On the stability of the solar system

Abstract

Some recent analytical and numerical studies of the dynamical stability of the solar system are reviewed. A numerical study is undertaken, based on the premises that the dynamical evolution of the solar system would take place on a shorter time scale if the planetary masses were larger and that secular trends may be detected by numerical integration if the masses are increased significantly. The analysis is applied to the Jupiter-Saturn-sun system with the actual planetary masses increased by factors ranging from unity to 1000. The results indicate that secular trends in the actual Jupiter-Saturn system (if they exist) should not be detectable for at least tens of millions of years, that the actual Jupiter-Saturn-sun system has a relatively strong stability, and that the inclusion of Uranus, Neptune, and small nongravitational forces will not upset the apparent stability of the three-body system considered.