What does this equation mean?

Comparative planetology treats a planet as a layered physical system rather than a point of light, and the physics of that layering is not exotic — it is gravitational settling under heat. A body accreting from a mixture of metal and silicate material differentiates because denser iron-rich material sinks relative to lighter silicate material, provided the interior is warm enough (from accretion energy, radioactive decay, and impacts) for solid-like material to behave as a slow-moving fluid over geological time. The basic settling physics is captured by a Stokes-law sinking velocity for a dense blob of radius r and density $\rho_m$ moving through a less dense, viscous mantle of density $\rho_s$ and viscosity $\eta$ : $v = \frac{2 g r^2 (\rho_m - \rho_s)}{9\eta}$. This is a first-order model, not a complete theory of core formation — real planetary interiors involve diapirism, iron rain, and turbulent entrainment rather than single isolated blobs — but it exposes the essential dependency: differentiation requires a large enough density contrast, a large enough body (so gravity g and blob size r are non-trivial), and a mantle viscosity $\eta$ low enough (i.e., hot enough) for sinking to complete within the age of the solar system. This is exactly why small, cold bodies — many asteroids among them — never fully differentiated and instead preserve primitive, unprocessed material from the solar system’s earliest few million years, which is the physical reason sample-return missions target asteroids rather than differentiated planets when the goal is recovering pristine early solar system chemistry.