Generalized Cassini's Laws
Abstract
All of the possible stable, coplanar configurations of a planet's or satellite's spin vector, orbit normal, and the vector designating the precession of the orbit are shown to represent extremes in the energy assodated with the body's orientation. It is shown that such a stable configuration yields a relation between the moment differences (C - A) /C and (B - A) /C, and bounds on their magnitudes if the spin angular velocity is commensurate with the orbital mean motion. Only a value of (C-A)/C is determined by a stable con- figuration for noncommensurate rotation. The effect of (B - A)/C on the value of (C-A)/C for the observed lunar configuration is less than the uncertainty introduced by observational error. Mercury is likely to be in one of two possible stable configurations. The value of (C- A)/C as a function of the obliquity of the equator plane to the orbit plane is derived for both configurations, and the effects of axial asymmetry, although small for the likely values of (C - A) /C for Mercury, are explicitly displayed for the entire range of (C - A ) /C.
- Publication:
-
The Astronomical Journal
- Pub Date:
- April 1969
- DOI:
- 10.1086/110825
- Bibcode:
- 1969AJ.....74..483P