Verified integration of dynamics in the solar system

The motion of objects in the solar system is studied with the use of verifi ed integration methods. Providing rigorous bounds for the possible coordina tes of objects whose initial coordinates are known to lie in a certain regi on, 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 m easured orbit data, great care has to be taken to limit overestimation of t he 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 sufficien t to guarantee absence-of collisions. Examples of orbit integrations are given, showing that even relatively larg e domain boxes can be transported over extended time periods with a relativ e overestimation in the range of only around 10(-5).