PDA

View Full Version : Mutual tidal lock stability



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?

hhEb09'1
2009-Mar-12, 01:07 PM
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?Let's have a look at it! Is it online now?

chornedsnorkack
2009-Mar-12, 01:49 PM
Let's have a look at it! Is it online now?
No, it is not.

But consider this: suppose that some of the angular momentum of the primary were transmitted to the satellite orbit, such that the primary rotational orbit is 1+x times initial. Obviously if x is small, the remaining angular moment is 1-x times initial. If the angular moment of the satellite orbit is 3 times the angular moment of rotation, the new orbital moment is 3+x, or 1+x/3 times initial - and the new orbital period is 1+x times initial.

Therefore, if the orbital angular momentum is at least 3 times rotational, a small violation of tidal lock will be removed by tidal friction.