THE LAST STAGES OF TERRESTRIAL PLANET FORMATION: DYNAMICAL FRICTION AND THE LATE VENEER

The final stage of terrestrial planet formation consists of the clean-up of residual planetesimals after the giant impact phase.Dynamically, a residual planetesimal population is needed to damp the high eccentricities and inclinations of the terrestrial planets to circular and coplanar orbits after the giant impact stage.Geochemically, highly siderophile element (HSE) abundance patterns inferred for the terrestrial planets and the Moon suggest that a total of about 0.01 M ⊕ of chondritic material was delivered as "late veneer" by planetesimals to the terrestrial planets after the end of giant impacts.Here, we combine these two independent lines of evidence for a leftover population of planetesimals and show that: (1) a residual population of small planetesimals containing 0.01 M ⊕ is able to damp the high eccentricities and inclinations of the terrestrial planets after giant impacts to their observed values.(2) At the same time, this planetesimal population can account for the observed relative amounts of late veneer added to the Earth, Moon, and Mars provided that the majority of the accreted late veneer was delivered by small planetesimals with radii 10 m.These small planetesimal sizes are required to ensure efficient damping of the planetesimal's velocity dispersion by mutual collisions, which in turn ensures sufficiently low relative velocities between the terrestrial planets and the planetesimals such that the planets' accretion cross sections are significantly enhanced by gravitational focusing above their geometric values.Specifically, we find that, in the limit that the relative velocity between the terrestrial planets and the planetesimals is significantly less than the terrestrial planets' escape velocities, gravitational focusing yields a mass accretion ratio of Earth/Mars ∼ (ρ ⊕ /ρ mars )(R ⊕ /R mars ) 4 ∼ 17, which agrees well with the mass accretion ratio inferred from HSEs of 12-23.For the Earth-Moon system, we find a mass accretion ratio of ∼200, which, as we show, is consistent with estimates of 150-700 derived from HSE abundances that include the lunar crust as well as the mantle component.We conclude that small residual planetesimals containing about ∼1% of the mass of the Earth could provide the dynamical friction needed to relax the terrestrial planet's eccentricities and inclinations after giant impacts, and also may have been the dominant source for the late veneer added to Earth, Moon, and Mars.