New research by a duo of French astronomers reveals that small perturbations in Mercury's orbit could result in Mars literally getting the boot from our brotherhood of planets, being flung out of the solar system thanks to the dynamics of a chaotic system. The equation that uses classical physics to describe how massive bodies interact is simple, but using it to describe how multiple bodies behave as a result of these forces is rather difficult.
It is known that two orbital bodies that begin as neighbors will increase the distance between themselves by an order of magnitude every 10 million years. But the Solar System has a bit more than two bodies, and attempts to deterministically model it over long periods of time will become useless due to the chaotic behavior that underlies the dynamics. Today's issue of Nature will contain a letter that describes an attempt to predict some possible outcomes for various bodies in the Solar System on time scales that run out to 5 billion years.
Previous work that attempted to model the behavior of the Solar System over gigayear time scales was forced to average the equations of motion over the fast orbital motion of the planets, while ignoring the lunar contributions and general relativity. This earlier work did find that, in a fraction of the scenarios, Mercury's eccentricity became very high—an eccentricity of zero is a circle, whereas an eccentricity of one is a parabola—and collisions with Venus became possible within a 5 Gyr time frame.
Using a complex numerical integration scheme, along with the computing power of JADE, a supercomputer at the French National Computing Center, the authors calculated 2,501 orbital solutions using a complete model of the Solar System that included relativistic factors and lunar contributions. All of the solutions started similarly, but differences arose from the size of Mercury's semi-major axis, which was varied by 0.38k mm from its current known value, where k ranged from -1,250 to 1,250.
These tiny changes resulted in huge effects for the Solar System as a whole. A number of computations resulted in Mercury's orbit collapsing and Mercury colliding with the Sun after about 4 Gyr. In a run where the minor axis was shrunk by 812 mm (32in), Mercury slammed into Venus just after 1.7 Gyr. In what the authors describe as their most interesting simulation—one where Mercury's axis was decreased by 468 mm (18.4 in)—Mars and Earth had a close encounter, passing within 794 km of one another.
Using this as an interesting starting point, the authors ran another series of 201 integrations where the semi-major axis of Mars was changed by up to 30 mm. Within 100 Myr of starting these integrations, five of the simulations resulted in Mars being ejected from the solar system. All of the remaining 196 cases resulted in various collisions between Earth, Mars, Venus, Mercury, and/or the Sun.
Out of the 2,500 runs that were performed, only about one percent resulted in a major disruptions in Mercury's orbit. This result is in agreement with prior works that had not taken general relativity or the lunar effects into account. However, when Mercury's orbit did become highly perturbed, large variations could occur, some of which saw disturbances in the dynamics of the entire inner Solar System—all of these using variances no larger than one meter.
Nature, 2009. DOI: 10.1038/nature08096
Listing image by Artistic design : J Vidal-Madjar; planet textures from NASA; copyright: IMCCE-CNRS