Question

show that angular momentum conservation is equivalent to kepler's 2nd law?​

Answer 1

Answer:

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.