Trip to Moon: Escape Earth's Gravity!

[aszymans]

Homework Statement

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:

mearth = 5.9742 x 1024 kg
rearth = 6.3781 x 106 m
mmoon = 7.36 x 1022 kg
rmoon = 1.7374 x 106 m
dearth to moon = 3.844 x 108 m (center to center)
G = 6.67428 x 10-11 N-m2/kg2

Homework Equations

)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?

The Attempt at a Solution

I have tried taking -GMm/r+h and using the Earth and moon masses and setting then equal to each other and solving and I am just getting confused on the set up of the problem.

 

[Spinnor]

Can you write down the gravitational potential for a general point between the surface of the Earth and the surface of the moon on the line through their centers? If so find the maximum for that potential and then the difference between that maximum and the potential on the surface of the Earth will tell you how much kinetic energy you need.