Forces and Motion Question
View this question.
Add this question to a group or test by clicking the appropriate button below.
One of the theories explaining the formation of Saturn rings shown below states that if an orbiting object gets close to a massive planet, the tidal force exerted on the object's surface will exceed the force of the object's own gravity, leading to the object's disintegration and eventual scattering along its orbit. The maximum distance from the planet for which this is possible is known as Roche limit after French astronomer Edouard Roche who first calculated this limit in 1848. Calculate Roche limit in a simplified case by equating the force of gravity exerted on a probe mass by a planet of mass Mp and radius Rp to the net force exerted on the same probe mass by a satellite of mass Ms and radius Rs orbiting the planet on a circular orbit of radius d (Roche limit). Assume that the satellite is orbiting with synchronous rotation, meaning that it makes one rotation about its axis in about the same time it takes it to orbit the planet, much like the Moon orbiting Earth. Take the centrifugal force of this rotation into account.
