Locate the position of a spaceship on the Earth-Moon center line such that, at that point, the tug of each celestial body exerted on it would cancel and the craft would literally be weightless. What is the distance (in m from the moon)
let x be the distance from center of moon.
let d be the distance from moonto earth
let me be mass earth, mm mass moon
forceEarth=forcemoon
GMe*m/(d-x)^2=GMm*m/x^2
solve for x