A meteorite of mass m collides with a satellite of mass 10 m. The satellite is orbiting a planet in a circular path of radius R. Due to the collision, the meteorite sticks to the satellite and the satellite goes into an orbit whose minimum distance from the planet is R/2. If the mass of the planet is M, what is the velocity of the meteorite before the collision?

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 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.