Question

is derivation for geometrical meaning of angular momentum same as keplers third law

Answer 1

Yes, the derivation for geometrical meaning of angular momentum is same as that of kepler's third law.

The geometrical meaning of the angular momentum is mathematically given as the twice the product of mass $m$ of the body and the rate of change of areal velocity $\frac{dA}{dt}$, that is,
$L=2m\frac{dA}{dt}$
And Kepler’s third law is derived by using Kepler’s second law which says that the rate of sweeping out of area is proportional to the angular momentum and is equal to $\frac{L}{2m}$, that is,
$\frac{L}{2m}=\frac{dA}{dt}$