(a)[2]
State Newton’s law of gravitation for point masses.
(b)[4]
Johannes Kepler found that the rotation period $T$ of a planet around the Sun is connected to its mean distance $R$ from the Sun’s centre by $\frac{R^3}{T^2} = k$, where $k$ is constant. Use Newton’s law to show that, for planets moving in circular orbits about the Sun of mass $M$, the constant $k$ is $k = \frac{GM}{4\pi^2}$, with $G$ the gravitational constant. Show your working.
(c)[2]
A satellite moves in a circular orbit around Mars. The radius of the satellite’s orbit is $4.38 \times 10^6\,\text{m}$. The orbital period is $2.44\,\text{hours}$. Use the expressions in (b) to calculate a value for the mass of Mars.