If we assume that all planets and planetesimals move on roughly circular orbits, then there is a finite supply of planetesimals for a growing planet to accrete. The mass at which the growing planet has consumed all of its nearby planetesimal supply is called the isolation mass .

The “feeding zone” of a planet accreting planetesimals is of order the Hill radius. Thus we can write , where is a constant of order unity, and is the Hill radius. Furthermore, we note that the mass within this feeding zone can be calculated from the surface density of the disk :

Finally we can set the isolation mass to be the mass at which the planet mass is equal to the mass of the planetesimals in its feeding zone: . We can solve this equation to find that .*

*See discussion in Armitage 2007

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