An astronaut is in equilibrium when he is positioned 140 km from planet X and 581 km from planey Y, along the straight line joining the planets' centers. What is the ration of the masses X/Y? I know the answer is 0.0581, I just do not know how to solve it.

Question

anonymous · Answer

How come, you know the answer is 0.0581 then?

anonymous · Answer

Gravitational force obeys an inverse square law - as in the the gravitational force depends on the distance as$$F  = \frac{ GMm }{ r ^{2} }$$
Small m is the mass of astronaut, M the planet, etc. equate the two forces to have the astronaut in equilibrium. G, m cancel, then arrange to get the Mass ratio: $$\frac{ M_{x} }{ M_{y} }\ = \frac{ 140^{2} }{ 581^{2} }$$