Chaotic Evolution of the Rotational and Orbital Elements of Mars.

As the obliquity of Mars is strongly chaotic, it is not possible to give a precise solution for its evolution over more than about 10 millions of years. The evolution over this time interval is characterized by a significant increase of the obliquity beyond 45 degrees, about 5 millions years ago. It is thus believed that the Martian climate was very different in the two different time intervals [-10Myr,-5Myr] and [-5 Myr, 0]. In the first time interval, the obliquity oscillates from 25 to 45 degrees, while in the more recent times, it varies from 15 to 35 degrees. Over much longer time span, the chaotic behavior of the obliquity prevent from computing a precise evolution of the past obliquity and we have performed an extensive statistical analysis of the possible past Martian behavior. The obliquity can reach very high values, beyond 60 degrees, or can recede to very small values. In order to analyse the possible past evolution of the Martian climate over its history, we have thus derived some density probability functions for the past evolution of the orbital and rotational elements of the planet (Laskar et al, 2004). We find that the probability for Mars' obliquity to have reached more than 60° in the past 1 Gyr is about 63.0%. Over 4 Gyr, the position of Mars' axis is given by a uniform distribution on a spherical cap limited by the obliquity 58.62°, with the addition of a random noise allowing a slow diffusion beyond this limit. We have also define a standard model of Mars' insolation parameters over 4 Gyr with the most probable values 0.068 for the eccentricity and 41.80° for the obliquity. Beyond this statistical global description, it may be interesting to search for typical behavior of the obliquity and insolation solutions in the past, which would eventually correspond to some typical climate regime on the planet surface. Ref : Laskar, J., Correia, A. C. M., Gastineau, M., Joutel, F., Levrard, B., Robutel, P. : 2004, Long term evolution and chaotic diffusion of the insolation quantities of Mars, Icarus, Volume 170, Issue 2, p. 343-364