GRIT: a package for structure-preserving simulations of gravitationally interacting rigid-bodies

TL;DR

GRIT is a new software package that accurately simulates the complex interactions between spinning, gravitationally interacting rigid bodies in planetary systems, including effects like tidal forces, with practical applications demonstrated on Trappist-I.

Contribution

The paper introduces symplectic Lie-group integrators and a user-friendly package for structure-preserving simulations of gravitationally interacting rigid bodies, including external forcings.

Findings

Transit timing variations due to spin-orbit coupling can reach a few minutes in ten years.

Strong planetary perturbations can disrupt synchronized states of planets.

The package effectively models complex dynamical interactions in planetary systems.

Abstract

Spin-orbit coupling of planetary systems plays an important role in the dynamics and habitability of planets. However, symplectic integrators that can accurately simulate not only how orbit affects spin but also how spin affects orbit have not been constructed for general systems. Thus, we develop symplectic Lie-group integrators to simulate systems consisting gravitationally interacting rigid bodies. A user friendly package (GRIT \url{https://github.com/GRIT-RBSim/GRIT}) is provided and external forcings such as tidal interactions are also included. As a demonstration, this package is applied to Trappist-I. It shows that the differences in transit timing variations due to spin-orbit coupling could reach a few min in ten year measurements, and strong planetary perturbations can push Trappist-I f, g and h out of the synchronized states.