Mathematics – Probability
Scientific paper
May 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009dda....40.1303l&link_type=abstract
American Astronomical Society, DDA meeting #40, #13.03; Bulletin of the American Astronomical Society, Vol. 41, p.907
Mathematics
Probability
Scientific paper
As the motion of the planets in the Solar System is chaotic (Laskar, 1989, 1990, Sussman and Wisdom, 1992), a single trajectory of the planet evolutions over 5 Gyr can only be thought as a random sample of the Solar System possible evolution. In (Laskar, 1994), I demonstrated, using the secular equations, that Mercury can reach very high eccentricity, allowing for possible collisions with Venus. This was established by constructing by pieces an orbit leading to very high eccentricity for Mercury. The drawback of the method, is that the secular equations lose their validity close to collision, and there was no probability estimate. In (Laskar, 2008), the same experiment was conducted on 1001 orbits providing these probabilities. I also demonstrated that in a non relativist system, the unstability of Mercury is much larger than in the full GR model. In the same paper, I thus conducted some direct numerical integrations for 10 orbits, without averaging, without general relativity (GR), and indeed, 4 orbits out of 10 lead to very high increase of Mercury's eccentricity, allowing collisions with Venus. Soon after, (Batygin and Laughlin, 2008), presented similar results. Indeed, they had followed my previous paper (laskar, 1994), and could thus construct a solutions by pieces, leading to a collision of Mercury with Venus in less than 5 Gyr, but this was also done with a non GR model that is much more unstable than the full model. It was thus necessary to study the possibility of collisions with a full model, including GR over 5 Gyr. I will report here the results of the very extensive study that we made over 2501 solutions of the full Solar System over 5 Gyr, including GR and lunar contributions, with direct numerical integration, without averaging.
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