A moon travels in a circular orbit of radius $r$ around a planet. The moon’s angular speed in its orbit is $\omega$. The planet and its moon may be treated as isolated point masses in space. Show that $r$ and $\omega$ are connected by the expression $r^3\omega^2 = \text{constant}$. Explain your working.
Phobos and Deimos are moons in circular orbits around the planet Mars. The data for Phobos and Deimos are given in Fig. 1.1.
Use the information in Fig. 1.1 to determine the mass of Mars.
Use the information in Fig. 1.1 to determine the period of Deimos in its orbit around Mars.
Mars rotates about its axis in 24.6 hours. Deimos follows an equatorial orbit and moves in the same direction as Mars spins about its axis. Use your answer in (i) to comment on the orbit of Deimos.