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Iapetus Hypothetical Sub-Satellite Re-Visited and it Reveals Celestial Body Formation Process in The Primary-Centric Framework

Bijay K Sharma*

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 R_Iap where it has de-spun Iapetus to 16 hour spin period. As the synchronous orbit sweeps past 4 R_Iap in about 1.68 M_y, SS Clarke’s orbit as abruptly collapses and leaves an ancient equatorial ridge 4.498 G_y 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 G_y old ridge and for q=0.04 it forms 3.7736 G_y 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 R_Iap 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 M_y 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.