Hi! I am struggling with this problem-- any help would be much appreciated--

Question

thank you

astronauts on their way to the moon reach a point --> at this point, the moon's gravitational pull becomes stronger than the earth's gravitational pull-----find the distance between this point and the center of the EARTH

Answer 1

Equate the gravitational pulls from the earth and the moon.

Let
D=distance between the centres of the earth and the moon.
x=distance of the equality point from the centre of the earth.
M=mass of the earth
m=mass of the moon

Then
GM/x² = Gm/(D-x)²
Solve for x in terms of D, M and m.