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

Kane Robinson

Mathematics

26 September, 21:02

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.

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Answers (1)

Know the Answer?

Mollie Macdonald · Answer 1

Well, yeah, sometimes we have that weird feeling that our guts know the answer but we don't know why. Let me show you how I got mine.

Gravitational force obeys an inverse square law - as in the gravitational force depends on the distance as F = 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: Mx / My = 140 ²/581²