Solar System Formation & Dynamics

In the standard model of terrestrial planet formation there are three stages to growth:

• Runaway growth
• Oligarchic growth
• Giant impact stage

The first two stages are distinguished by the importance of dynamical feedback from the growing protoplanets on the orbits of nearby planetesimals. In the runaway growth phase, the protoplanet grows from planetesimals whose random velocities are set by some other process (normally, by a balance between excitation due to planetesimal-planetesimal encounters, and residual aerodynamic damping against the gas disk). If is fixed, the gravitational focusing term increases as the protoplanet grows, making it easier for the protoplanet to grow still faster. Hence, “runaway” growth.

Runaway growth ends when the assumptions that underlie it break down, specifically when the assumption that the planetesimal swarm maintains a fixed velocity dispersion fails. Once a protoplanet gets massive enough, its own gravitational perturbations are enough to excite the velocity dispersion of nearby planetesimals. This leads to a negative feedback effect, as the protoplanet gets more massive it reduces the amount of gravitational focusing of collisions, leading to slower growth. The result is that, in neighboring regions of the disk, we expect oligarchic growth to set in. A series of oligarchs form, all much more massive than the surviving planetesimals, but none able to grow much faster than the others. These oligarchs might eventually attain masses comparable to the Moon or Mars, so they are well on the way to being terrestrial planets.

The final stage of terrestrial planet formation involves giant impacts among the oligarchs, which develop crossing orbits due to longer term dynamical instabilities. This phase is best studied with numerical simulations. Shown here is a movie of a “standard” simulation done by my collaborator Sean Raymond, in which the Earth assembles within about 100 Myr from a smoothly distributed population of smaller bodies. (The colors here represent the assumed water fraction of the bodies.)

Simulations of this kind do a generally reasonable job at explaining the properties of the Solar System’s terrestrial planets. The most discussed problem is a possible discrepancy in the mass of the real Mars compared to the mass of planets that form at the orbital distance of Mars in simulations. Almost always, the real Mars is lower in mass than one would expect based on theory. This problem remains open. One possible explanation is that the Mars region of the inner Solar System was dynamically depleted of planetesimals during an epoch when Jupiter moved temporarily closer to the Sun. This idea, known as the “Grand Tack”, is discussed in more detail by Sean Raymond on his web pages if you’re interested.