Kolmogorov and Nekhoroshev theory for the problem of three bodies

TL;DR

This paper applies Nekhoroshev's theory to the Sun-Jupiter-Saturn three-body problem, demonstrating long-term stability over cosmological timescales through computer algebra and perturbation expansions.

Contribution

It introduces a novel application of Nekhoroshev theory to the three-body problem using computer algebra for large perturbation expansions.

Findings

Stability over a timescale comparable to the universe's age.

Effective perturbation expansions with strong truncations.

Potential for improved stability results in future work.

Abstract

We investigate the long time stability in Nekhoroshev's sense for the Sun-Jupiter-Saturn problem in the framework of the problem of three bodies. Using computer algebra in order to perform huge perturbation expansions we show that the stability for a time comparable with the age of the universe is actually reached, but with some strong truncations on the perturbation expansion of the Hamiltonian at some stage. An improvement of such results is currently under investigation.