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W. B. Hayes (University of California, Irvine)
Consider a multi-hundred-million-year integration of the 5-body system consisting of the Sun, Jupiter, Saturn, Uranus, and Neptune. We term such an integration a long-term integration of the Outer Solar System. Such integrations have been performed repeatedly since the late 1980s and early 1990s, and many researchers performing such integrations have found that the isolated Outer Solar System is chaotic, with a Lyapunov timescale of about 10 million years. Using the Wisdom-Holman sympletic mapping, a typical timescale in early integrations was 400 days. Recently, some researchers have found that the 10-million year Lyapunov time can be reproduced when integrating the Outer Solar System with a 400 day timestep, but that the Lyapunov time becomes infinite (ie., the chaos disappears) when the integration timestep is reduced to 50 days or less. Since it is well-known that symplectic integrators with too-large a timestep can introduce chaos into integrable systems, this throws into question the conclusion that the isolated Outer Solar System is chaotic.
However, researchers today often use timesteps much smaller than 400 days, and many researchers today still find chaos, even when using a timestep of 50 days or less. Thus we are left with the disturbing story that some researchers see chaos in the Outer Solar System, while others do not.
Murray and Holman (Science 1999) demonstrated that among the sets of initial conditions very close to our Solar System, there exist both initial conditions that do, and do not, display chaotic behaviour over a 200-million-year timescale. However, they were confident that their integration errors were small enough to conclude that the chaos they observed was robust aginst integration error over the 200-million-year timescale.
In this talk, we demonstrate that Murray and Holman's integrations are indeed reliable. We also demonstrate that the effect of the inner planets is large enough so that initial conditions taken from ephemerides at different times cause the isolated Outer Solar System to ``ride the boundary'' between chaos and integrability. Thus, one can observe both chaos and integrability in the Outer Solar System based solely upon from what date one's initial conditions are drawn.
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Bulletin of the American Astronomical Society, 37 #4
© 2005. The American Astronomical Soceity.