The Sky Nobody Shares

Visibility here is the pure geometric horizon: a star counts as visible from a latitude if, at its highest, its centre climbs above the true horizontal by any amount at all. That is a clean, model-free line, but it is more generous than a real observer's sky in three ways, and one honest way it is stingy.

It ignores atmospheric refraction, which lifts an object at the horizon by about 0.57°, so it slightly understates how far south you can technically see. It ignores terrain: a hill, a building, or your own eyelevel raises the effective horizon. And it treats one degree of altitude the same as overhead, which observationally it is not: a star culminating at 1.5° spends its whole night smeared through the thickest, murkiest air at the horizon, drowned in haze and light. When this page says the top of the Southern Cross still “clears” Alexandria's horizon in 2026, it means by about a degree and a half. Technically up, practically lost. The geometric line is the honest, reproducible one; the observable sky is a smaller thing inside it.

The page reports the geometry and names this gap rather than papering a fuzzy “practical” threshold over it. You can feel how little the headline depends on the exact horizon: demanding a full 10° of clearance instead of 0° moves the least-seen point of the sky from … to … of humanity.

The people are the GHS-POP R2023A gridded population surface for epoch 2020, at 30 arc-second resolution (about 1 km at the equator), summed across every column of the grid into one number per row of latitude. Its own global total is …, a little below the ~7.84 billion mid-2020 UN estimate, because a modelled surface is not a census. It is a model built from censuses and built-up-area imagery, and it carries every census's uncertainty plus the model's own.

“Audience” means the population at latitudes from which the star ever rises, using each person's home latitude. It is not the number of people who have seen the star, or who could travel to see it, or who have a dark enough sky to see it at all. A city dweller under a sodium glow whose home latitude admits a star is counted; a sailor at the other pole is not. The claim is precisely about the sky over where people live. Latitudes are geographic; the geometric horizon uses geographic latitude, which differs from geocentric latitude by up to ~0.19°, below the resolution of anything reported here.

The inhabited band this grid finds runs from about … in the far south to … in the Arctic. Everything south of the southern figure and north of the northern one is, to this model, empty of permanent residents.

Carrying a star's declination back three thousand years is where the arithmetic gets delicate, so the study uses two independent precession models and reports where they part. The live curves use the Vondrák, Capitaine & Wallace (2011) long-term model, built to stay accurate over ±200,000 years. Every date is cross-checked against the current IAU 2006 standard.

Across the whole historical window the two agree to within a handful of years: the year the Southern Cross left each of these cities is identical to the year in both models; the largest disagreement anywhere in the drift table is about four years, six millennia back, for Canopus at Alexandria. Both models are ports of the C in ERFA (the open re-release of the IAU's SOFA library), and the JavaScript port is checked element-by-element against ERFA itself, at fifteen epochs, to within 3×10⁻¹⁶, machine precision. The constellation boundaries are Delporte's own B1875.0 rectangles, densified along each edge before precession so a boundary's extreme declination is never missed between two corners; as a check that the whole polygon machinery is sound, the 88 areas sum to the sphere's 41252.96 square degrees and match the published Delporte figures.