Comparative Study of Tidal Evolution of Mars-Phobos-Deimos Based on Kinematic Model and Based on Seismic Model

Abstract

Phobos, a moon of Mars, is in sub-synchronous orbit and hence it is in-spiraling towards Mars to its complete destruction on a gravitational runaway course. On the other hand Deimos, the second moon of Mars is in extra-synchronous orbit and almost stay put in the present orbit. My results predict that Phobos is losing its altitude at a rate of 21cm/yr and is likely to crash with Mars in 10My whereas recent Mars Express (Burns 1978, Witasse et.al 2013) results show that the altitude loss is at 1.8cm/yr and the doomsday will occur in 100My. Bills et.al.(2005) and Ramslay & Head III(2013) have reported altitude loss rate at 4cm/yr and remaining life-time for Phobos as 30-50My. The author had proposed a planetary-satellite dynamics based on detailed study of Earth-Moon [personal communication: http://arXiv.org/abs/0805.0100 ] which he calls the Kinematic Model. Based on this Kinematic Model, 1.8cm/yr and 4cm/y approach velocity leads to the age of Phobos to be 53 Gyrs and 24 Gyrs which is physically untenable since our Solar System’s age is 4.567Gyrs. Assuming that Phobos is co-accreted body along with Mars or formed from impact generated debris, the age of Mars-Phobos-Deimos system should be 4.5Gy. Within this constraint, the present altitude loss of Phobos is 21 cm/y and the dooms day of Phobos is predicted to be much shorter at 10My. Deimos is also assumed to be a co-accreted body with an age of 4.5Gyrs and launched in super-synchronous orbit hence it is on an expanding spiral path but its insignificant mass ratio with respect to Mars makes it almost stay put in its present orbit and it has negligible tidal evolution history. Considering that Phobos is trapped in a gravitational runaway death spiral the rapid decay of Phobos orbit at 21cm/y and its early doom seems to be reasonable but we do not have a conclusive proof .The conclusive validation of Kinematic Model will be made by Phobos Laser Ranging(PLR) Mission to be set up at Phobos. Though one thing is very clear that results obtained by Bills et.al.(2005) and Ramslay & Head III(2013) depend on several elastoviscous properties of the planetary bodies which are hard to obtain for the variety of Planetary Systems being encountered in this era of Exo-Planet hunting whereas the Kinematic Model analysis depends only on the age of the secondary component which is readily available. Hence this study definitely establishes that the tidal evolutionary history of Planet-Satellite systems can be easily arrived at through Kinematic Model. Regarding its accuracy, we have to wait for the results from PLR Mission.