(a)[2]
State Newton’s law of gravitation as the force law between masses.
(b(i))[1]
Each planet moves in a circular orbit at constant speed. Explain whether the planets are in equilibrium.
(b)
A distant star is orbited by several planets, and each planet follows a circular orbit with a different radius.
(b(ii))
The orbital radius of a planet is $R$ and its period is $T$. Data for some of the planets are shown in Fig. 1.1. The relationship between $R$ and $T$ is given by $R^3 = kT^2$.
(main)[3]
Show that the constant $k$ is given by $k = \dfrac{GM}{4\pi^2}$, where $G$ is the gravitational constant and $M$ represents the mass of the star.