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I report results from accurate numerical integrations of Solar System orbitsover the past 100Myr with the integrator package HNBody. The simulations useddifferent integrator algorithms, step sizes, initial conditions, and includedeffects from general relativity, different models of the Moon, the Sun'squadrupole moment, and up to sixteen asteroids. I also probed the potentialeffect of a hypothetical Planet 9, using one set of possible orbital elements.The most expensive integration (Bulirsch-Stoer) required 4~months wall-clocktime with a maximum relative energy error <~3e{-13}. The difference in Earth'seccentricity (DeE) was used to track the difference between two solutions,considered to diverge at time tau when max|DeE| irreversibly crossed ~10\% ofmean eE (~0.028x0.1). The results indicate that finding a unique orbitalsolution is limited by initial conditions from current ephemerides and asteroidperturbations to ~54Myr. Bizarrely, the 4-month Bulirsch-Stoer integration anda symplectic integration that required only 5~hours wall-clock time (12-daytime step, Moon as a simple quadrupole perturbation), agree to ~63Myr.Internally, such symplectic integrations are remarkably consistent even forlarge time steps, suggesting that the relationship between time step and tau isnot a robust indicator for the absolute accuracy of symplectic integrations.The effect of a hypothetical Planet~9 on DeE becomes discernible at ~65Myr.Using tau as a criterion, the current state-of-the-art solutions all differfrom previously published results beyond ~50Myr. I also conducted an eigenmodeanalysis, which provides some insight into the chaotic nature of the innerSolar System. The current study provides new orbital solutions for applicationsin geological studies.

Numerical Solutions for the orbital motion of the Solar System over the Past 100 Myr: Limits and new results