Journal Article

On a time-symmetric Hermite integrator for planetary <i>N</i>-body simulation

Eiichiro Kokubo, Keiko Yoshinaga and Junichiro Makino

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 297, issue 4, pages 1067-1072
Published in print July 1998 | ISSN: 0035-8711
Published online July 1998 | e-ISSN: 1365-2966 | DOI:
On a time-symmetric Hermite integrator for planetary N-body simulation

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We describe a P(EC)n Hermite scheme for planetary N-body simulation. The fourth-order implicit Hermite scheme is a time-symmetric integrator that has no secular energy error for the integration of periodic orbits with time-symmetric time-steps. In general N-body problems, however, this advantage is of little practical significance, since it is difficult to achieve time-symmetry with individual variable time-steps. However, we can easily enjoy the benefit of the time-symmetric Hermite integrator in planetary N-body systems, where all bodies spend most of the time on nearly circular orbits. These orbits are integrated with almost constant time-steps even if we adopt the individual time-step scheme. The P(EC)n Hermite scheme and almost constant time-steps reduce the integration error greatly. For example, the energy error of the P(EC)2 Hermite scheme is two orders of magnitude smaller than that of the standard PEC Hermite scheme in the case of an N = 100, m = 1025 g planetesimal system with the rms eccentricity 〈e21/2 ≲0.03.

Keywords: methods: numerical; celestial mechanics; stellar dynamics; Solar system: formation

Journal Article.  0 words. 

Subjects: Astronomy and Astrophysics

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