Gravitational Effects of 2 Bodies

[petern]

There is a point b/t the Earth and the Moon where the gravitational effects of the 2 bodies balance each other. How far apart from the center of the Earth is this point? Answer: x = 3.44 x 10^8 m (from the earth) or 3.82 x 10^7 m (from the moon).

I have no clue what to do. I assume you would use either the equation Fg = (Gm1m2)/(r^2) or T^2 = kr^3.

I really don't know what to do next. Please help.

 

[Galileo's Ghost]

let the distance from Earth to the point = r, and let the distance from the Moon to the point = Earth/Moon distance - r

Since the force of gravitation from the Moon and the Earth will be equal to each other, set the gravitation equations for each equal to each other and solve for r.

 

[Shooting Star]

I have no clue what to do. I assume you would use either the equation Fg = (Gm1m2)/(r^2) ...

Use this one, as said before.