Question

Consider a spaceship located on the Earth-Moon center line (i.e. a line that intersects the centers of both bodies) such that, at that point, the tugs on the spaceship from each celestial body exactly cancel, leaving the craft literally weightless. Take the distance between the centers of the Earth and Moon to be 3.72E+5 km and the Moon-to-Earth mass ratio to be 1.200E-2. What is the spaceship's distance from the center of the Moon?

Answer 1

Let R be the distance from Earth to Moon.

Let r be the distance from Earth to the spaceship, and R-r the distance from Moon to spaceship.

Then the force of gravity from spacecraft to Earth is EQUAL to the force of gravity from Spacecraft to Moon.

Set them equal, and solve for r.