Meditations on GR–Induced/Perturbed Secular Resonances

Abstract

The study of resonant dynamics provides a powerful framework for probing formation histories and dynamical pathways of planetary systems. General relativity (GR) plays an important role in this context, as relativistic precession can induce, shift, or perturb resonances that shape planetary architectures and their long-term stability. In this thesis, we explore the workings of GR-driven secular resonances, in the presence of non-conservative forces, namely orbital migration and tidal evolution.

In the first part of the thesis, we develop a hierarchy of toy models to study the dynamics of Mercury, whose large eccentricity and sensitivity to secular resonances raise the question of whether its orbit could have been excited during the early evolution of the Solar System. The main questions we address in these models are the following: (i) under what conditions can planetary migration lead to capture into secular resonance and drive significant eccentricity increase in Mercury’s orbit, (ii) how does GR modify the structure and location of these resonances, and (iii) does the same framework disturb the other terrestrial planets and lead to substantial excitation in their eccentricities.

In the second part of our work, we move to tidally evolving systems, focusing on P-type systems and a hot-Jupiter system, and examine whether tidal evolution can lead to resonance capture and eccentricity excitation of the inner body or its companion.