# Angular momentum in orbital mechanics

#### kiwiheretic

Depending on whether you use the sun or earth as the centre of your reference frame (origin of co-ordinate system) can result in different answers for the calculation of angular momentum. Is there a preferred reference point for the calculation of such a value? In a two body system is it the centre of mass of each body orbiting body? Or does it not really matter as long as a consistent frame of reference is used throughout?

The background to this problem is substituting
$image=http://latex.codecogs.com/png.latex?L&space;=&space;r&space;\dot{\phi}&hash=a0d804762667f9bed2ae61249dcadf25$
into
$image=http://latex.codecogs.com/png.latex?\frac{G&space;M}{r^2}&space;=&space;\ddot{r}&space;-&space;r&space;\dot{\phi}^2&hash=bfbfb3cc6ace28b0baa86a51f5f57483$
to get
$image=http://latex.codecogs.com/png.latex?\frac{G&space;M}{r^2}&space;=&space;\ddot{r}&space;-&space;\frac{L^2}{r}&hash=6e495e8b7dcd135d73404231da234463$
The terms on the right hand side is the standard acceleration terms of a rotating frame in polar co-ordinates.

The problem is that r is the spatial separation of the two bodies and is not dependent upon choice of co-ordinate system, yet L is. How does that work?

Edit: I think I forgot the mass term in L which should be something like L=m*r*phi_dot. However which mass of the two body system would I use? Just the smaller orbiting one or both or what?

Last edited:

#### ChipB

PHF Helper
You should measure angular momentum of the system from the barycenter of the two bodies (i.e., the center of mass), and you need to include the angular momentum contributions of both bodies based on their masses and distances form the barycenter to the center of each body.