Chaos and stability of the solar system

doi:10.1073/pnas.231384098

Chaos and stability of the solar system

^*University of Arizona, Tucson, AZ 85721; ^‡Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138; and ^§National Astronomical Observatory, Tokyo 181, Japan

Abstract

Over the last two decades, there has come about a recognition that chaotic dynamics is pervasive in the solar system. We now understand that the orbits of small members of the solar system—asteroids, comets, and interplanetary dust—are chaotic and undergo large changes on geological time scales. Are the major planets' orbits also chaotic? The answer is not straightforward, and the subtleties have prompted new questions.

Footnotes

↵ † To whom reprint requests should be addressed. E-mail: renu{at}lpl.arizona.edu.
This paper is a summary of a session presented at the third annual Japanese–American Frontiers of Science symposium, held September 22–24, 2000, at the Arnold and Mabel Beckman Center of the National Academies of Science and Engineering in Irvine, CA.
↵ ¶ For consideration of dynamical stability of two planets of mass m ₁ and m ₂, orbital radius a ₁ and a ₂, a natural unit of separation is their mutual Hill radius (after the 19th century mathematician, G. W. Hill), defined by $\text{[math]}$ where m _⊙ is the mass of the sun. With this measure, the separations among terrestrial planets exceed 26R _H, whereas those among Jovian planets are less than 14R _H.