From the fundamental definition of angular momentum applied to a point mass of the orbiting body.Derivation of the Angular Momentum of Orbiting Body.
From the fundamental definition of angular momentum applied to a point mass of the orbiting body.
|
L
|
= angular momentum |
|
m
|
= mass of the orbiting body |
|
r
|
= radial distance of the orbiting body from the primary body. |
|
vT
|
= the velocity of the orbiting body perpendicular to the radial direction |
There are two points where we know that the velocity is purely tangential and those are at perihelion and apohelion.
We also know the velocity at these points from orbital velocity equation.
Calculating the angular momentum L at the perihelion,
Since the angular momentum is the same at any point in a body's orbit we have found the angular momentum in terms of the orbital parameters.