COMPARISON OF ANALYTICAL AND PHYSICAL MODELING OF PLANETESIMAL ACCUMULATION

In recent work on the accumulation of planetesimals to form planetary embryos, a physical model for the evolution of the mass distribution was used (Wetherill and Stewart, 1989, Icarus 77, 330-357). In this paper the mathematical validity of this technique is tested by comparison with the three cases for which analytic solutions to the coagulation equation are known: coagulation rate constant, rate proportional to the sum of the masses of the two colliding bodies, and rate proportional to the product of their masses. The first two cases correspond to orderly growth and the third to runaway growth. In all cases excellent agreement is found between the results of numerical physical modeling and the corresponding analytic solutions. Full treatment of the runaway case requires an extension of the work of Trubnikov (1971, Doklady Akad. Nauk USSR 196, 1316-1319) and leads to development of an analytic solution for the growth of both the runaway body and the residual swarm. Additional calculations for collision probabilities of the form (m1 + m2)λ, where m1 and m2 are the colliding masses, confirm the expectation that runaway occurs when λ > 1, and orderly growth when λ ≤ 1. © 1990.