Capture and escape in the elliptic restricted three-body problem

Abstract

Several families of irregular moons orbit the giant planets. These moons are thought to have been captured into planetocentric orbits after straying into a region in which the gravitation of the planet dominates solar perturbations (the Hill sphere). This mechanism requires a source of dissipation, such as gas drag, in order to make capture permanent. However, capture by gas drag requires that particles remain inside the Hill sphere long enough for dissipation to be effective. Recently we have proposed that in the circular restricted three‐body problem (CRTBP) particles may become caught up in sticky chaotic layers, which tends to prolong their sojourn within the Hill sphere of the planet thereby assisting capture. Here, we show that this mechanism survives perturbations due to the ellipticity of the orbit of the planet. However, Monte Carlo simulations indicate that the ability of the planet to capture moons decreases with increasing orbital eccentricity. At the actual orbital eccentricity of Jupiter, this results in approximately an order of magnitude lower capture probability than estimated in the circular model. Eccentricities of planetary orbits in the Solar system are moderate but this is not necessarily the case for extrasolar planets, which typically have rather eccentric orbits. Therefore, our findings suggest that these extrasolar planets are unlikely to have substantial populations of irregular moons.