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My goal is to find a velocity vector for two planets so that they orbit each other. The planets' masses and distances are known, just not their velocities.

When googling for an equation, I found a few that seemed on the right track but not quite what I need. Such as the equation for orbits where one body is significantly more massive than the other (e.g. the earth and the sun). Or equations that give the period of the orbit, but not a vector I can use.

Is there a straightforward way to approach this?

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    $\begingroup$ Are these co-orbiting planets also orbiting a star? Do you just want a planar orbit, or do you need a full 3D solution? Anyway, take a look at en.wikipedia.org/wiki/Gravitational_two-body_problem en.wikipedia.org/wiki/Orbit_equation and maybe en.wikipedia.org/wiki/Kepler%27s_equation Also check for related questions on Astronomy.SE. $\endgroup$ – PM 2Ring Apr 29 at 11:48
  • $\begingroup$ @PM2Ring No they're just two planets orbiting each other in a circular orbit. Much like that second animation on that wikipedia article you linked. Thanks for the links, I'll check those out! :) $\endgroup$ – Daffy Apr 29 at 18:17
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    $\begingroup$ Ok. Flat circular orbits are pretty easy. The 1st Wiki link should have all the info you need. $\endgroup$ – PM 2Ring Apr 29 at 18:45
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    $\begingroup$ Critical term to look for in your reading: "reduced mass". $\endgroup$ – dmckee Apr 30 at 1:29

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