Existence of collisional trajectories of Mercury, Mars and Venus with the Earth

Abstract

It has been established that, owing to the proximity of a resonance with Jupiter, Mercury’s eccentricity can be pumped to values large enough to allow collision with Venus within 5 Gyr (refs 1–3). This conclusion, however, was established either with averaged equations^1,2 that are not appropriate near the collisions or with non-relativistic models in which the resonance effect is greatly enhanced by a decrease of the perihelion velocity of Mercury^2,3. In these previous studies, the Earth’s orbit was essentially unaffected. Here we report numerical simulations of the evolution of the Solar System over 5 Gyr, including contributions from the Moon and general relativity. In a set of 2,501 orbits with initial conditions that are in agreement with our present knowledge of the parameters of the Solar System, we found, as in previous studies², that one per cent of the solutions lead to a large increase in Mercury’s eccentricity—an increase large enough to allow collisions with Venus or the Sun. More surprisingly, in one of these high-eccentricity solutions, a subsequent decrease in Mercury’s eccentricity induces a transfer of angular momentum from the giant planets that destabilizes all the terrestrial planets ∼3.34 Gyr from now, with possible collisions of Mercury, Mars or Venus with the Earth.