General relativistic precession and the long-term stability of the solar system

Abstract: The long-term evolution of the solar system is chaotic. In some cases, chaotic diffusion caused by an overlap of secular resonances can increase the eccentricity of planets when they enter into a linear secular resonance, driving the system to instability. Previous work has shown that including general relativistic contributions to the planets' precession frequency is crucial when modelling the solar system. It reduces the probability that the solar system destabilizes within 5 Gyr by a factor of 60. We run 1280 additional N-body simulations of the solar system spanning 12.5 Gyr where we allow the GR precession rate to vary with time. We develop a simple, unified, Fokker-Planck advection-diffusion model that can reproduce the instability time of Mercury with, without, and with time-varying GR precession. We show that while ignoring GR precession does move Mercury's precession frequency closer to a resonance with Jupiter, this alone does not explain the increased instability rate. It is necessary that there is also a significant increase in the rate of diffusion. We find that the system responds smoothly to a change in the precession frequency: There is no critical GR precession frequency below which the solar system becomes significantly more unstable. Our results show that the long-term evolution of the solar system is well described with an advection-diffusion model.