Physics
Scientific paper
May 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008dda....39.0804h&link_type=abstract
American Astronomical Society, DDA meeting #39, #8.04
Physics
Scientific paper
The orbital positions and masses of the Jovian planets are known only to a few parts in 107. At the 2006 DDA meeting in Halifax, I presented results, recently published in Nature Physics and MNRAS, which demonstrated the existence of both chaotic and near-regular orbits within the current observational error volume. In this talk, joint work with Chris Danforth of the University of Vermont, we present results demonstrating extremely rich structure of Lyapunov times within the uncertainty volume across many two-dimensional slices through initial-condition space. These slices include the Cartesian product of every pair of orbital semi-major axes ap, plus Cartesian products between ap and eccentricity ep for each Jovian planet p. Some of the observed structure is reminiscent of Guzzo's "Web of 3-body resonances", although it is not clear that 3-body resonances are the cause in this case since the structure extends several orders of magnitude below the scale at which Murray + Holman's 3-body resonance theory has been explored. Some of the structure is entirely unlike that seen in Guzzo's Web, and may require further theoretical development to understand. Finally, several "zoom-in” plots, reminiscent of those done for the Mandelbrot set, demonstrate that the structure continues down, at least, to scales of about one part in 109.
In all cases, we verify the reliability of our integrations using convergence tests to demonstrate that the picture does not change even when the integration timestep is decreased significantly.
Danforth Christopher M.
Hayes Wayne B.
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