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Philip J. Armitage develops the theory of planet formation and the early evolution of planetary systems. His lecture notes follow the sequence from the evolution of protoplanetary disks through planetesimal growth to terrestrial and gas giant formation.

An important physical connection is that formation and orbital evolution occur together. Planets exchange angular momentum with their surrounding gas, scatter smaller bodies and interact gravitationally with other planets. The resulting planetary migration means that an observed orbit need not identify the location where a planet originally acquired its mass.^[ref]

A growing solid protoplanet dynamically important compared with the surrounding smaller planetesimals. The term identifies a formation stage, rather than a single sharply specified mass.

A planetesimal is a solid body participating in the growth and collisional evolution of a planetary system. Its collisions can build larger bodies or fragment existing ones; the result depends on relative velocity, material strength and self-gravity. Gravitational encounters can increase random motion, while gas drag and dynamical friction can reduce it.

The category marks a physical role rather than one sharply defined diameter. A population can feed planetary embryos during planet formation or act as the parent bodies of a later debris disk. The same measured total mass can have very different collision behaviour when distributed among many small bodies or a few large ones.

Planet formation is the growth of planets from material around a young star. Solid grains in a protoplanetary disk can collide and stick through protoplanetary dust coagulation, concentrate into planetesimals, and build planetary embryos. Their gravity modifies further encounters through gravitational focusing, while collisions can merge or fragment the bodies.

In core accretion, a growing solid core can acquire a gas envelope if the gas can cool and remain bound. Direct formation from a self-gravitating gas concentration is a distinct route involving gravitational instability of an astrophysical disk. Planetary migration and planetary scattering can subsequently change the orbits, so present location alone does not identify formation location. Planetary differentiation then reorganizes the material inside an assembled body.

Consider equal-density planetesimals with projectile differential number distribution $n(d)\propto d^{-\alpha }$, $\alpha >1$, and a fixed encounter speed. For projectiles small compared with a target of diameter $D$, the minimum projectile diameter needed to exceed specific impact energy $Q$ is proportional to $Q^{1/3}$. If this threshold is well below the upper projectile cutoff, integration over the projectile population gives a collision rate $R(>Q)\propto Q^{(1-\alpha )/3}$.

Write the catastrophic disruption threshold as $Q_D^{\ast }=Q_s+Q_g$, with strength term $Q_s=Q_a{D}^{-a}$ and gravity term $Q_g=Q_b{D}^b$. Let $R_{\mathrm{rub}}=R(>Q_s)$ count all strength-shattering impacts and $R_{\mathrm{cc}}=R(>Q_D^{\ast })$ count dispersive impacts. ThenWith this inclusive convention, the rate of rubblising collisions that leave a bound remnant is $R_{\mathrm{rub}}-R_{\mathrm{cc}}$, rather than $R_{\mathrm{rub}}$ alone.

For $a=1/2$, $b=3/2$ and $\alpha =3$, define $D_w$ as the actual minimum of $Q_D^{\ast }$ at the strength-gravity disruption transition. Differentiation gives $Q_b/Q_a=1/(3D_w^2)$, soin the gravity-dominated limit. Defining the crossover instead by $Q_s=Q_g$ changes the reference diameter and the apparent coefficient, but not the collision-rate scaling. Variable speeds, comparable projectile and target sizes, and finite-cutoff corrections require a different collision integral.

A growth regime in which larger planetesimals have shorter fractional growth times. In a dispersion-dominated population with nearly mass-independent random speed and strong gravitational focusing, fixed material density gives $\dot{M}\propto M^{4/3}$. The displayed scaling is an illustrative limit, not a universal law once large bodies control the random velocities.

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]

The streaming instability is a collective instability of mutually coupled gas and solids in a protoplanetary disk. Gas pressure support creates relative drift; drag both acts on the particles and feeds their reaction force back into the gas. That feedback can amplify particle-density disturbances even without self-gravity. The concentration can help prepare solids for subsequent gravitational collapse, but linear growth alone is not a demonstration that planetesimals have formed.^[ref]