A computer assisted proof for 100,000 years stability of the solar system

TL;DR

This paper provides an analytical proof, supported by extensive computer calculations, demonstrating that the main planets and Pluto will remain dynamically stable over the next 100,000 years, with minimal changes in their orbital parameters.

Contribution

It introduces a computer-assisted analytical proof of the long-term stability of the solar system's main planets and Pluto for 100,000 years, using a novel numerical integration approach.

Findings

Planetary semi-major axes remain stable over 100,000 years.

Eccentricities and inclinations stay sufficiently small.

Numerical integration involved over 6 million steps with error estimates.

Abstract

We present an analytical proof assisted by computer calculations for the dynamical stability of the eight main planets and Pluto for the next 100,000 years. It means that the semi-major axes of the planets will not change significantly during this period. Also the eccentricities and inclinations of the orbits will remain sufficiently small. A standard linear four-step numerical method is used to integrate approximately the orbits of Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto. Written in orbital elements, the dynamics of the nine planets manifests a system of 54 first-order ordinary differential equations. The step-size of the numerical method -- about six days, has been performed 6,290,000 times. We estimate the total accumulation of rounding-off errors, deviations related to possible uncertainty in the astronomical data and the accuracy of the computer calculations.