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There are a lot of images and animations on the internet depicting two bodies orbiting around their common barycenter. The barycenter is defined as the (let's say right) focus of the ellipse.

If we define the right focus as the star instead of the barycenter, then the right focus will move in a tiny ellipse around the barycenter just as the star does.

First question: What does physics say about the left focus? Will it stay put or also move around?

Second question: If the focuses are moving around, then won't the orbit eccentricity expand and contract at different points in the orbit, and also result in some kind of precession?

(I have put together a geometric simulation where the right and left foci of the orbit move around in small ellipses, in opposite directions, resulting in a wobbly orbit with "precession"--sort of; and am trying to figure out how this translates into orbital mechanics of planets).

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marked as duplicate by dmckee May 16 '13 at 20:22

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keep in mind that in your situation, the orbiting body is moving around the barycenter as well. Since the barycenter would represent the true, non-moving focus of an ellipse, when you shift it to the star, the motion of the new focus will correspond to motions of the actual ellipse. What I mean is, the orbiting body only draws out an ellipse around the barycenter, you cannot run a simulation of what the orbit looks like when the focus moves because you cannot draw an orbital ellipse around the star. It isn't valid –  Jim May 13 '13 at 20:16
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1 Answer 1

The trajectories of the two bodies each trace out separate ellipses. The barycenter is located at the left focus of one trajectory, and the right focus of the other.

The orbit of the two bodies is the ellipse generated by the polar graph of the re distance between the bodies as a function of the azimuthal angle. This ellipse is larger than either of the elliptical trajectories. The orbit is the trajectory of one body as seen from the non-inertial frame centered at the other body.

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