Planetesimal

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.

For an impactor number density per size $n(D_{\mathrm{im}})$, relative speed $v_{\mathrm{rel}}$, and collision cross-section $\sigma (D,D_{\mathrm{im}})$, the differential collision rate of one target is $n(D_{\mathrm{im}})v_{\mathrm{rel}}\sigma (D,D_{\mathrm{im}})d{D}_{\mathrm{im}}$.

The specific impact energy is an impactor's kinetic energy divided by the target mass. For equal-density spherical bodies,

A binary planetesimal is a gravitationally bound pair of planetesimals. Its internal two-body problem and its centre of mass orbit respond differently to external forces, including gas drag.

For linear gas drag with aerodynamic stopping times $t_1,t_2$, masses $m_1,m_2$, total mass $m=m_1+m_2$, and relative velocity $\mathbf{v}$, defineIf $\mathbf{w}$ is the gas velocity relative to the centre of mass, the relative drag acceleration is $-\kappa \mathbf{v}+\Delta \mathbf{w}$. The first term dissipates internal specific orbital energy; the second is a differential headwind that vanishes for equal aerodynamic stopping times.

For a weakly perturbed circular binary planetesimal, the constant differential headwind does zero work averaged over the unperturbed orbit. Orbit-averaged drag work givesWith constant aerodynamic stopping times, $a(t)=a_0{e}^{-t/\tau }$. This averaging assumes drag is slow compared with the orbital period and does not appreciably distort the circular orbit within one period.

For a nearly circular stellar orbit of radius $a_b$ in gas moving at $(1-\eta )$ times the local circular speed, the averaged tangential gas drag on the centre of mass is $-\eta {\kappa }_b{v}_K$. Orbit-averaged drag work givesIf $m_2/m_1=ϵ\ll 1$ and aerodynamic stopping time scales as $m^k$, $0<k<1$, then $\tau /{\tau }_b\simeq \eta {ϵ}^k\ll 1$. Internal contraction can outpace stellar migration. Tightly gas-coupled drift requires solving radial and azimuthal motion together instead of this weak-drag approximation.