orbitN: A symplectic integrator for planetary systems dominated by a central mass -- Insight into long-term solar system chaos

Abstract

Reliable studies of the long-term dynamics of planetary systems require numerical integrators that are accurate and fast. The challenge is often formidable because the chaotic nature of many systems requires relative numerical error bounds at or close to machine precision (~1e-16, double-precision arithmetic), otherwise numerical chaos may dominate over physical chaos. Currently, the speed/accuracy demands are usually only met by symplectic integrators. For example, the most up-to-date long-term astronomical solutions for the solar system in the past (widely used in, e.g., astrochronology and high-precision geological dating) have been obtained using symplectic integrators. Yet, the source codes of these integrators are unavailable. Here I present the symplectic integrator orbitN (lean version 1.0) with the primary goal of generating accurate and reproducible long-term orbital solutions for near-Keplerian planetary systems (here the solar system) with a dominant mass M0. Among other features, orbitN-1.0 includes M0's quadrupole moment, a lunar contribution, and post-Newtonian corrections (1PN) due to M0 (fast symplectic implementation). To reduce numerical roundoff errors, Kahan compensated summation was implemented. I use orbitN to provide insight into the effect of various processes on the long-term chaos in the solar system. Notably, 1PN corrections have the opposite effect on chaoticity/stability on 100-Myr vs. Gyr-time scale. For the current application, orbitN is about as fast or faster (factor 1.15-2.6) than comparable integrators, depending on hardware. The orbitN source code (C) is available at github.com/rezeebe/orbitN.

Published

References in corpus (7)

• On the Dynamical Stability of the Solar System
• Chaotic Disintegration of the Inner Solar System
• Numerical Solutions for the orbital motion of the Solar System over the Past 100 Myr: Limits and new results
• Dynamic stability of the Solar System: Statistically inconclusive results from ensemble integrations
• Stepsize errors in the $N$-body problem: discerning Mercury's true possible long-term orbits
• Reduced variations in Earth's and Mars' orbital inclination and Earth's obliquity from 58 to 48 Myr ago due to solar system chaos
• General relativistic precession and the long-term stability of the solar system

Cited by in corpus (1)

• WHFast512: A symplectic N-body integrator for planetary systems optimized with AVX512 instructions