# Gravitational pull of Earth and Moon on spaceship

1. Aug 23, 2009

### mckayl2

1. The problem statement, all variables and given/known data

A spaceship is launched and starts moving directly towards the Moon. At what distance from the Earth will the pull of the Moon on the spaceship exceed the pull of the Earth? Ignore the effect of the Sun in this calculation.

2. Relevant equations

F = Gm1m2/r2
F = ma = mg
g=9.80m/s2
Mass of earth = 5.86 x 1024
Mass of moon = 7.35 x 1022

3. The attempt at a solution

For the earth:
Using F=mg=Gm1m2/r2, radius of Earth to Moon is calculated to be 2.24 x 106km

For the moon:
Using mg = Gm1m2/r2, the gravitational pull of the moon is calculated to be 1.618m/s2

I'm not sure where to go from here, any help is much appreciated :)

2. Aug 23, 2009

### Staff: Mentor

Hint: If the spaceship is a distance X from the center of the earth, how far is it from the center of the moon? If you call the mass of the spaceship m, what's the earth's gravitational force on the ship in terms of X? What's the moon's gravitational force? Set up an equation and solve for X.