Spin-orbit coupling in the solar system

Abstract

view Abstract Citations (295) References (17) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Spin-orbit coupling in the solar system Goldreich, Peter ; Peale, Stanton Abstract Two possible types of resonant spin rates for planets and satellites are investigated. The first occurs in eccentric orbits at rotation rates which are commensurate with the orbital mean motion. A resonant spin state exists at each half-integer multiple of the mean motion, the simplest case being the well-known syn- chronous rotation. The second class of resonant spins involves the presence of another planet or satellite. A planet (or satellite) with such a resonant spin always aligns the same axis toward the second planet (or satellite) at each conjunction. Averaged equations of motion are derived, and stability criteria are formulated for both types of resonance. Probabilities of capturing a planet (or satellite) into one of the commensurate rotation states as it is being despun by tidal friction are calculated. Application ot the results to Mercury reveals that the very small value of (B-A)/ -0 would suffice to stabilize Mercury's rotation period at -22 of its orbital period. The probability that Mercury would be cap- tured at this resonance is calculated for several assumed forms of tidal torques. Venus may be in a resonant spin state of the second kind. A sidereal rotation period of 243.16 days retrograde would be commensurate with its synodic motion. However, a large value of (B-A)/C( > 10- ) seems to be required to stabilize this rotation. In addition, the capture probability at this resonance appears to be small. Publication: The Astronomical Journal Pub Date: August 1966 DOI: 10.1086/109947 Bibcode: 1966AJ.....71..425G full text sources ADS |