Growth of rocky planets

The probability of a collision between two objects depends on their relative velocity urei. When two bodies are moving slowly with respect to each other, there is time for gravity to pull them closer together, focusing their trajectories towards each other. The increase in a planetesimal s mass M as it accretes smaller bodies is roughly 

Embryos accrete most of their mass from a feeding zone centered on their orbit, with a full width 10 Hill radii - roughly 0.01 AU for a 10-3M body at 1 AU. Because embryos mostly accrete local material, objects in different regions of the disk are likely to have different compositions. However, the inward drift of planetesimals and collision fragments means that some radial mixing occurs at this stage. 

Embryos larger than Mars acquire significant atmospheres of captured nebular gas. Planetesimals passing through these atmospheres are slowed, increasing the probability of capture and speeding up growth (Inaba Ikoma 2003). The 

In the absence of planetary migration, oligarchic growth forms lunar to Marssized bodies in the inner few astronomical units of a disk in 106 years (Weidenschilling el al. 1997 Kokubo Ida 2002 Chambers 2006 see Fig. 10.4). 

The low Fe abundance in the lunar mantle suggests the Moon-forming impact happened late in Earth s accretion (Canup Asphaug 2001). It may have been the last collision with another embryo. Simulations of terrestrial-planet formation find that low-velocity, oblique impacts are common (Agnor et al. 1999), so that planets like Earth and Venus are likely to experience at least one such impact during their formation. This suggests large satellites may be a common outcome of terrestrial-planet formation. 

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