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
into
to get
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?

The background to this problem is substituting

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?

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