How we reconstruct a night sky
A star map is three problems stacked on top of each other: which stars exist, which half of the sky was turned towards your place at that moment, and how to flatten a hemisphere onto paper. Here is how each one is solved.
1. The stars we draw
We draw the stars brighter than magnitude 5.5 from the HYG database, which combines the Yale Bright Star Catalog with Hipparcos and Tycho-2 astrometry. Their J2000 right ascension and declination are precessed to the equinox of your date with the IAU 1976 expressions (Meeus, Astronomical Algorithms, chapter 21).
Proper motion is deliberately left out: between 1900 and 2100 a typical catalogued star drifts by well under 0.01 degrees, far less than one pixel on the finished chart. Sizes follow apparent magnitude and colours follow the B-V colour index, which is why Betelgeuse comes out orange and Rigel blue-white.
2. Which half of the sky you were facing
This is decided by a single number: local apparent sidereal time. We compute Greenwich apparent sidereal time with the IAU 1982 series and add your east longitude. The result is the right ascension crossing your meridian at that instant.
From there, each star's hour angle gives its altitude and azimuth through the standard spherical transformation. Your clock time is converted using the historical time zone offset, so the daylight saving rules of the year in question are respected.
3. Flattening the hemisphere
We use a stereographic projection with the zenith at the centre and the horizon exactly on the rim. It is conformal, so the shape of Orion or the Southern Cross stays undistorted, unlike a plain plot of altitude against azimuth.
The disc follows the printed-chart convention: north at the top, east on the left. That is the orientation you get when you lie on your back and look up, and it is why the chart matches the sky you see rather than a map of the ground.
4. The Moon and the planets
The Moon uses the ELP2000-82B truncated lunar theory, the Sun uses the apparent longitude series of Meeus chapter 25, and Mercury through Saturn use the full VSOP87 series with light-time and annual aberration corrections.
These are the same series our natal chart calculator uses, where they were checked against NASA JPL Horizons to better than one arcminute. Ecliptic latitude is included, so the Moon's marker falls on the correct side of the ecliptic.
5. The Milky Way band
The soft glow across the disc is drawn from the galactic coordinate system: we trace circles of constant galactic latitude and project them along with everything else. It shows where the band runs, not how bright it looked.
It is a visual approximation, not photometry - decoration that happens to be in the right place.
Data sources and references
- HYG database (Hipparcos, Yale Bright Star Catalog and Tycho-2 astrometry), distributed with three-starmap under the MIT licence.
- d3-celestial constellation line data, BSD-3-Clause.
- Meeus, J. Astronomical Algorithms, 2nd ed. (Willmann-Bell, 1998): chapters 12, 21, 22, 25 and 32.
- VSOP87 planetary theory (Bretagnon & Francou, 1988) and ELP2000-82B lunar theory (Chapront-Touze & Chapront, 1983), via the astronomia library.
What this chart is, and what it is not
It is a geometrically correct picture of where the stars were: positions, rotation and projection are computed, not drawn by hand. It is not a photograph. Refraction lifts stars near the horizon by up to half a degree, city light hides everything fainter than about magnitude 4, and the Milky Way is a stylised band. If you want to know whether one particular faint star was visible that night, the chart tells you where it was, not whether you could have seen it.