High-order regularised symplectic integrator for collisional planetary systems

Antoine C. Petit (1) , Jacques Laskar (2) , Gwenaël Boué (2) , Mickaël Gastineau (2)

1 Hôpital Avicenne [AP-HP]
2 IMCCE - Institut de Mécanique Céleste et de Calcul des Ephémérides

We present a new mixed variable symplectic (MVS) integrator for planetary systems that fully resolves close encounters. The method is based on a time regularisation that allows keeping the stability properties of the symplectic integrators while also reducing the effective step size when two planets encounter. We used a high-order MVS scheme so that it was possible to integrate with large time-steps far away from close encounters. We show that this algorithm is able to resolve almost exact collisions (i.e. with a mutual separation of a fraction of the physical radius) while using the same time-step as in a weakly perturbed problem such as the solar system. We demonstrate the long-term behaviour in systems of six super-Earths that experience strong scattering for 50 kyr. We compare our algorithm to hybrid methods such as MERCURY and show that for an equivalent cost, we obtain better energy conservation.

Mots clés: celestial mechanics; planets and satellites: dynamical evolution and stability; methods: numerical

Domaines: Astrophysique [astro-ph]; Physique [physics]

Antoine C. Petit, Jacques Laskar, Gwenaël Boué, Mickaël Gastineau. High-order regularised symplectic integrator for collisional planetary systems. Astronomy and Astrophysics - A&A, 2019, 628, pp.A32. ⟨10.1051/0004-6361/201935786⟩. ⟨hal-02918712⟩