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

Numerical modelling of the future evolution of planetary orbits in the Solar System requires computing power on a massive scale, largely because of the element of chaos introduced by the interdependence of the various orbiting masses. Jacques Laskar and Mickael Gastineau have used the JADE teraflop supercomputer to simulate a set of 2,501 solutions for the evolution of the Solar System over a 5-billion-year period, and they find that 1% of the solutions lead to a large increase in Mercury's eccentricity, sufficient to allow collisions with Venus or the Sun. Surprisingly, in one high eccentricity solution, a subsequent decrease of Mercury's eccentricity induces a transfer of angular momentum from the giant planets that destabilizes all the terrestrial planets after about 3.34 billion years, with possible collisions of Mercury, Mars or Venus with the Earth.