Other
Scientific paper
Jun 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006dda....37.0301h&link_type=abstract
American Astronomical Society, DDA meeting #37, #3.01; Bulletin of the American Astronomical Society, Vol. 38, p.667
Other
Scientific paper
The existence of chaos among the system of Jovian planets (Jupiter, Saturn, Uranus, and Neptune) is not yet firmly established. Although Laskar originally found no chaos in the outer Solar System, his "averaged" integrations did not account for the possibility of mean-motion resonances. Once full n-body integrations were performed, a dichotomy arose. On one hand, many investigators (Sussman, Wisdom, Murray, Holman, among many others) consistently measured a Lyapunov time of between 5 and 12 million years in the outer Solar System; the chaos can even be explained as the overlap of three-body resonances (Murray + Holman, Science 283, 1999). Furthermore, Murray + Holman's theory has been recently corroborated across a wide range of system parameters (Guzzo 2005), and the chaos does not disappear with decreasing timestep. On the other hand, some other investigators (Newman, Grazier, and Varadi, among several others) have compelling evidence against chaos. Namely, they have convincingly demonstrated that a sympletic integration using the famous Wisdom + Holman (1992) symplectic mapping with a 400-day timestep reproduces the chaos seen by others, but that the chaos disappears and the orbit converges to being regular as the timestep decreases. Their integration remains regular, showing beautiful convergence with decreasing timestep, down to a 2 day timestep.
The resolution of this apparent paradox is simple. The orbital positions of the Jovian planets is known only to a few parts in 107, and it turns out that within that observational error ball, there exist both chaotic and regular solutions. I will demonstrate this fact using several initial conditions and several accurate integration algorithms. Thus, whether a particular investigator will see chaos or not depends (essentially randomly) upon the details of how that investigator draws their initial conditions. Thus, some investigators legitimately find chaos, while others legitimately find no chaos.
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