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Everything in the Solar System revolves around the "barycenter": the overall center of mass. This barycenter is not in the center of the Sun. Some articles and essays I've read go so far as to suggest that the position of the barycenter does not have a set of fixed coordinates within the System: it fluctuates.

Well. Since everything, including the Sun, revolves around this barycenter, the Sun must have its own orbit around it. What does it look like? How large is it? How elliptic?

(In my research, I have tried and failed to establish whether the barycenter is within the Sun or outside it. Either way, an orbit is an orbit).

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    $\begingroup$ Did your research include an internet search for "solar system barycentre"? E.g an image 4.bp.blogspot.com/-40miHh9ddms/UkdtFuAj-UI/AAAAAAAAEa0/… or a movie m.youtube.com/watch?v=_IHXj8k2jqc $\endgroup$ – Rob Jeffries Apr 26 '16 at 23:01
  • $\begingroup$ @RobJeffries: As did yours, obviously. So, were you able to establish, based on those two links, the size and shape of the Sun's orbit? Just curious. Cause I wasn't. $\endgroup$ – Ricky Apr 26 '16 at 23:29
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    $\begingroup$ Slightly further down the search list, it is shown the other way around. qph.is.quoracdn.net/… $\endgroup$ – Rob Jeffries Apr 27 '16 at 0:38
  • $\begingroup$ @RobJeffries: The picture is just as beautiful as the other ones. The fact that it does not inform is just a minor flaw, I suppose. $\endgroup$ – Ricky Apr 27 '16 at 1:44
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In case anyone can't follow the links in my comment (above), here are the two pictures I mentioned. From: here and here.

Motion of the barycenter of the Solar System relative to the Sun

track of the solar centre

The first claims to show the track of the solar system barycentre in the heliocentric reference frame. The outer yellow circle marks the photosphere of the Sun. The second plot claims to show the track of the centre of the Sun in the barycentric reference frame. The yellow circle shows the photosphere of the Sun to scale. As you can see, the plots are actually (almost) the same! Given that to go from one frame to the other is just a translation, I suppose they can both be right providing the x and y axes are defined appropriately.

To answer the questions posed: "What does it look like" - it looks like these two pictures. "How large is it?" As you can see, the maximum separation between the barycentre and the solar centre appears to be about 2 solar radii over the timescale covered by these plots, but is as small as a tenth of a solar radius (e.g. in 1950). "How elliptic?" Not at all really, it is a complicated superposition caused by the orbits mainly of Jupiter and Saturn, but all the planets contribute to a greater or lesser extent.

The barycenter is calculated from the instantaneous positions of all the discrete masses in the solar system. I do not know for sure, but I assume that it includes all of the planets, and that everything else is negligible at the scale of the thickness of the line.

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  • $\begingroup$ Could you include the links and explain the sources of these images in your answer? It would be a lot more interesting and informative if you could explain how these are generated rather than just saying "here they are!". $\endgroup$ – FJC Apr 27 '16 at 14:39
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    $\begingroup$ You can use JPL HORIZONS output to make your own plot; choose Vectors, Sun, and Solar System Barycenter. If each planet's product of mass and orbital radius is proportional to its contribution to the Sun's offset from the barycenter, I figure Jupiter accounts for 49%, Saturn 27%, Uranus 8%, Neptune 15%. $\endgroup$ – Mike G Apr 27 '16 at 18:28
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    $\begingroup$ (Rob, I know this is old but,) sorry for a newbie question, can you point towards some starting point/some details of how exactly is an orbit sketched if one knows the instantaneous positions of the an object in orbit? $\endgroup$ – 299792458 Jun 21 '17 at 19:44

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