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.)
- M - total mass of the system.
- m1 - mass of inner planet.
- m2 - mass of outer planet.
- m3 - mass of star.
- M* - m1m2 + m1m3 + m2m3
- G - gravitational constant.
- c - total angular momentum of the system.
- h - total energy (kinetic energy + potential energy, the latter of which is a negative number).
(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