  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.
