Also, another point to make. 

Here is a little physics for you.  Gravity falls by the square of the distance.  Hence, the further you go from an object, the lower its gravitational effect on you.

Even you and me are affected by the Moon's gravity.  The reason you dont float off into space is because Earth's gravity is so much stronger than the moon's gravity where we are.

If you get 7/8ths the distance from the earth to the moon, the effect of gravity of the moon and the earth is nearly the same.  From then on, the moon's gravity is stronger than earths.