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Verified Integration of Dynamics in the Solar System

Abstract

The motion of objects in the solar system is studied with the use of verified integration methods. Providing rigorous bounds for the possible coordinates of objects whose initial coordinates are known to lie in a certain region, the methods are applied to the study of near-earth asteroids within an advanced relativistic NASA model of the solar system with the ultimate goal of assessing the possibility of collision with earth.

Because of the relatively large set of initial conditions compatible with measured orbit data, great care has to be taken to limit overestimation of the possible range of final coordinates. This is achieved using the approach of Taylor models. Within this framework, it is possible to control the so-called dependency problem as well as the wrapping effect commonly observed in verified integration. This approach yields accuracies that are sufficient to guarantee absence of collisions.

Examples of orbit integrations are given, showing that even relatively large domain boxes can be transported over extended time periods with a relative overestimation in the range of only around 10^-5.

M. Berz, K. Makino, J. Hoefkens, Nonlinear Analysis 47 (2001) 179-190

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