Kepler's Second Law Revisited

Consider a small wedge of the orbit traced out in time dt:

So the area of the wedge is

And the rate at which area is swept out on the orbit is

Now, remember(?) the definition of Angular Momentum:

Inserting this previous equation , we get

"Equal areas in equal times" means the rate at which area is swept out on the orbit (dA/dt) is constant.

So Kepler's Second Law Revised:

The rate at which a planet sweeps out area on its orbit is equal to one-half its angular momentum divided by its mass (the specific angular momentum). Angular momentum is conserved.