Astrophysics (Index)About

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 an adjacent pair of (coplanar) planets and their host star:

    2M
- ——————— c2h
   G2M*3

> 1 +

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

+ ...

(These are the most significant terms of a series.)


(orbits,celestial mechanics)
Further reading:
http://faculty.washington.edu/rkb9/publications/bg08a.pdf
https://arxiv.org/abs/1210.0321
https://ui.adsabs.harvard.edu/abs/1982CeMec..26..311M/abstract

Index