Gravitational pull of Earth and Moon on spaceship

[mckayl2]

Homework Statement

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.

Homework 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

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 :)

 

[Doc Al]

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.