The chaotic orbits of asteroids and Earth

The chaotic orbits of asteroids and Earth. Ever since Isaac Newton, astronomers and mathematicians have sought to understand the dynamics of the solar system, but even the seemingly simple case of the three-body Sun-Earth-Moon system eludes an analytical solution (see PHYSICS TODAY, January 2010, page 27 ). Obtaining accurate results for Earth’s motion requires numerical calculations that include not only the Sun, Moon, and other planets but also the larger asteroids such as Ceres (now considered a dwarf planet), whose mass is 1/6000 of Earth’s, and Vesta, less massive still by a factor of 4. Long-term knowledge of Earth’s position is useful for paleoclimate studies, since the changes in incident sunlight allow calibration of geological records (see PHYSICS TODAY, December 2002, page 32 ). In 2004 Jacques Laskar and colleagues at the Paris Observatory calculated Earth’s position back 40 million years, allowing calibration of the Neogene period, which began 23 Myr ago. But Earth’s orbit is chaotic, with uncertainties increasing by an order of magnitude every 10 Myr, and it was not known how far the numerical solutions could be extended and still be valid. Laskar and coworkers have now established that the limit is 60 Myr. The researchers found that the motions of the five large asteroids they included were much more chaotic than previously thought. Furthermore, the effects of close encounters between asteroids—particularly Ceres and Vesta—on planetary motion are the limiting factor for establishing a longer-term history of Earth’s orbit. (J. Laskar et al., Astron. Astrophys. 532, L4, 2011.)