Chaotic Disintegration of the Inner Solar System
On timescales that greatly exceed an orbital period, typical planetary orbits evolve in a stochastic yet stable fashion. On even longer timescales, however, planetary orbits can spontaneously transition from bounded to unbound chaotic states. Large-scale instabilities associated with such behavior appear to play a dominant role in shaping the architectures of planetary systems, including our own. Here we show how such transitions are possible, focusing on the specific case of the long-term evolution of Mercury. We develop a simple analytical model for Mercury's dynamics and elucidate the origins of its short-term stochastic behavior as well as of its sudden progression to unbounded chaos. Our model allows us to estimate the timescale on which this transition is likely to be triggered, i.e., the dynamical lifetime of the solar system as we know it. The formulated theory is consistent with the results of numerical simulations and is broadly applicable to extrasolar planetary systems dominated by secular interactions. These results constitute a significant advancement in our understanding of the processes responsible for sculpting of the dynamical structures of generic planetary systems.
© 2015 American Astronomical Society. Received 2014 June 21; accepted 2014 November 18; published 2015 January 21. We are grateful to Norm Murray, Greg Laughlin, Fred Adams, Gongjie Li, and Daniel Tamayo for useful discussions. Additionally, we are thankful to Molei Tao for sharing his expertise in stochastic calculus with the authors. Finally, we thank the anonymous referee, whose insightful report led to a substantial improvement of the paper.
Published - 0004-637X_799_2_120.pdf
Submitted - 1411.5066v1.pdf