Interval Algorithm for the Planetary Problem

To calculate the dynamics of celestial bodies, we suggest the nonclassic interval algorithm based on taking into account explicitly the limitations of the resolving capacity of instrumental observation facilities. This algorithm is consistent with the correspondence principle (has a classic limit) and is a system of integer mappings of a recurrent type which is free of the effect of the round-off error accumulation. Another feature is its relative simplicity, which allowed us to make the calculations less time-consuming as compared to the classic approach. This algorithm was used to calculate the evolution of the Solar System's planetary orbits over times of about 500 million years. The calculations support the results obtained earlier by classic methods and make it possible to conclude that the suggested interval approach can be adequately applied to the planetary problem under consideration.