Chaos in the Solar System

Abstract

The physical basis of chaos in the solar system is now better understood: in all cases investigated so far, chaotic orbits result from overlapping resonances. Perhaps the clearest examples are found in the asteroid belt. Overlapping resonances account for its Kirkwood gaps and were used to predict and find evidence for very narrow gaps in the outer belt. Further afield, about one new ``short-period'' comet is discovered each year. They are believed to come from the ``Kuiper Belt'' (at 40 AU or more) via chaotic orbits produced by mean-motion and secular resonances with Neptune. Finally, the planetary system itself is not immune from chaos. In the inner solar system, overlapping secular resonances have been identified as the possible source of chaos. For example, Mercury, in 10^{12} years, may suffer a close encounter with Venus or plunge into the Sun. In the outer solar system, three-body resonances have been identified as a source of chaos, but on an even longer time scale of 10^9 times the age of the solar system. On the human time scale, the planets do follow their orbits in a stately procession, and we can predict their trajectories for hundreds of thousands of years. That is because the mavericks, with shorter instability times, have long since been ejected. The solar system is not stable; it is just old!Comment: 65 pages, 27 figure

Chaos in navigation satellite orbits caused by the perturbed motion of the Moon

“…Orbital resonances are ubiquitous in the Solar System and are harbingers for the onset of dynamical instability and chaos (Duncan et al 1995;Lecar et al 2001;Morbidelli 2002;Colwell et al 2009;Tsiganis 2010;Asphaug 2014;Lithwick & Wu 2014). Our knowledge of such phenomena in celestial mechanics comes mainly from studies on asteroid dynamics-attempts to describe the stunningly complex dynamical structure of the asteroid belt since the discovery of the Kirkwood gaps (Morbidelli 2002;Tsiganis 2010).…”

Orbital Stability of Multi-Planet Systems: Behavior at High Masses

“…The mechanism responsible for chaotic behavior on the timescales explored here is expected to be MMR overlap (Lecar et al 2001 and references therein). Neighboring first order resonances are spaced more closely as the distance toward the orbiting planet decreases, and resonance libration widths increase with planet mass.…”

Infrequent visitors of the Kozai kind: the dynamical lives of 2012 FC71, 2014 EK24, 2014 QD364, and 2014 UR

“…Overlapping secular resonances have been identified as the source of long-term chaos in the orbits of the terrestrial planets (Lecar et al 2001;Morbidelli 2002;Lithwick & Wu 2014). The topic of overlapping secular resonances and its effects on the dynamics of asteroids was first studied by Michel (1997) in the particular case of objects moving in Venus horseshoe orbits.…”