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Hill stability

(planetary orbits which will remain in the same order)

Hill stability is the stability of a planetary system such that the planetary orbits will remain as is, i.e., the innermost orbit will remain innermost. It does not exclude the possibility of the outermost planet being ejected.

A sufficient-but-not-necessary criterion is the following inequality regarding adjacent (coplanar) planets and the star:

    2M
- ——————— c2h
   G2M*3

> 1 +

          m1m2
34/3 —————————————————
     m32/3(m1+m2)4/3

+ ...

(orbits,celestial mechanics)
http://faculty.washington.edu/rkb9/publications/bg08a.pdf
https://arxiv.org/abs/1210.0321

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