Gravitational scattering by giant planets

We seek to characterize giant-planet systems by their gravitational scattering properties. We do this to a given system by integrating it numerically along with a large number of hypothetical small bodies that are initially in eccentric habitable zone (HZ)-crossing orbits. Our analysis produces a single number, the escape rate, which represents the rate at which the small-body flux is perturbed away by the giant planets into orbits that no longer pose a threat to terrestrial planets inside the HZ. Obtaining the escape rate this way is similar to computing the largest Liapunov exponent as the exponential rate of divergence of two nearby orbits. For a terrestrial planet inside the HZ, the escape rate value quantifies the "protective" effect that the studied giant-planet system offers. Therefore, escape rates could provide information on whether certain giant-planet configurations produce a more desirable environment for life than the others. We present some computed escape rates on selected planetary systems, focusing on effects of varying the masses and semi-major axes of the giant planets. In the case of our Solar System we find rather surprisingly that Jupiter, in its current orbit, may provide a minimal amount of protection to the Earth.