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:

- ——————— c2h

> 1 +

34/3 —————————————————

+ ...
  • 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)