Journal of Research and Development
Open Access
ISSN: 2311-3278
ISSN: 2311-3278
Levison, et al., have carried out a simulation of the hypothetical Sub-Satellite (SS) of Iapetus, the third largest walnut-shaped moon of Saturn, and examined its contributions towards de-spinning of Iapetus and if it could possibly give rise to an ancient equatorial ridge as confirmed by close fly-by Cassini mission in 2004 for different mass ratios ‘q’=SS mass/Iapetus mass. The same study has been carried out inprimary-centric frame-work analytically in the present paper. It is found that initially when Iapetus was formed at Roche limit in circum-saturnian impact generated disc it was spinning at 13 hours spin period. Subsequently in few hundred years after the formation of the hypothetical Sub-Satellite (SS), it de-spunto 16 hours spin-period, simultaneously it cooled and froze its contemporary hydro-static equilibrium shape which we observe today as non-hydrostatic equilibrium anomaly corresponding to 16 hours. This study shows that in mass ratios q=0.3 to q=1.0, there is no circum-iapetian disc and no core-accretion formation of SS. Instead there is the formation of SS by hydrodynamic instability and at a very short time scale SS assumes stable Keplerian equilibrium configuration at outer Clarke’s orbit 4 RIap where it has de-spun Iapetus to 16 hour spin period. As the synchronous orbit sweeps past 4 RIap in about 1.68 My, SS Clarke’s orbit as abruptly collapses and leaves an ancient equatorial ridge 4.498 Gy old. In mass ratios 0.006<q<0.2, SS is doomed to a death spiral right from the time of formation. In the sub-synchronous orbit it contributes nothing to de-spinning of Iapetus and it can contribute to the formation of not too ancient an equatorial ridge. For q=0.1, it creates 4.324 Gy old ridge and for q=0.04 it forms 3.7736 Gy old ridge which is not too ancient. In mass ratios q=0.0001 to q=0.006, SS is in super-synchronous orbit and SS at 20 RIap is stripped off by Saturn but during the tidal de-spinning it de-spins Iapetus from 13 hours to 16 hours only in 16.11 My for q=0.006 and de-spins Iapetus in 0.247 year for q=0.0001. So q=0.0001 is suitable for obtaining the present day non-hydrostaic equilibrium anomaly. In all there is a big conflict between simulation results of Levison, et al., and analytical results in this paper hence the issues can be settled only by carrying out the simulation by symplectic integrator.
Published Date: 2023-12-19; Received Date: 2023-11-17