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


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 equations1,2 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 Mercury2,3. 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.

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Figure 1: Mercury’s eccentricity over 5 Gyr.
Figure 2: Example of collisional trajectory for Mars and the Earth.
Figure 3: Collisional trajectories for Mars and Venus with the Earth.


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This work benefited from support from the Planetology Programme of the French National Research Centre, from Paris Observatory and from National Research Agency grant ASTS-CM. The authors thank the computing centres of Paris Observatory, the Institut de Physique du Globe Paris, the Institute of Development and Resources in Scientific Computing, the Linear Accelerator Laboratory Grid and especially the French National Computing Centre CINES, for providing the necessary computational resources for this work.

Author Contributions J.L. designed the study, performed the simulations and their analysis, and wrote the paper. M.G. wrote the computer code.

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Correspondence to J. Laskar.

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Laskar, J., Gastineau, M. Existence of collisional trajectories of Mercury, Mars and Venus with the Earth. Nature 459, 817–819 (2009).

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