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Eiichiro Kokubo uses numerical dynamics to investigate planet formation. His work with Shigeru Ida identified a regime of oligarchic growth, where neighboring large protoplanets accrete smaller planetesimals while remaining dynamically separated.

The large bodies alter the very population from which they grow: their gravity increases small-body random velocities, changing subsequent collision and capture rates. Following this feedback distinguishes the oligarchic regime from a simple extrapolation in which the largest object keeps outgrowing all its neighbors indefinitely.^[ref]

A protoplanet is a growing planetary body within a planet-forming system. It has accumulated enough mass for gravity to strongly influence subsequent collisions and accretion, while its final orbit, composition and mass may still change substantially.

Accreting a small mass $\Delta m$ onto a body of mass $M$ and radius $R$ can release energy of order $GM\Delta m/R$. Heating, melting and chemical differentiation can therefore accompany growth. A protoplanet may continue to accumulate, merge with another body, lose material or be scattered; the name describes a stage of evolution rather than guaranteeing a particular final planet.

Shigeru Ida studies the assembly of planets from smaller orbiting bodies. With Eiichiro Kokubo, he investigated oligarchic growth, in which a relatively small population of large protoplanets grows by accreting surrounding planetesimals.

The large bodies also stir the random motion of the smaller ones. That dynamical heating changes their capture efficiency, so growth cannot be inferred from mass alone. Their numerical calculations connected growth and orbital spacing, helping explain how a disk of many small bodies can develop a more orderly population of planetary embryos.^[ref]