(a)[2]
State the law of gravitation proposed by Newton.
(b)
Planets have been found orbiting a star in another solar system. The orbital radius $r$ and the period $T$ of each planet are measured. The way $T^2$ changes with $R^3$ is shown in Fig. 1.1.
(b(i))[3]
The connection between $T$ and $R$ is described by $T^2 = \frac{4\pi^2 R^3}{GM}$, where $G$ is the gravitational constant and $M$ is the mass of the star. Determine the mass $M$.
(c)
A rock of mass $m$ is also orbiting the star in (b). The orbit radius is $r$.
(c(i))[3]
Explain why the gravitational potential energy of the rock has a negative value.
(c(ii))[2]
Show that the rock’s kinetic energy $E_k$ is $E_k = \frac{G M m}{2r}$.
(c(iii))[2]
Use the expression in (c)(ii) to obtain an expression for the rock’s total energy.