Orbital Evolution of the Sun–Jupiter–Saturn–Uranus–Neptune Four-Planet System on Long-Time Scales
- Authors: Perminov A.S.1, Kuznetsov E.D.1
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Affiliations:
- Ural Federal University
- Issue: Vol 52, No 3 (2018)
- Pages: 241-259
- Section: Article
- URL: https://journal-vniispk.ru/0038-0946/article/view/171008
- DOI: https://doi.org/10.1134/S0038094618010070
- ID: 171008
Cite item
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
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