Astrophysics (index)

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 planets and the star:

    2M
- ——————— c2h
   G2M*3

> 1 +

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

+ ...
  • M - total mass of the system
  • m1 - mass of inner planet
  • m2 - mass of outer planet
  • m3 - mass of star
  • M* - m1m2 + m1
  • G - gravitation constant
  • c - total angular momentum of the system
  • h - the energy

(orbits,celestial mechanics)
http://faculty.washington.edu/rkb9/publications/bg08a.pdf

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