A study of symplectic integrators for planetary system problems: error analysis and comparisons
Abstract
The symplectic Wisdom-Holman map revolutionized long-term integrations of planetary systems. There is freedom in such methods of how to split the Hamiltonian and which coordinate system to employ, and several options have been proposed in the literature. These choices lead to different integration errors, which we study analytically and numerically. The Wisdom-Holman method in Jacobi coordinates and the method of Hernandez, H16, compare favourably and avoid problems of some of the other maps, such as incorrect centre-of-mass position or truncation errors even in the one-planet case. We use H16 to compute the evolution of Pluto's orbital elements over 500 million years in a new calculation.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- July 2017
- DOI:
- 10.1093/mnras/stx547
- arXiv:
- arXiv:1612.05329
- Bibcode:
- 2017MNRAS.468.2614H
- Keywords:
-
- gravitation;
- methods: analytical;
- methods: numerical;
- celestial mechanics;
- planets and satellites: dynamical evolution and stability;
- Astrophysics - Earth and Planetary Astrophysics;
- Astrophysics - Instrumentation and Methods for Astrophysics
- E-Print:
- 24 pages, 9 figures, 1 table. Matches accepted MNRAS version