describing elliptic orbits in barycenter frame of reference?

[h4tt3n]

Hello,

 

Recently I've been reading the wikipedia articles on orbital elements and orbital state vectors. I've used the equations to write a small program which calculates the elliptic trajectory of an orbiting body from its state vectors.

 

The trouble is that all equations in the articles seem to assume that the orbiting bodys mass is neglible and that the barycenter (or center of mass) is placed exactly at the center of the heavier parent body. If I want to describe the trajectories of two bodies of nearly the same mass orbiting their barycentre (like in the animation below), the equations in the articles cannot be used.

 

 

So, my question is: how do you calculate orbital elements like semimajor axis, eccentricity and so on, not from a parent body frame of reference, but from a barycentric frame of reference?

 

Cheers,

Mike

[h4tt3n]

One week later bump!

 

Seriously, since all real elliptic trajectories have the barycentre at one focus point, how come there apparently aren't any examples or tutorials available to calculate such an orbit?

 

Cheers,

Mike