Moon packing around an Earth-mass planet

Abstract

ABSTRACT All four giant planets in the Solar system host systems of multiple moons, whereas the terrestrial planets only host up to two moons. The Earth can capture small asteroids as temporary satellites, which begs the question as to how many moons could stably orbit the Earth, or an Earth-mass exoplanet. We perform a series of N-body simulations of closely spaced equal-mass moons in nested orbits around an Earth-mass planet orbiting a Sun-like star. The innermost moon begins near the host planet’s Roche radius, and the system is packed until the outermost moon begins near the stability limit for single moons. The initial spacing of the moons follows an iterative scheme commonly used for studies of compact planetary systems around single stars. For the three-moon system, we generate MEGNO maps to calculate periodic and chaotic regions and to identify the destabilizing mean motion resonances. Our calculations show that the maximum number of moons depends on the assumed masses of the satellites (Ceres-, Pluto-, and Luna-mass) that could maintain stable orbits in a tightly packed environment. Through our N-body simulations, we find stable configurations for up to 7 ± 1 Ceres-mass, 4 ± 1 Pluto-mass, and 3 ± 1 Luna-mass moons. However, outward tidal migration will likely play a substantial role in the number of moons on stable orbits over the 10 Gyr stellar lifetime of a Sun-like star.