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Mercury’s orbit can destabilize, generally resulting in a collision with either Venus or the Sun. Chaotic evolution can cause g _1 to decrease to the approximately constant value of g _5 and create a resonance. Previous work has approximated the variation in g _1 as stochastic diffusion, which leads to a phenomological model that can reproduce the Mercury instability statistics of secular and N -body models on timescales longer than 10 Gyr. Here we show that the diffusive model significantly underpredicts the Mercury instability probability on timescales less than 5 Gyr, the remaining lifespan of the solar system. This is because g _1 exhibits larger variations on short timescales than the diffusive model would suggest. To better model the variations on short timescales, we build a new subdiffusive phenomological model for g _1 . Subdiffusion is similar to diffusion but exhibits larger displacements on short timescales and smaller displacements on long timescales. We choose model parameters based on the behavior of the g _1 trajectories in the N -body simulations, leading to a tuned model that can reproduce Mercury instability statistics from 1–40 Gyr. This work motivates fundamental questions in solar system dynamics: why does subdiffusion better approximate the variation in g _1 than standard diffusion? Why is there an upper bound on g _1 , but not a lower bound that would prevent it from reaching g _5 ?

We introduce ASSIST, a software package for ephemeris-quality integrations of test particles. ASSIST is an extension of the REBOUND framework and makes use of its IAS15 integrator to integrate test-particle trajectories in the field of the Sun, Moon, planets, and 16 massive asteroids, with the positions of the masses coming from the Jet Propulsion Laboratory’s DE441 ephemeris and its associated asteroid perturber file. The package incorporates the most significant gravitational harmonics and general-relativistic corrections. ASSIST also accounts for position- and velocity-dependent nongravitational effects. The first-order variational equations are included for all terms to support orbit fitting and covariance mapping. This new framework is meant to provide an open-source package written in a modern language to enable high-precision orbital analysis and science by the small-body community. ASSIST is open source, freely distributed under the GNU General Public license v3.0.

The long-term stability of the solar system is an issue of significant scientific and philosophical interest. The mechanism leading to instability is Mercury’s eccentricity being pumped up so high that Mercury either collides with Venus or is scattered into the Sun. Previously, only three five-billion-year N -body ensembles of the solar system with thousands of simulations have been run to assess long-term stability. We generate two additional ensembles, each with 2750 members, and make them publicly available at https://archive.org/details/@dorianabbot . We find that accurate Mercury instability statistics can be obtained by (1) including only the Sun and the eight planets, (2) using a simple Wisdom–Holman scheme without correctors, (3) using a basic representation of general relativity, and (4) using a time step of 3.16 days. By combining our solar system ensembles with previous ensembles, we form a 9601-member ensemble of ensembles. In this ensemble of ensembles, the logarithm of the frequency of a Mercury instability event increases linearly with time between 1.3 and 5 Gyr, suggesting that a single mechanism is responsible for Mercury instabilities in this time range and that this mechanism becomes more active as time progresses. Our work provides a robust estimate of Mercury instability statistics over the next five billion years, outlines methodologies that may be useful for exoplanet system investigations, and provides two large ensembles of publicly available solar system integrations that can serve as test beds for theoretical ideas as well as training sets for artificial intelligence schemes.

We have collected transit times for the TRAPPIST-1 system with the Spitzer Space Telescope over four years. We add to these ground-based, HST, and K2 transit-time measurements, and revisit an N -body dynamical analysis of the seven-planet system using our complete set of times from which we refine the mass ratios of the planets to the star. We next carry out a photodynamical analysis of the Spitzer light curves to derive the density of the host star and the planet densities. We find that all seven planets’ densities may be described with a single rocky mass–radius relation which is depleted in iron relative to Earth, with Fe 21 wt% versus 32 wt% for Earth, and otherwise Earth-like in composition. Alternatively, the planets may have an Earth-like composition but enhanced in light elements, such as a surface water layer or a core-free structure with oxidized iron in the mantle. We measure planet masses to a precision of 3%–5%, equivalent to a radial-velocity (RV) precision of 2.5 cm s ^−1 , or two orders of magnitude more precise than current RV capabilities. We find the eccentricities of the planets are very small, the orbits are extremely coplanar, and the system is stable on 10 Myr timescales. We find evidence of infrequent timing outliers, which we cannot explain with an eighth planet; we instead account for the outliers using a robust likelihood function. We forecast JWST timing observations and speculate on possible implications of the planet densities for the formation, migration, and evolution of the planet system.