High precision Symplectic Integrators for the Solar System
Ariadna Farr\'es, Jacques Laskar, Sergio Blanes, Fernando Casas,, Joseba Makazaga, Ander Murua
TL;DR
This paper evaluates high-order symplectic integrators for long-term Solar System simulations, finding that advanced methods like the (10,6,4) scheme offer superior accuracy and practicality.
Contribution
It provides a comprehensive comparison of symplectic integrators in different coordinate systems and introduces detailed implementation guidance for optimal long-term planetary simulations.
Findings
High order integrators outperform lower order ones in accuracy.
The (10,6,4) integrator is recommended for Solar System studies.
Implementation details facilitate practical adoption of advanced integrators.
Abstract
Using a Newtonian model of the Solar System with all 8 planets, we perform extensive tests on various symplectic integrators of high orders, searching for the best splitting scheme for long term studies in the Solar System. These comparisons are made in Jacobi and Heliocentric coordinates and the implementation of the algorithms is fully detailed for practical use. We conclude that high order integrators should be privileged, with a preference for the new method of (Blanes et al., 2012)
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