Hint 5

Use the perigee and apogee distances to find the semimajor axis. With this and the period, you can get the mass from Kepler's Third Law. (If, like me, you can't remember this law, you can always rederive it by considering a circular orbit whose radius is equal to the semimajor axis of the actual orbit.) This gives a mass for the Moon of $7.34\times 10^{22}$ kg.