The Great Inequality and the Dynamical Disintegration of the Outer Solar System

Abstract

Using an ensemble of N-body simulations, this paper considers the fate of the outer gas giants (Jupiter, Saturn, Uranus, and Neptune) after the Sun leaves the main sequence and completes its stellar evolution. Due to solar mass-loss -- which is expected to remove roughly half of the star's mass -- the orbits of the giant planets expand. This adiabatic process maintains the orbital period ratios, but the mutual interactions between planets and the width of mean-motion resonances (MMR) increase, leading to the capture of Jupiter and Saturn into a stable 5:2 resonant configuration. The expanded orbits, coupled with the large-amplitude librations of the critical MMR angle, make the system more susceptible to perturbations from stellar flyby interactions. Accordingly, within about 30 Gyr, stellar encounters perturb the planets onto the chaotic sub-domain of the 5:2 resonance, triggering a large-scale instability, which culminates in the ejections of all but one planet over the subsequent $\sim10$ Gyr. After an additional $\sim50$ Gyr, a close stellar encounter (with a perihelion distance less than $\sim200$ AU) liberates the final planet. Through this sequence of events, the characteristic timescale over which the solar system will be completely dissolved is roughly 100 Gyr. Our analysis thus indicates that the expected dynamical lifetime of the solar system is much longer than the current age of the universe, but is significantly shorter than previous estimates.