(a)[2]
State Newton’s law of gravitation.
(b)
Several planets orbit a distant star. Each planet follows a circular orbit with a different radius.
(b(i))[1]
Each planet moves with constant speed. Explain whether the planets are in equilibrium.
(b(ii))
For a planet, the orbital radius is $R$ and the orbital period is $T$. Some planets’ data are shown in Fig. 1.1. The link between $R$ and $T$ is written as $R^3 = kT^2$.
(c)[3]
Show that the constant $k$ is defined by $k = \dfrac{GM}{4\pi^2}$, where $G$ is the gravitational constant and $M$ is the mass of the star.
(d)[3]
Use the three planets’ data from Fig. 1.1 and the expression for $k$ to calculate the star’s mass $M$.