Grain abundance in the primordial atmosphere of the Earth

For models of planetary accumulation in the presence of solar nebular gas, the initial surface temperature of the Earth is controlled by the grain opacity of the atmosphere. The surface temperature in turn controls the quantity of neon dissolved and trapped within the interior of the Earth. To compare accumulation theory with observation calculations have been made of the grain opacity expected to be associated with accumulation in a gaseous nebula. There are two parameters that are in principle determined by the theory, but actually are at present uncertain: the mean eccentricity e of the planetesimal swarm, and the fraction ξ of the accretional energy that is expended in the release of grains into the atmosphere by ablation of the incoming planetesimal. It is found that if the eccentricity of swarm is low (10^?3), rather low values of ξ(10^?5) are required to match the observed neon data. In contrast higher values of ξ are required (10^?1) for the most probable case, intermediate eccentricity (10^?2). For the high eccentricity case (e ～ 0.1) ξ must be >10^?2. The results show that avoidance of excess trapped neon of solar composition places restrictive, but not necessarily impossible, conditions on the parameters of the accumulation theory.