You are an astronaut on the moon. You look into the sky, and see the Earth in its Full phase. What lunar phase is observed by people on Earth? What if you saw a first quarter Earth? New Earth? third quarter Earth? (A diagram of the lunar phases will help with this!)
Which declinations can be observed from the North Pole? the South Pole? the Equator? Our latitude (47.6 degrees North)?
Which right ascensions can be seen from the above locations each day?
What is the latitude of the North Pole? Why is it impossible to give the longitude?
How many "hands" would be needed to measure completely around the horizon?
What range of azimuth would include all the locations on the horizon at which a star can rise? Would this question make sense at the North and South poles?
How would the length of the solar day change if the Earth rotated in the opposite direction? (A diagram of the solar vs. sidereal day will be useful to you!)
Why do we have seasons (summer and winter for example)?
Why is it that the positions of the stars in the sky are different at the same time of night in different seasons?
Suppose that the ecliptic and the celestial equator were not tilted with respect to each other. How would the azimuth of sunrise vary throughout the year? How would the length of day and night vary throughout the year?
Assume that the Moon has oceans. What will the tides be like? How many high and low tides will occur in the course of a day?