Proving Kepler's third law

[vectorhelpp]

deleted

deleted

 

[stapel]

Third law: The square of the period of a planet's orbit is proportional to the cube of the mean distance between the planet and the sun.
p = period
d = distance

p²= Kd³

I will assume that "K" is the proportionality constant.

A = 1/2 integral from 0 to P of (r² dt)
= 1/2 ||L||p
= pi ab

What are the definitions of A, P, L, p, r, t, a, and b? How do they relate to the given information? (Are you doing something with ellipses?) Thank you!