The rigid body obliquity history of mars

The primary objective of this study is to explore the range of uncertainty in the obliquity history of Mars associated with the present uncertainty in the axial precession rate. The obliquity, or angular separation between the spin axis and the orbit normal, is the most important parameter for determining the seasonal and latitudinal pattern of insolation. Thus significant variations in obliquity are a likely source of major climatic variations on Mars. The present obliquity is well known, and the torques acting to reorient the spin axis of Mars can be readily calculated for time spans of order 107 years into the past (or future). The primary limitation to reconstructing the obliquity history is uncertainty in the mean moment of inertial of Mars, which governs its response to the applied torques. The range of axial precession rates corresponding to recent theoretical estimates of the moment of inertial is 8.29-8.77 arc sec/yr, but even the most recent observational limits are still much broader: 8-12 arc sec/yr. Nominal estimates of the axial precession rate suggest that resonant amplification of a number of small terms in the orbital inclination series will lead to significant variations in the obliquity of Mars, a behavior much different from the Earth. The major variations are on a 105 year time scale, with significant amplitude modulation on a 106 year time scale. Because of this resonant amplification, estimates of the obliquity history depend very sensitively on assumed values for the axial precession rate. Three different analytic techniques are applied to the obliquity problem. Both linear perturbation analysis and direct numerical integration of the governing differential equations can be used to obtain an obliquity time series, once a model value is selected for the moment of inertia