Orbital Evolution of the Sun–Jupiter–Saturn–Uranus–Neptune Four-Planet System on Long-Time Scales


Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

The four-planet problem is solved by constructing an averaged semi-analytical theory of secondorder motion by planetary masses. A discussion is given of the results obtained by numerical integration of the averaged equations of motion for the Sun–Jupiter–Saturn–Uranus–Neptune system over a time interval of 10 Gyr. The integration is based on high-order Runge–Kutta and Everhart methods. The motion of the planets is almost periodic in nature. The eccentricities and inclinations of the planetary orbits remain small. Short-period perturbations remain small over the entire interval of integration. Conclusions are drawn about the resonant properties of the motion. Estimates are given for the accuracy of the numerical integration.

About the authors

A. S. Perminov

Ural Federal University

Author for correspondence.
Email: perminov12@yandex.ru
Russian Federation, Yekaterinburg

E. D. Kuznetsov

Ural Federal University

Email: perminov12@yandex.ru
Russian Federation, Yekaterinburg

Supplementary files

Supplementary Files
Action
1. JATS XML

Copyright (c) 2018 Pleiades Publishing, Inc.