Final spin states of planets and satellites
Abstract
The spin of a planet or satellite which is losing angular momentum through tidal friction may approach one of at least two distinct final states. We derive a criterion which determines whether or not the final state will be one of synchronous rotation. If the tidal phase lag is independent of the amplitude and frequency of the tide, then synchronous rotation will result when [3 (B - A )/C] >1 (9 Sire2). If this inequality is not satisfied, the body will end up spinning with a mean angular velocity which is somewhat larger than its orbital mean motion. This criterion is only slightly altered if the phase lag varies with amplitude and/or fre- quency. It is easily seen that the moon fails to satisfy the condition for synchronous rotation with the present value of its orbital eccentricity. However, the moon could have attained synchronous rotation if its mean orbital eccentricity was less than 0.041 at some time in the past. No analytical treatment of commensurate spin states other than synchronous rotation is included in the present investigation. However, the results of a separate study of these commensurate spins are briefly described.
- Publication:
-
The Astronomical Journal
- Pub Date:
- February 1966
- DOI:
- 10.1086/109844
- Bibcode:
- 1966AJ.....71....1G