Question

The mass of the Moon is 7.35x10 to the 22nd Kg. At some point between the Earth and the Moon, the for of Earth's gravitational attraction on an object is cancelled by the Moon's force of gravitational attraction. If the distance between Earth and the Moon (centre to centre) is 3.84x10 to the 5th km, calculate where this will occur, relative to Earth.

Answer 1

Let X be the distance from Earth. You will need the mass of the Earth also. Call it M and the moon's mass m.
Let D = 3.84*10^5 km

For the forces to be equal,

G M/x^2 = G m/(D-x)^2
G (the universal law of gravity constant) cancels out.
Solve for x/D in terms of M/m

[(D-x)/x]^2 = (D/x -1]^2 = m/M
D/x -1 = sqrt (m/M)