Explain what is meant by a central force acting on a particle moving in three dimensions.

Show that the angular momentum of a particle about the origin for a central force is conserved, and hence that its path lies in a plane.

Show that, in the approximation in which the Sun is regarded as fixed and only its gravitational field is considered, a straight line joining the Sun and an orbiting planet sweeps out equal areas in equal time (Kepler's second law).