Jupiter - Friend or Foe? IV: The influence of orbital eccentricity and   inclination
  For many years, it was assumed that Jupiter prevented the Earth from being subject to a punishing impact regime that would greatly hinder the development of life. Here, we present the 4th in a series of studies investigating this hypothesis. Previously, we examined the effect of Jupiter's mass on the impact rate experienced by Earth. Here, we extend that approach to consider the influence of Jupiter's orbital eccentricity and inclination on the impact rate.   We first consider scenarios in which Jupiter's orbital eccentricity was somewhat higher and somewhat lower than that in our Solar System. 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 higher impact rate of asteroids than for more circular orbits. This is particularly pronounced at high "Jupiter" masses. For short-period comets, the same effect is clearly apparent, albeit to a lesser degree. The flux of short-period comets impacting the Earth is slightly higher for more eccentric Jovian orbits.   We also consider 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. 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 five and twenty-five degrees were essentially identical. 
J. Horner and B. W. Jones
astro-ph.EP