You plan to take a trip to the moon. Since you do not have a traditional spaceship with rockets, you will need to leave the earth with enough speed to make it to the moon. Some information that will help during this problem:

m _earth = 5.9742 x 10 ²⁴ kg
r _earth = 6.3781 x 10 ⁶ m
m _moon = 7.36 x 10 ²² kg
r _moon = 1.7374 x 10 ⁶ m
d _{earth to moon} = 3.844 x 10 ⁸ m (center to center)
G = 6.67428 x 10 ^-11 N-m ² /kg ²

1) On your first attempt you leave the surface of the earth at v = 5534 m/s. How far from the center of the earth will you get?

2) Since that is not far enough, you consult a friend who calculates (correctly) the minimum speed needed as v _min = 11068 m/s. If you leave the surface of the earth at this speed, how fast will you be moving at the surface of the moon? Hint carefully writes out an expression for the potential and kinetic energy of the ship on the surface of earth, and on the surface of moon. Be sure to include the gravitational potential energy of the earth even when the ship is at the surface of the moon!

3) Which of the following would change the minimum velocity needed to make it to the moon?

The mass of the earth

The radius of the earth

The mass of the spaceship