Exam 3: Eclipses and the Motion of the Moon

The fact that the Earth-Moon system orbits the Sun (covering 30° per month) in a clockwise direction viewed from the celestial north pole while the Moon orbits Earth, also in a clockwise direction, means that the time between successive full moons, the synodic month, compared to one lunar orbital (sidereal) period is:

As seen by a distant observer who is fixed with respect to the stars, approximately how long does it take for the Moon to rotate once around its own axis?

What is the diameter of the Moon compared to that of Earth, as measured by the ancient Greek astronomer Aristarchus of Samos?

If Earth orbited the Sun in half the time it does now, how would the length of time between full moons change?

How did the ancient Greek astronomer Aristarchus of Samos determine that the Moon's diameter was about 1/3 that of Earth?

The Moon rises later each day because each day it has moved farther along its orbit around Earth (except for observers at polar latitudes, for whom the Moon can remain above or below the horizon for 24 hours each day). On average, how much later does it rise each day (you might attempt to verify this by observation)? (Hint: What fraction of a month does a day take up?)

If the Moon is now in its waxing crescent phase, 1 week from now it will be: