Stable, Closely-Spaced Three-Planet Systems

We explore the orbital dynamics of systems consisting of three planets, each as massive as the Earth, on coplanar, initially circular, orbits about a one solar mass star. The initial semi-major axes of the planets are equally-spaced in terms of their mutual Hill radius, which is equivalent to a geometric progression of orbital sizes for small, equal-mass, planets. Our simulations explore a wide range of spacings of the planets and were integrated for virtual times of up to 10 billion years or until the orbits of any pair of planets crossed. Our results for three-planet systems are qualitatively similar to those found for analogous five-planet systems for which system lifetimes depend primarily on orbital separation. Three-planet systems are generally longer-lived, but we find narrow regions of long-lived systems for surprisingly closely-spaced three-planet systems, away from the separation beyond which systems are expected to be long-lived due to three-body resonances, that we do not find in five-planet systems. These regions are located far from strong mean motion resonances. We present an analysis of these regions and find that differences in initial longitudes can have larger effects on lifetimes than differences in initial orbital separations. We compare the early evolution of short-lived with long-lived systems using similar orbital separations. We find that early conjunctions play a major role in the angular momentum deficit evolution, which greatly affects the system lifetime.