Presentation #205.04 in the session Architectures 1.
Current observations indicate that the planet formation process often produces multiple planet systems with nearly circular orbits, regular spacing, a narrow range of inclination angles, and similar planetary masses of order 10 earths. Motivated by the observational sample, this talk discusses tidal equilibrium states for forming planetary systems — subject to conservation of angular momentum, constant total mass, and fixed orbital spacing. In the low-mass limit, valid for superearth-class planets, energy optimization leads to nearly equal mass planets, with circular orbits confined to a plane. As a result, the observed architectures correspond to the lowest energy states accessible to planetary systems. We then generalize the treatment to include the self-gravity of the planetary bodies. For systems with sufficiently large total mass in planets, the optimized energy state switches over from the case of nearly equal mass planets to a configuration where one planet contains most of the material. This transition occurs for a critical mass threshold of approximately 40 earth masses per planetary pair (where the value depends on the semimajor axes of the orbits, the stellar mass, and other system properties). These considerations of energy optimization apply over a wide range of mass scales, from binary stars to planetary systems to the moons orbiting the giant planets in our solar system.