Question

on which fundamental law of physics is keplers second law is based

Answer 1

On which fundamental law of physics is Kepler's second law is based?

Answer

Kepler's second law is a consequence of the principle of conservation of angular momentum.

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

So the area of the wedge is

$$d A = \frac {1}{2} (r) (r d \theta).$$

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

$$\frac {d A}{d t} = \frac {1}{2} (r) \left(r \frac {d \theta}{d t}\right) = \frac {1}{2} r v _ {\theta}.$$

Now, remember the definition of angular momentum:

$$\vec {L} = m (\vec {r} \times \vec {v}), L = m r v _ {\theta}.$$

Inserting this previous equation, we get

$$\frac {d A}{d t} = \frac {1}{2} \frac {L}{m}.$$

"Equal areas in equal times" means the rate at which area is swept out on the orbit $\frac{dA}{dt}$ is constant.

It means one-half its angular momentum divided by its mass is constant. So Angular momentum is conserved.