A planet is moving around the sun (mass M_s) in an elliptical orbit. When it is at a distance r_o from the sun, its velocity is v_o and the angle between the radius vecor r_o and the velocity vector v_o is equal to ø. Find the maximum and the minimum distance that will separate this planet from the sun.

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.

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?