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Equation 5 · Part 13 · From Origins to Frontier: A History of Planetary Science and Exploration

Denominator: 9eta

v=2gr2(ρm−ρs)9ηv = \frac{2 g r^2 (\rho_m - \rho_s)}{9\eta}
9η9\eta

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

9eta occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

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 ρm\rho_m moving through a less dense, viscous mantle of density ρs\rho_s…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

The article lists its research sources here.