Answer to the extra-credit problem with explanation:

The question

Suppose that the gravity holding the Moon in orbit suddenly disappeared when the Moon was in the First Quarter phase. Make a sketch like that shown below. At the First Quarter moon draw an arrow showing the direction in which the Moon would move in that case. I told you that you did not have to worry about the gravity of the Sun for the purposes of this problem.

Answer. This a Newton’s first law problem. Newton’s first law states that an object will move in a straight line at constant speed unless an outside force acts upon it. In this case we have turned off the outside force, gravity. So the moon will move in a straight line at constant speed. The direction of that motion will be the same direction that the Moon was moving when the gravity disappeared. The Moon will move in a straight line to the left.