Once planetesimals have formed, the dominant physical process that controls further growth is their mutual gravitational interaction. Conventionally the only further role the gas disk plays in terrestrial planet formation is to provide a modest degree of aerodynamic damping of protoplanetary eccentricity and inclination. In this limit the physics involved – Newtonian gravity – is simple and the problem of terrestrial planet formation is well posed. It is not, however, easy to solve. It would take 4 × 109 planetesimals with a radius of 5 km to build the Solar System's terrestrial planets, and it is infeasible to directly simulate the N-body evolution of such a system for long enough (and with sufficient accuracy) to watch planets form. Instead a hybrid approach is employed. For the earliest phases of terrestrial planet formation a statistical approach, similar to that used in the kinetic theory of gases, is both accurate and efficient. When the number of dynamically significant bodies has dropped to a manageable number (of the order of hundreds or thousands), direct N-body simulations become feasible, and these are used to study the final assembly of the terrestrial planets. Using this two-step approach has known drawbacks (for example, it is difficult to treat the situation where a small number of protoplanets co-exist with a large sea of very small bodies), but nevertheless it provides a reasonably successful picture for how the terrestrial planets formed.

Planets form from protoplanetary disks of gas and dust that are observed to surround young stars for the first few million years of their evolution. Disks form because stars are born from relatively diffuse gas (with particle number density n ~ 105 cm−3) that has too much angular momentum to collapse directly to stellar densities (n ~ 1024 cm−3). Disks survive as well-defined quasi-equilibrium structures because once gas settles into a disk around a young star its specific angular momentum increases with radius. To accrete, angular momentum must be lost from, or redistributed within, the disk gas, and this process turns out to require time scales that are much longer than the orbital or dynamical time scale.

In this chapter we discuss the structure of protoplanetary disks. Anticipating the fact that angular momentum transport is slow, we assume here that the disk is a static structure. This approximation suffices for a first study of the temperature, density, and composition profiles of protoplanetary disks, which are critical inputs for models of planet formation. It also permits investigation of the predicted emission from disks that can be compared to a large body of astronomical observations. We defer for Chapter 3 the tougher question of how the gas and solids within the disk evolve with time.

The formation of terrestrial planets from micron-sized dust particles requires growth through at least 12 orders of magnitude in size scale. It is conceptually useful to divide the process into three main stages that involve different dominant physical processes:

• Planetesimal formation. Planetesimals are defined as bodies that are large enough (typically of the order of 10 km in radius) that their orbital evolution is dominated by mutual gravitational interactions rather than aerodynamic coupling to the gas disk. With this definition it is self-evident that aerodynamic forces between solid particles and the gas disk are of paramount importance in the study of planetesimal formation, since these forces dominate the evolution of particles in the large size range that lies between dust and substantial rocks. The efficiency with which particles coagulate upon collision – loosely speaking how “sticky” they are – is also very important.

• Terrestrial planet formation. Once a population of planetesimals has formed within the disk their subsequent evolution is dominated by gravitational interactions. This phase of planet formation, which yields terrestrial planets and the cores of giant planets, is the most cleanly defined since the basic physics (Newtonian gravity) is simple and well-understood. It remains challenging due to the large number of bodies – it takes 500 million 10 km radius planetesimals to build up the Solar System's terrestrial planets – and long time scales involved.

• Giant planet formation and core migration. Once planets have grown to about an Earth mass, coupling to the gas disk becomes significant once again, though now it is gravitational rather than aerodynamic forces that matter. […]

The study of planet formation has a long history. The idea that the Solar System formed from a rotating disk of gas and dust – the Nebula Hypothesis – dates back to the writings of Kant, Laplace, and others in the eighteenth century. A quantitative description of terrestrial planet formation was already in place by the late 1960s, when Viktor Safronov published his now classic monograph Evolution of the Protoplanetary Cloud and Formation of the Earth and the Planets, while the main elements of the core accretion theory for gas giant planet formation were developed in the early 1980s. More recently, a wealth of new observations has led to renewed interest in the problem. The most dramatic development has been the identification of extrasolar planets, first around a pulsar and subsequently in large numbers around main-sequence stars. These detections have furnished a glimpse of the Solar System's place amid an extraordinary diversity of extrasolar planetary systems. The advent of high resolution imaging of protoplanetary disks and the discovery of the Solar System's Kuiper Belt have been almost as influential in focusing theoretical attention on the initial conditions for planet formation and the role of dynamics in the early evolution of planetary systems.

