Non-chaotic Obliquity Variations of Mars

Introduction: In the absence of energy dissipation, obliquity variations of Mars would likely be chaotic. However, relatively small amounts of dissipation suffice to suppress the chaotic variations. Tidal dissipation within Mars, as constrained by the observed evolution of the orbit of Phobos, appears sufficient to regularize the obliquity variations. If Mars has a fluid core, viscous core-mantle coupling would also tend to damp the obliquity variations. An adequate rate of dissipative damping is a necessary, but not sufficient, condition to establish that the obliquity variations are fully damped. Evidence in support of this stronger conclusion comes from two further observations. First is that the current orientation of the spin pole of Mars (in both obliquity and azimuth) is close to that predicted for a fully damped spin state. Second is that numerical integrations of the equations of motion for the spin pole, over an interval of a few million years, when performed both with and without dissipation, differ only slightly, suggesting that the spin pole has been driven to the fully damped state. It thus appears that the free obliquity of Mars is small, and that dissipation plays an important role in the rotational dynamics of this body, not unlike the situation for Mercury and Venus. Obliquity without dissipation: It has been claimed that the obliquity variations of Mars are chaotic in nature [1,2,3], and this claim has been widely embraced by the Mars paleoclimate research community. We first discuss how the system would behave without any dissipative processes, and then consider how dissipation changes that state. The obliquity of Mars is, of course, just the angular separation between the spin pole s and the orbit pole n. These two unit vectors determine the relative orientations of the orbit plane and the equator plane, and this orientation is the dominant influence on the seasonal and latitudinal pattern of insolation [4,5,6]. The obliquity is given by s n ] cos[ (1)