Gravitation Force Question | Tricky

[Raza]

Hi, I am taking Physics Grade 12 at home, so I get teacher's help for 2 hours once a week. They basically give me booklets to do at home and just simply hand it in. But the negative side to this that it's only 2 hours of help and teachers don't know most of the questions (they're new). And also the books are COMPLETE crap; there is little or no explanation behind the physic's equation and leave you to think about equation yourself. There's more questions that I don't get but here's the 1st question from the booklet.

Homework Statement

The mass of the Moon is 7.35 x 10²²kg. At some point between Earth and the Moon, the force of Earth's gravitational attraction on an object is canceled by the Moon's force of gravitational attraction. If the distance between Earth and the Moon (center to center) is 3.84 x 10⁵km, calculate where this will occur, relative to Earth.

Homework Equations

$$F_{g}=\frac{Gm_{1}m_{2}}{r^2}$$
M_Moon=7.35 x 10²²kg
M_Earth=5.98 x 10²⁴kg
G_constant=6.67 x 10^-11N x m^2/kg^2

The Attempt at a Solution

I think it must be:
$$\frac{F_{(G)moon}}{F_{(G)earth}}=1$$
and you are trying to figure out r.

 

[exec]

Using your solution, you've got a wrong answer? r^2 = (3.84E5)^5?

 

[Raza]

Well, is my solution right?

 

[Hootenanny]

How about trying;

$$\frac{GM_e}{d^2}-\frac{GM_m}{(r-d)^2} = 0$$

Where d is the distance from the Earth to the equilibrium position and r is the distance from Earth to the moon. Does that make sense?