# Homework Help: Kepler's 2nd law and potential energy relation

1. Nov 23, 2007

### karnten07

1. The problem statement, all variables and given/known data

A particle moves under the influence of a central potential V(r). Show that Kepler's second law, that the radius vector from the force centre to the particle sweeps out area at a constant rate, is true whatever the form of V, as long as it is central. Derive the law in the form
.
dA/dT = 0.5 r^2 (theta)

Where (r,theta) are polar coordinates in the orbital plane with origin at the force centre. There is meant to be a dot above theta!!
2. Relevant equations

3. The attempt at a solution

All i have at the moment (after trawling the net, and searching in books) is a statement and a derivation for the above equation given. But i don't know how to link it to the potential energy.

I get the equation given as equal to L/2m and the fact that it is a constant. The statement i have is:

It is true no matter what the forms of the force and potential energy functions are because it is entirely a result of the conservation of angular momentum.

Any thoughts on how to include the potential energy in a more quantitative way??

Last edited: Nov 23, 2007