1) Assume that you, the earth, and the moon are the only objects in the universe and the earth and the moon are in their current locations. (note: Express your answers in terms of some or all of the following: mass of the earth Me, mass of the moon Mm, the distance between the centers of earth and the moon Dme, your mass m, and the gravitational constant G.)
a) Find the zero force point, the place in the universe (not infinity) where you will experience no force.
b) What is the gravitational potential energy at the zero force point, assuming the gravitational potential is zero at infinity?
c) What is the gravitational potential energy at surface of the earth Re, assuming the gravitational potential is zero at infinity?
d) What is the work required to bring you from infinity to the zero force point?
e) If you started at surface of the earth a distance Re from the center of the earth what speed would you need to just reach the zero force point?
2) You are in a circular orbit around the moon at a radius of 1.5 times the radius of the moon. The radius of the moon is 1.738 x 106 m and the mass of the moon is 7.35x10^22 kg.
a) What is the period of your orbit?
b) What is your speed?
c) What is your total energy?
d) Which of the previous answer a-c would change if you orbit were an ellipse?