(a)[1]
State the meaning of gravitational force.
(b)
(c(i))[2]
The stars $S_1$ and $S_2$ turn with the same angular velocity $\omega$ about point $P$, as shown in Fig. 1.2. Point $P$ is a distance $x$ from the centre of star $S_1$. The rotation period of the stars is $44.2$ years. Calculate the angular velocity $\omega$.
(c(ii))[2]
By considering the forces on the two stars, show that the ratio of the masses of the stars is $$\frac{\text{mass of } S_1}{\text{mass of } S_2} = \frac{d - x}{x}.$$
(c(iii))[3]
The mass $M_1$ of star $S_1$ is given by $$G M_1 = d^2 (d - x) \omega^2,$$ where $G$ is the gravitational constant. The ratio in (ii) is $1.5$. Use the data from (b) and your answer in (c)(i) to find the mass $M_1$.