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## Homework Statement

On the way to the moon the apollo astronauts reached a point where the Moon's gravitational pull became stronger than the Earth's.

A) Determine the distance of this point from the center of the Earth.

B)What is the acceleration due to the Earth's gravitation at this point?

## Homework Equations

[tex]F_G = \frac{Gm_1m_2}{r^2}[/tex]

## The Attempt at a Solution

I tried to solve this but am not sure if I am doing it right:

d= distance from earth to moon

h= height above the earth

[tex]g_{earth} = \frac{GM_E}{h^2}[/tex]

[tex]g_{moon} = \frac{GM_M}{(d-h)^2}[/tex]

set the equations equal to eachother and solve for h

[tex]d^2 - 2dh + h^2 = \frac{M_m}{M_E}h^2[/tex]

is this right so far?