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New Methods for Long-Time Numerical Integration of Planetary Orbits

Published online by Cambridge University Press:  07 August 2017

Hiroshi Kinoshita  and
Hiroshi Nakai
Hiroshi Kinoshita
Affiliation:
National Astronomical Observatory 2-21-1 Osawa, Mitaka, Tokyo 181, Japan E-Mail address:Kinoshita@c1.mtk.nao.ac.jp
Hiroshi Nakai
Affiliation:
National Astronomical Observatory 2-21-1 Osawa, Mitaka, Tokyo 181, Japan E-Mail address:Kinoshita@c1.mtk.nao.ac.jp

Abstract

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When planetary orbits are numerically integrated for a long time by conventional integrators, the most serious problem is secular errors in the energy and the angular momentum of the planetary system due to discretization (truncation) errors. The secular errors in the energy and the angular momentum mean that the semi-major axes, the eccentricities, and the inclinations of planetary orbits have a secular error which grows linearly with time. Recently symplectic integrators and linear symmetric multistep integrators are found not to produce the secular errors in the energy and the angular momentum due to the discretization errors. Here we describe briefly both methods and discuss favorable properties of these integrators for a long-term integration of planetary orbits.

Keywords

Numerical IntegrationSymplectic IntegratorsLinear Symmetric Multistep IntegratorsPlanetary Orbits
Type
Part VII - Dynamical Systems. Maps. Integrators
Information
Symposium - International Astronomical Union , Volume 152: Chaos, Resonance and Collective Dynamical Phenomena in the Solar System , 1992 , pp. 395 - 406
Copyright
Copyright © Kluwer 1992 

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