  Numerical integrations of the Solar System have been carried out for decades.
Their results have been used, for example, to determine whether the Solar
System is chaotic, whether Mercury's orbit is stable, or to help discern
Earth's climate history. We argue that all of the past studies we consider in
this work are affected by numerical chaos to different degrees, affecting the
possible orbits and instability probability of Mercury, sometimes
significantly. We show how to eliminate the effects of numerical chaos by
resolving Mercury's pericentre passage. We also show that several higher order
symplectic maps do not exhibit significant differences in resolving pericentre
passage of Mercury (at fixed time step), making their advantages suspect for
calculating long-term orbits. Resolving pericentre passage affects a wide array
of orbital numerical studies, like exoplanet studies, studies of the galactic
centre, and other $N$-body problems.
