fig. 1.1 to find $A$ and $B$. Include units with your answers.