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Given their tendency to be incorporated into the core during differentiation,the highly-siderophile elements (HSEs) in Earth's mantle are thought to havebeen accreted as a `late veneer' after the end of the giant impact phase.Bottke et al (2010) proposed that the large Earth-to-Moon HSE abundance ratiocan be explained if the late veneer was characterized by large (D =1000-4000km) impactors. Here we simulate the evolution of the terrestrialplanets during a stochastic late veneer phase from the end of accretion untilthe start of the late heavy bombardment ~500 Myr later. We show that a lateveneer population of 0.05 Earth masses dominated by large (D > 1000km) bodiesnaturally delivers a ~0.01 Earth mass veneer to Earth, consistent withconstraints. The eccentricities and inclinations of the terrestrial planets areexcited by close encounters with the largest late veneer bodies. We find thebest agreement with their post-veneer orbits if either a) the terrestrialplanets' pre-veneer angular momentum deficit AMD_0 was less than half of thecurrent one AMD_now, or b) AMD_0 <= AMD_now and the veneer was limited tosmaller (D_max <= 2000km) bodies. Veneer impacts on Venus, Earth and Mars weremostly accretionary but on Mercury and the Moon they were mostly erosive. In~20% of simulations an energetic impact occurred that could have removed >25%of Mercury's mass, thereby increasing its iron mass fraction. We show that, dueto the erosive nature of larger impacts, the Moon cannot accrete any materialfrom objects larger than 500-1000km. The large Earth-to-Moon HSE abundanceratio is explained if the late veneer included large impactors (D >=500-1000km) regardless of their size distribution, as long as most of Earth'sveneer came from large bodies. The spin angular momenta imparted by stochasticlate veneer impacts was far in excess of the current ones for Mercury andVenus.

Dynamical and collisional constraints on a stochastic late veneer on the terrestrial planets