Physics 9702/42 — October/November 2019

State Newton’s law of gravitation.

The astronomer Johannes Kepler showed that the period $T$ of rotation of a planet about the Sun is related to its mean distance $R$ from the centre of the Sun by the expression

where $k$ is a constant.

Use Newton’s law to show that, for planets in circular orbits about the Sun of mass $M$, the constant $k$ is given by

where $G$ is the gravitational constant. Explain your working.

A satellite is in a circular orbit about Mars.
The radius of the orbit of the satellite is $4.38 \times 10^6\ \text{m}$. The orbital period is $2.44$ hours.

Use the expressions in (b) to calculate a value for the mass of Mars.

mass = ______ $\text{kg}$