Past obliquity oscillations of Mars: The role of the Tharsis Uplift

Abstract

The present gravitational quadrupole moment of Mars contains a 6½% nonhydrostatic contribution from the uncompensated Tharsis construct. Prior to the Tharsis uplift, the rate of spin axis precession was nearly equal to the frequency of a minor term in the expression for the orbital precession of Mars developed by Bretagnon (1974). In such a situation, small changes in the J2 of Mars could have caused the spin axis precession rate to drift repeatedly through the orbital frequency. We show that even minor, low‐amplitude orbital components can have a significant impact on the obliquity oscillations due to secular spin‐orbit resonance. Our approach to this problem is in three stages. First, we examine a number of processes which have the potential to alter the spin axis precession rate, discussing both the expected magnitude and time scales involved. Of these, Tharsis plays a dominant role, but other processes, i.e., differentiation, mantle convection, etc., may also have significantly influenced the planet's quadrupole moment in the past. Second, a theory describing the consequences of passage through a secular spin‐orbit resonance is developed. The problem is solved analytically for the case of uniform orbital precession. It is then shown that the resonance behavior is almost undisturbed by the presence of other orbital terms (i.e., nonuniform precession), even if these terms are appreciably larger than the resonance terms. Third, numerical integrations of the full equations of motion for Mars are presented that demonstrate the resonance and indicate that the obliquity of Mars may have intermittently been as low as ∼9° and as high as 46° (or more) in its early history.