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To give some insight, I'm creating a simulation, with gravity, planets, forces... And I would like to increase performance, by not doing unnecessary calculations. I could know what calculations, to not perform, if I know whether a planet, body or star is revolving an other body and no the other way around.

I don't know if this is even possible, because both bodies creates attraction forces between them, but:

Imagine a Two-body problem, a body with more mass than the other is located at the center of a reference system, and it has a moon orbiting. How I can, mathematically, know which body is orbiting the other and not the other way around? And if the both have similar masses, is this even possible? If this is not possible let me know I'm wrong.

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I don't know what you're trying to achieve, but even in a two body problem, the center of revolution is always between the centers of masses of two bodies. This phenomenon, is so intense between Jupiter and Sun that their center of revolution is actually outside the sun. And for your simulation, check out https://prappleizer.github.io/Tutorials/RK4/RK4_Tutorial.html

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  • $\begingroup$ Jupiter, which is closer to the Sun than Saturn and by far the most massive planet is the greatest influence to sometimes place the solar system's barycenter outside the Sun, not neccessarily Saturn which is the only planet to have a density less than water. $\endgroup$ Commented Dec 24, 2020 at 3:27
  • $\begingroup$ @AdrianHoward Yes, you are correct. I was meant to write Jupiter, I don't know why I wrote Saturn. Maybe because I saw so many news about the great conjunction :) $\endgroup$ Commented Dec 24, 2020 at 5:39
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    $\begingroup$ Understandable, now I can upvote your answer. $\endgroup$ Commented Dec 24, 2020 at 6:10
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Any two bodies orbiting each other will both orbit the center of their combined masses, the barycenter. If they are of equal mass the barycenter will be of equal distance from each. If one has greater mass the barycenter will be closer to it.

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  • $\begingroup$ I don't know if this is possible, but if I calculate this barycenter, and see that this point is more near to a body than to the other, I could somehow, know which one is more influenced by the other, in other words, which body is orbiting the other (unless they have same masses) even when this is not an 100% accurate. No? $\endgroup$ Commented Dec 24, 2020 at 9:52
  • $\begingroup$ Here is a lot of information; en.wikipedia.org/wiki/Orbit $\endgroup$ Commented Dec 24, 2020 at 15:06

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