Orbital stability of compact four-planet systems

Abstract:

We investigate the orbital dynamics of four-planet systems consisting of Earth-mass planets on initially circular, coplanar orbits around a star of one solar mass. The initial semi-major axis of the innermost planet was designated at 1 A.U., with the remaining planets semi-major axes equally-spaced by multiples of their mutual Hill radii. For the majority of simulations, consecutive planet initial longitudes were spaced by 2π multiplied by (1 + 5^0.5) / 2. We explore the stability of each system until either an orbital crossing occurs (defined as an inner planet’s semi-major axis exceeding an outer planet’s semi-minor axis), the orbital eccentricity of a planet reaches or exceeds 1, or the simulated lifetime exceeds a pre-determined limit of up to years. The primary objective of this investigation is to determine the relationships between the simulated lifetimes of systems of four-planet systems and previous studies of analogous three- and five-planet systems. We further investigate the effects of different initial longitudes on the lifetimes of the systems, since the lifetimes of three-planet systems can be much more sensitive to changes in initial longitudes than are lifetimes of five-planet systems.