In this talk I illustrate some of these features by drawing on some recent work I have done with Hal Levison and/or Jack Lissauer designed to study the stability of planetary systems. The simulations fall into two categories:

  1. Studies of the dependence on the masses of the satellites of the dynamical lifetime of the inner Uranian satellites,22 equal-mass three-planet systems, and the four giant planets.23 This set of simulations demonstrates interesting and as yet unexplained mass-scaling behaviour (especially for low-mass satellites).

  2. Studies using our new adaptive-timestep, symplectic code24 together with a crude recipe for gas drag and accretion designed to generate plausible giant-planet systems from a large number of planetary embryos.25 This set demonstrates the possible diversity, of giant-planet systems that are all ultimately stable for roughly 1 billion years. Of the approximately 30 systems generated, some are very similar to ours, some have somewhat more closely spaced planets, and some contain only two very widely spaced planets. Some systems have planets locked in mean-motion resonances, and the planets in some systems show large changes in eccentricity and inclination while remaining stable. In short, the systems show much of the behaviour that would have been thought highly unrealistic 2 to 3 years ago!


M.J. Duncan and J.J. Lissauer, “Orbital Stability of the Uranian Satellite System,” Icarus, 119: 1, 1997.


M.J. Duncan and J. J. Lissauer, “The Effects of Post-Main Sequence Solar Mass Loss on the Stability of our Planetary, System.” Icarus, in press, 1998.


M.J. Duncan, H.F. Levison, and M.H. Lee, “A Multiple Timestep Symplectic Algorithm for Integrating Close Encounters, ” Astronomical Journal, in press, 1998.


H.F. Levison, J.J. Lissauer, and M.J. Duncan, “Modeling the Diversity of Outer Planetary Systems.” Astronomical Journal, 116: 1998, 1998.

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