chornedsnorkack

2009-Mar-12, 12:15 PM

When is mutual tidal lock stable?

Nothing is locked to areosynchronous orbit. Deimos is slightly above areosynchronous. As Deimos recedes from Mars, the rotation of Mars slows only slightly, so the orbit gets less areosynchronous. Likewise with Phobos: as Phobos approaches Mars, its revolution speeds up, while the rotation of Mars is much less affected.

The angular momentum of a rotating body is proportional to the inverse of rotational period.

However, as for the orbiting bodies, the further they get the bigger their angular momentum. The angular momentum is proportional to the cubic root of the period.

I have a hunch that double tidal lock is stable when at least three quarters of the total angular momentum is in the orbital motion, and less than a quarter is in the rotation of the two bodies combined. Can anybody check my algebra?

Nothing is locked to areosynchronous orbit. Deimos is slightly above areosynchronous. As Deimos recedes from Mars, the rotation of Mars slows only slightly, so the orbit gets less areosynchronous. Likewise with Phobos: as Phobos approaches Mars, its revolution speeds up, while the rotation of Mars is much less affected.

The angular momentum of a rotating body is proportional to the inverse of rotational period.

However, as for the orbiting bodies, the further they get the bigger their angular momentum. The angular momentum is proportional to the cubic root of the period.

I have a hunch that double tidal lock is stable when at least three quarters of the total angular momentum is in the orbital motion, and less than a quarter is in the rotation of the two bodies combined. Can anybody check my algebra?