Which grains the light wins

At its defaults it draws which grains the light wins. The radiation force on a spherical grain divided by the gravitational force on it, against the grain's radius, on logarithmic axes. Both forces fall as the inverse square of the distance, so the ratio does not depend on how far away the grain is — only on how big it is. Light acts on the cross-section and gravity on the volume, so the ratio goes as 1/a, and the two are equal at 287 nm for material of density 2000 kg/m³. Anything smaller than that is expelled; anything larger stays.

radiation-pressure is one function in lib/figures/extremes.js — radiation, cross-sections and self-gravity. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

The radiation force on a spherical grain divided by the gravitational force on it, against the grain's radius, on logarithmic axes. Both forces fall as the inverse square of the distance, so the ratio does not depend on how far away the grain is — only on how big it is. Light acts on the cross-section and gravity on the volume, so the ratio goes as 1/a, and the two are equal at 287 nm for material of density 2000 kg/m³. Anything smaller than that is expelled; anything larger stays.

The radiation force on a spherical grain divided by the gravitational force on it, against the grain's radius, on logarithmic axes. Both forces fall as the inverse square of the distance, so the ratio does not depend on how far away the grain is — only on how big it is. Light acts on the cross-section and gravity on the volume, so the ratio goes as 1/a, and the two are equal at 287 nm for material of density 2000 kg/m³. Anything smaller than that is expelled; anything larger stays.

At 1361 W/m² the radiation pressure on a perfect absorber is 4.54·10⁻⁶ Pa, which on a 10 mm vane is 4.54·10⁻¹⁰ N — about the weight of a hundredth of a grain of pollen. It would push the black face away from the light. A radiometer's vanes move the other way, so whatever drives them is not this. The curve is the mean free path of the residual gas against pressure: the vanes turn only where it is comparable with the vane itself, near 0.681 Pa, which is the signature of a gas effect and not a light one. Pump harder and the radiometer stops.

The radiation force on a spherical grain divided by the gravitational force on it, against the grain's radius, on logarithmic axes. Both forces fall as the inverse square of the distance, so the ratio does not depend on how far away the grain is — only on how big it is. Light acts on the cross-section and gravity on the volume, so the ratio goes as 1/a, and the two are equal at 71.8 nm for material of density 8000 kg/m³. Anything smaller than that is expelled; anything larger stays.

The Eddington luminosity against mass, with the main sequence drawn beside it. Radiation pushes outward on the electrons and gravity pulls inward on the protons, and both go as one over the distance squared — so the radius cancels out of the comparison entirely, checked here at three radii spanning four decades and coming out identical to 1e-20. What is left is a luminosity: L = 4πGMc/κ, which is 1.47 × 10³¹ watts per solar mass, or 3.8·10⁴ solar luminosities. Above it, radiation drives the outer layers away faster than gravity can hold them. The Sun is at 2.6e-5 of its own limit and in no danger; a star of 10 solar masses is at 1.2e-2; and a star of 100 is at 0.83, which is why the two lines converge at the top of the chart and why the most massive stars known are a few hundred solar masses rather than a few thousand. They do not fail to form for lack of gas; they blow away the gas that would have made them heavier, and once formed they shed mass continuously in a radiation-driven wind. The limit is the same expression for an accreting black hole, where it caps not the brightness but the rate at which mass can be taken on.

The ratio of radiation force to gravity against grain radius, with the radiation-pressure efficiency included: a grain much smaller than the wavelength of the light barely interacts with it — the efficiency falls as the fourth power of the size, which is Rayleigh's law — so the ratio stops rising and turns over. The dashed line is the same ratio with the efficiency taken as one, which is the usual drawing and is right only to the right of the turnover at 115 nm. The consequence is that a grain can be too small to be blown out as well as too large. Taking the threshold at a half — the value at which a grain released from a circular orbit is unbound — the band runs from 48.2 nm to 574 nm, and the largest ratio any grain of this material reaches is 1.87. Everything outside that band stays, and what stays does not stay put: it spirals.

physicscheck asserts something about radiation-pressure that could fail — it draws it and measures the result against a value reached some other way.

Across the library: 100 interrogated, 2 exercised only, 1 untouched, of 103. Read out of the gate's source by the gate's own two patterns — and the gate's last claim fails the build if that read disagrees with what it was handed while running.