Mathematics – Logic
Scientific paper
Sep 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011ess.....2.0901l&link_type=abstract
American Astronomical Society, ESS meeting #2, #9.01
Mathematics
Logic
Scientific paper
The motion of the planets in the Solar System is chaotic (Laskar, 1989, 1990, Sussman and Wisdom, 1992). The resulting exponential divergence sets limits on the time validity of long-term integrations
aimed for paleoclimate studies. The solution La2004 (Laskar et al, 2004)
is valid over 40 Myr, and has been recently extended to 50 Myr (Laskar et al, 2011a). The big question is then : how far can we extend this time of validity, knowing that every additional 10 Myr, the model needs an improvement by a factor of 10 due to exponential divergence.
In the most recent models, we consider the full Solar System including (1) Ceres and some of the main asteroids, (2) Pallas, (4) Vesta, (7) Iris, and (324) Bamberga. We show that close encounters among these small bodies induce strong chaotic behavior in their orbits and in
those of many asteroids that are much more chaotic than previously thought. Even if space missions will allow very precise measurements
of the positions of Ceres and Vesta, their motion will be unpredictable over 400 kyr. As a result, it will never be possible to recover the precise evolution of the Earth’s eccentricity beyond 60 Myr. Ceres and Vesta thus appear to be the main limiting factors for any precise reconstruction of the Earth orbit, which is fundamental for the astronomical calibration of geological timescales. Moreover, collisions of Ceres and Vesta are possible, with a collision probability of 0.2% per Gyr (Laskar et al, 2011b).
Laskar, J., Fienga, A., Gastineau, M., Manche, H.: 2011a, La2010: a new orbital solution for the long-term motion of the Earth , A&A, 532, A89
Laskar, J., Gastineau, M., Delisle, J.-B., Farrés, A., Fienga, A.: 2011b, Strong chaos induced by close encounters with Ceres and Vesta, A&A, 532, L4
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