Jupiter - friend or foe? IV: the influence of orbital eccentricity and inclination

For many years, it has been assumed that Jupiter has prevented the Earth from being subject to a punishing impact regime that would have greatly hindered the development of life. Here, we present the fourth in a series of dynamical studies investigating this hypothesis. In our earlier work, we examined the effect of Jupiter's mass on the impact rate experienced by the Earth. Here, we extend that approach to consider the influence of Jupiter's orbital eccentricity and inclination on the impact rate from asteroidal bodies and short-period comets. We first considered scenarios in which Jupiter's orbital eccentricity was somewhat higher and somewhat lower than that in our Solar System, for a variety of `Jupiter' masses. We find that Jupiter's orbital eccentricity plays a moderate role in determining the impact flux at Earth, with more eccentric orbits resulting in a noticeably higher impact rate of asteroids than is the case for more circular orbits. This is particularly pronounced at high `Jupiter' masses. For the short-period comets, the same effect is clearly apparent, albeit to a much lesser degree. The flux of short-period comets impacting the Earth is slightly higher for more eccentric Jovian orbits. We also considered scenarios in which Jupiter's orbital inclination was greater than that in our Solar System. Increasing Jupiter's orbital inclination greatly increased the flux of asteroidal impactors upon the Earth. However, at the highest tested inclination, the disruption to the Asteroid belt was so great that the belt would be entirely depleted after an astronomically short period of time. In such a system, the impact flux from asteroid bodies would therefore be very low, after an initial period of intense bombardment. By contrast, the influence of Jovian inclination on impacts from short-period comets was very small. A slight reduction in the impact flux was noted for the moderate and high inclination scenarios considered in this work - the results for inclinations of 5° and 25° were essentially identical.