A particle of mass m is located on the outside of a uniform sphere of mass M at a distance r from its center. Find the potential energy of gravitational interaction between the particle and the sphere.

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 body is thrown vertically upwards with a velocity v_o at the north pole. Neglecting air drag, find the height to which the body will rise in terms of the Earth's radius R, the gravitational acceleration g and v_o.