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In this solar system, there are three K-type main sequence stars, or "orange dwarves", named Odin, Vili and Ve. At the center of this solar system, Odin is 80% the mass of our sun. The middle star, Vili, is 65% the mass of our sun. Finally, the outermost of the three orange dwarves, Ve, is half the mass of our sun. This info concludes that Ve and Vili orbit Odin, but from how great a distance? Using the specific information provided, how far can both Ve and Vili orbit Odin without clashing into each other?

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  • $\begingroup$ how far can or shall be? $\endgroup$ – L.Dutch Jul 10 at 9:22
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    $\begingroup$ Or be far can shall how? $\endgroup$ – Willk Jul 10 at 12:14
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With masses that similar, you aren't going to get a clear-cut case of two stars orbiting the third. Rather, you will get a binary system of two stars, which is orbited by the third star.

Which two you put together to be the binary pair doesn't really matter. And whichever stars you pick to pair up, you can put them pretty much as close together as you like (at least until their Roche lobes start to overlap and you get an overcontact binary). Thematically, it would seem that Ve and Vili ought to go together... but their combined mass means that Odin will appear to orbit them more than they orbit Odin (although really all three stars will be orbiting around their common barycenter, somewhere out in empty space between them).

Once you have decided which two stars go together and how closely they are bound, a good rule of thumb is that the third star's orbit around the binary pair should be at least 5 times larger than the binary stars' orbit around each other. You may be able to get closer, but it is difficult, if not impossible, to calculate stability conditions for such a system without just brute-forcing it through numerical simulation over a very long time.

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