A&A 630, A102 (2019) Astronomy https://doi.org/10.1051/0004-6361/201936336 & © ESO 2019 Astrophysics Spin-orbit coupling for close-in planets Alexandre C. M. Correia1,2 and Jean-Baptiste Delisle2,3 1 CFisUC, Department of Physics, University of Coimbra, 3004-516 Coimbra, Portugal e-mail:
[email protected] 2 ASD, IMCCE, Observatoire de Paris, PSL Université, 77 Av. Denfert-Rochereau, 75014 Paris, France 3 Observatoire de l’Université de Genève, 51 chemin des Maillettes, 1290 Sauverny, Switzerland Received 17 July 2019 / Accepted 20 August 2019 ABSTRACT We study the spin evolution of close-in planets in multi-body systems and present a very general formulation of the spin-orbit problem. This includes a simple way to probe the spin dynamics from the orbital perturbations, a new method for computing forced librations and tidal deformation, and general expressions for the tidal torque and capture probabilities in resonance. We show that planet–planet perturbations can drive the spin of Earth-size planets into asynchronous or chaotic states, even for nearly circular orbits. We apply our results to Mercury and to the KOI-1599 system of two super-Earths in a 3/2 mean motion resonance. Key words. celestial mechanics – planets and satellites: general – chaos 1. Introduction resonant rotation with the orbital libration frequency (Correia & Robutel 2013; Leleu et al. 2016; Delisle et al. 2017). The inner planets of the solar system, like the majority of the Despite the proximity of solar system bodies, the determi- main satellites, currently present a rotation state that is differ- nation of their rotational periods has only been achieved in ent from what is believed to have been the initial state (e.g., the second half of the 20th century.