Stability of planetary systems with bifurcation theory

Abstract

view Abstract Citations (25) References (9) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Stability of planetary systems with bifurcation theory. Szebehely, V. ; McKenzie, R. Abstract Conditions, based on zero-velocity surfaces, for the stability of planetary systems with three members are established. The results are applied to the sun-Jupiter-Saturn system, and the critical mass factor (gamma) introduced by the Kuiper-Nacozy-Szebehely (1973) theory is recomputed. Depending on the models and physical constants used, the system becomes unstable when the masses of Jupiter and Saturn are increased about 14 times their present value. This compares favorably with Nacozy's (1976) gamma value of 29 obtained by numerical integration, since the present stability condition is expected to give lower values. Instability is defined by the change in the topology of the zero-velocity surfaces allowing mixing, exchange, and bifurcation of the solution. Publication: The Astronomical Journal Pub Date: January 1977 DOI: 10.1086/112011 Bibcode: 1977AJ.....82...79S Keywords: Astronomical Models; Dynamic Stability; Planetary Systems; Solar System; Three Body Problem; Branching (Physics); Celestial Mechanics; Gravitational Constant; Jupiter (Planet); Kepler Laws; Mathematical Models; Numerical Integration; Planetary Orbits; Saturn (Planet); Lunar and Planetary Exploration full text sources ADS |