Assume the Earth to be a uniform sphere of mass M and radius R. Find the pressure P inside the sphere caused by the gravitational compression as a function of r, the distance from the center.

A binary system of stars consists of two stars moving around the center of inertia of the system due to gravitation. What is the distance between the stars if the mass of the whole system is m and the time period of revolution is T?

A small asteroid starts falling onto the sun from a distance equal to the radius of the Earth's orbit. Initially the body starts off with zero velocity. Using Kepler's law, find in terms of the Earth's orbital time period T how long the rock will take to fall into the sun.