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 3.92E+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?
you don't need the q
Let M1 = moon mass; M2 = Earth mass,
r = distance from spaceraft to moon, and
D = Earth-moon distance
When the two gravity pulls are equal,
M1/r^2 = M2/(D-r)^2
[(D-r)/r]^2 = M2/M1 = 1/(0.012)
(D-r)/r = 9.13 = R/r -1
D/r = 10.13
Look up D and compute r.