Satellite - Planet-Satellite Mass Ratio · Physics Brawl 2012 #FoL.9
Physics · mechanics
Problem
Consider a planet and its natural satellite orbiting about their common centre of mass, where the motion takes place in a plane. The magnitude of the tangent velocity of the satellite, defined with respect to the centre of mass of the system, is 2.5 km·s⁻¹. Find the ratio of the mass of the planet to the mass of the satellite in order for the centre of mass of the system to be located at the planet's surface, given that the orbits are circular. The mass of the planet is Mp = 7.6·10²⁴ kg, it has a radius of Rp = 7436 km and the radius of the satellite is Rm = 1943 km.