# Finding the position of a planet between two other planets of known mass and distance

Here is the question:

A planet with mass $m$ and a second with mass $M$ are separated by a distance $d$. A third planet with mass $m_3$ happens to be midway between $M$ and $m$. Where could the third planet be positioned (distance from the larger planet $M$ in meters) so that the net gravitational force is zero?

My confusion lies with how to solve for the position of the third planet. I am given this equation to find the force between two planets at a given distance $r$: $$F = {GMm}/{r^2}$$ With this I can then set the sum of the two forces to zero: $$0 = {GMm_3}/r_1^2 + {Gmm_3}/r_2^2$$ My confusion lies in the fact that both $r_1$ and $r_2$ are unknown. However, we do know that $r_1 + r_2 = d$. But I am confused with how to solve for either $r_1$ or $r_2$.

• Planets use to circle a star. In that context I do not understand this question at all. – Georg Jul 29 '11 at 8:08
• @user768900 , it might be that your homework question as it has been set is a little unclear. When it says "give the distance from the larger planet M in meters", it can't expect an answer that's a number, like 1 million, or something, if none of the values m,M,m3,d are given as absolute values. So express the answer as a function of those variables. – EnergyNumbers Jul 29 '11 at 9:22
• This is the same question as physics.stackexchange.com/questions/12751/… just camouflaged as "planets" instead of masses. That original version was closed as "too localized". – Georg Jul 29 '11 at 9:39
• If I'm interpreting the question correctly, in addition to the sign issue pointed out by Marek, the main issue is that you don't know how to do the algebra to solve these two equations for two unknowns. I don't want to be rude, but I think it's worth saying that, if that's the case, you're going to have continual troubles in any physics course. I'd recommend a systematic review of algebra before trying to take a physics course. I tried to supply some general algebraic hints in the previous iteration of this question. Did those make any sense at all? – Ted Bunn Jul 29 '11 at 14:43
• It is indeed puzzling that the previous question, which basically the same one, got closed and this one didn't. – Marek Jul 29 '11 at 15:00