Question

Can anyone help me with this problem?

Answer 1

I need to know which would be the position of an object where it would not move from the gravity

Answer 2

Not moving from gravitational forces would mean that the acceleration is 0 (and so the force would be 0 from F=ma), so, first define the two forces using Newton's universal law of gravitation:
\[F_N=G \frac{M_N\cdot m}{r_N^2}\]\[F_M=G \frac{M_M \cdot m}{r_M^2}\]By setting the forces equal to each other, you're setting net force to 0 and net acceleration to 0. You'll be able to find some expression that is useful from this, but you'll need to do a little extra geometric analysis to get your final answer.

Answer 3

But what am I supposed to do? Which variable will give me the position? r2M or r2N or which one?

Answer 4

You are going to solve a distance, in the above you need to solve for r.