Differences between the impact regimes of the terrestrial planets: Implications for primordial D:H ratios

It is often assumed that the terrestrial worlds have experienced identical impact regimes over the course of their formation and evolution, and, as a result, would have started life with identical volatile budgets. In this work, through illustrative dynamical simulations of the impact flux on Venus, the Earth, and Mars, we show that these planets can actually experience greatly different rates of impact from objects injected from different reservoirs. For example, we show scenarios in which Mars experiences far more asteroidal impacts, per cometary impactor, than Venus, with the Earth being intermediate in value between the two. This difference is significant, and is apparent in simulations of both quiescent and highly stirred asteroid belts (such as could be produced by a mutual mean-motion resonance crossing between Jupiter and Saturn, as proposed in the Nice model of the Late Heavy Bombardment). We consider the effects; such differences would have on the initial volatilisation of the terrestrial planets in a variety of scenarios of both endogenous and exogenous hydration, with particular focus on the key question of the initial level of deuteration in each planet's water budget. We conclude that each of the terrestrial worlds will have experienced a significantly different distribution of impactors from various reservoirs, and that the assumption that each planet has the same initial volatile budget is, at the very least, a gross over-simplification.