GRIT: A Package for Structure-Preserving Simulations of Gravitationally Interacting Rigid Bodies

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