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 length of wire of mass M is bent into an arc of a circle of radius R, subtending an angle of ø at the center. A particle of mass m is placed at the center. What force does the wire apply on the particle?

A satellite of mass M_s is orbiting the Earth in a circular orbit of radius R_s. Due to a critical failure in its solar panels, it starts losing power at a constant rate C. If M_e and R_e denote the mass and radius of the Earth, then find the time it takes the satellite to fall to the surface of the Earth.