The point $P$ in Fig. 1.1 is a point mass. On Fig. 1.1, sketch lines to show the gravitational field surrounding $P$.
A moon moves in a circular orbit around a planet. Explain why the moon’s path is circular.
Many moons travel in circular orbit around a planet. A moon has angular velocity $\omega$ when its orbital radius is $r$ about the planet. Fig. 1.2 shows how $r^3$ varies with $\frac{1}{\omega^2}$ for these moons. Show that the planet’s mass $M$ is given by $M = \frac{\text{gradient}}{G}$, where $G$ is the gravitational constant.
Use Fig. 1.2 and the result in (c)(i) to show that the planet’s mass $M$ is $1.0 \times 10^{26}\,\text{kg}$.
Find the speed of a moon orbiting the planet at an orbital radius of $1.2 \times 10^8\,\text{m}$.
Use Fig. 1.2 and the result in (c)(i) to show that the planet’s mass $M$ is $1.0 \times 10^{26}\,\text{kg}$.
Find the speed of a moon orbiting the planet at an orbital radius of $1.2 \times 10^{8}\,\text{m}$. speed $=\;\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\; \text{m s}^{-1}$