My goals in writing this text are to provide a concise introduction to the classical theory of planet formation and to more recent developments spurred by new observations. Inevitably, the range of topics covered is far from comprehensive.

Planets can be defined informally as large bodies, in orbit around a star, that are not massive enough to have ever derived a substantial fraction of their luminosity from nuclear fusion. This definition fixes the maximum mass of a planet to be at the deuterium burning threshold, which is approximately 13 Jupiter masses for Solar composition objects (1 MJ = 1.899 × 1030 g). More massive objects are called brown dwarfs. The lower mass cut-off for what we call a planet is not as well defined. Currently, the International Astronomical Union (IAU) requires a Solar System planet to be massive enough that it is able to clear the neighborhood around its orbit of other large bodies. Smaller objects that are massive enough to have a roughly spherical shape but which do not have a major dynamical influence on nearby bodies are called “dwarf planets.” It is likely that some objects of planetary mass exist that are not bound to a central star, either having formed in isolation or following ejection from a planetary system. Such objects are normally called “planetary-mass objects” or “free-floating planets.”

Complementary constraints on theories of planet formation come from observations of the Solar System and of extrasolar planetary systems. Space missions to all of the planets have yielded exquisitely detailed information on the surfaces (and in some cases interior structures) of the Solar System's planets, satellites, and minor bodies.

Understanding the formation of giant planets with substantial gaseous envelopes forces us to confront once again the physics of the gas within the protoplanetary disk. Unlike the case of terrestrial planet formation, two qualitatively different theories have been proposed to account for the formation of massive planets. In the core accretion theory of giant planet formation, the acquisition of a massive envelope of gas is the final act of a story that begins with the formation of a core of rock and ice via the identical processes that we discussed in the context of terrestrial planet formation. The time scale for giant planet formation in this model – and to a large extent its viability – hinges on how quickly the core can be assembled and on how rapidly the gas in the envelope can cool and accrete on to the core. In the competing disk instability theory, giant planets form promptly via the gravitational fragmentation of an unstable protoplanetary disk – a purely gaseous analog of the Goldreich–Ward mechanism for planetesimal formation that we discussed in Chapter 4. Fragmentation turns out to require that the disk be able to cool on a relatively short time scale that is comparable to the orbital time scale, and whether these conditions are realized within disks is the main theoretical issue that remains unresolved. Drawing on our prior results on gravitational instabilities in disks and on terrestrial planet formation, the goal in this chapter is to describe the physical principles behind both models and to provide a summary of some of the relevant observational constraints.

The classical theory of giant planet formation described in the preceding chapter predicts that massive planets ought to form on approximately circular orbits, with a strong preference for formation in the outer disk at a few AU or beyond. Most currently known extrasolar planets have orbits that are grossly inconsistent with these predictions and, irrespective of the still open question of what the typical planetary system looks like, their existence demands an explanation. Even within the Solar System the existence of a large resonant population of Kuiper Belt Objects, and the time scale problem for the formation of Uranus and Neptune, suggest that the classical theory is at best incomplete.

In this chapter we describe a set of physical mechanisms – gas disk migration, planetesimal scattering, and planet–planet scattering – that promise to reconcile the observed properties of extrasolar planetary systems with theory. The common feature of all of these mechanisms is that they result in energy and angular momentum exchange either among newly formed planets, or between planets and leftover solid or gaseous debris in the system. The exchange of energy and angular momentum drives evolution of the planetary semi-major axis and eccentricity, which can be substantial enough to make the final architecture of the system unrecognizable from its state immediately after planet formation.