The interval description of dynamics of celestial bodies in the planetary problem

TL;DR

This paper introduces an interval-based computational method for celestial dynamics that avoids round-off errors, demonstrating its effectiveness through Kepler's problem and long-term Solar system stability analysis.

Contribution

It presents a novel interval approach that provides exact, error-free calculations of celestial body dynamics over billions of years, improving upon classical methods.

Findings

Interval method conserves the difference between classical and interval coordinates over time.

Results align with classical predictions for planetary orbital dynamics.

Supports the validity of the interval approach for long-term celestial simulations.

Abstract

The interval approach to computation of dynamics of celestial bodies in the planetary problem has been considered. It is based on the refusal from idealization of infinitely high resolving capacity of measuring tools, and forms an absolutely exact algorithm free of round-off error accumulation effect. The possibilities of the proposed approach are shown by the examples of Kepler's Problem and the problem of stability of the Solar system major planets for time interval of 6 billion years. The comparison of the interval and classical predictions of Kepler's particle location in Kepler's orbit provides support for the effect predicted by the theory, namely - conservation of the interval within which the values of difference of interval and classical coordinates lay with time. The computational results of the Solar system major planet orbital dynamics agree with the results obtained with the classical approach.