Physics 9702/43 — October/November 2013

State Newton’s law of gravitation.

A star and a planet are isolated in space. The planet orbits the star in a circular orbit of radius $R$, as illustrated in Fig. 1.1.

The angular speed of the planet about the star is $\omega$.
By considering the circular motion of the planet about the star of mass $M$, show that $\omega$ and $R$ are related by the expression

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

The Earth orbits the Sun in a circular orbit of radius $1.5 \times 10^8\ \text{km}$. The mass of the Sun is $2.0 \times 10^{30}\ \text{kg}$.
A distant star is found to have a planet that has a circular orbit about the star. The radius of the orbit is $6.0 \times 10^8\ \text{km}$ and the period of the orbit is $2.0\ \text{years}$.

Use the expression in (b) to calculate the mass of the star.

mass = ______ $\text{kg}$