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We know that two celestial bodies rotate around a center of mass. How does this concept work in case of solar systems where there are several planets versus one/two stars? (Even if the center of mass lies within a star, the center of mass for every planet would be different.) How is it that the rotation of celestial bodies does not become unsteady?enter image description here

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    $\begingroup$ All the planets (and the star itself) revolve around a common "barycenter" that is the center of mass of the entire system. $\endgroup$ – barrycarter Aug 16 '15 at 14:03
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    $\begingroup$ @barrycarter You know, almost every time I see your name, I mentally read it as 'barycenter' and have to go back and mentally correct myself. ;) $\endgroup$ – Stan Liou Aug 16 '15 at 14:05
  • $\begingroup$ Yes the system's barycenter wiggles a little over time as the planets move through their orbits. It's a tiny effect. Jupiter masses only 1/1052 of the sun. $\endgroup$ – Wayfaring Stranger Aug 16 '15 at 15:34
  • $\begingroup$ @WayfaringStranger Thanks, I guess this concept also applies on the entire galaxy where billion of stars revolve around a black hole. $\endgroup$ – Sirius Aug 16 '15 at 17:30
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We know that two celestial bodies rotate around a center of mass.

"We" do not know that. Rhetorical question: Pick up an apple and drop it at high noon. Does it fall towards the solar system barycenter? The answer is of course "No." It falls away from the barycenter, towards the Earth.

I'll steal a graph from an answer I wrote to a question at the sister site, physics.stackexhange.com, Do the planets really orbit the Sun?:

Given the above graph, it appears that it's much better to say that Venus orbits the Sun (red curve) rather than the solar system barycenter (black curve). So why do people consistently use a barycentric frame rather than a heliocentric frame? The answer is simple: The barycentric frame is the frame in which the equations of motion undertake their simplest form. This is particularly so when one wants to incorporate some of general relativity into the equations of motion.

Our solar system is well-behaved. Other star systems aren't quite as well-behaved. For an example of a hypothetical system that is extremely far from well-behaved, I suggest you read Saari and Xia, "Off to infinity in finite time," Notices of the AMS.

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You are missing a step in the understanding of this concept. "Two celestial bodies rotate around a centre of mass" in a system which only has two bodies. In larger systems all objects will rotate about the centre of mass of the whole system. So each planet in our solar system and the sun will all be rotating around this common centre of mass, called the barycentre.

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