Measured gates

A gate is a comparison that was run and written to a file. A registry row is not a gate.

1 Almagest against van Gent’s calculator

File gates/almagest.json. Two hundred Egyptian dates, seven bodies, fourteen hundred longitudes. The equation of time in his calculator was left off, and the same choice is made here. The worst difference was \(6.8 \times 10^{-12}\) arcminutes. The limit was one arcminute. The gate passed.

2 DE441 against Horizons

File gates/horizons.json. Fifty Julian Dates, the Sun, apparent ecliptic longitude of date, UT1 on both sides. The kernel is DE441 part 1, 1,651,119,104 bytes. The worst difference was 0.035 arcminutes. The gate passed.

An earlier comparison by calendar date was about nine degrees off before 1582, because Horizons reads those dates as Julian and a proleptic Gregorian date is a different instant. The gate uses one Julian Date for both sides.

3 Table reading against the sky

File gates/table_vs_sky.json. The same two hundred Egyptian dates. The Julian Date is the expression transcribed from van Gent’s calculator. The largest difference, in degrees:

Body	Worst difference
Sun	8.02
Moon	8.76
Mercury	12.03
Venus	10.73
Mars	8.87
Jupiter	4.92
Saturn	7.30

4 Catalogues

The star tables match the CDS ReadMe counts: Ptolemy 1028, Ulugh Beg 1018, Kepler’s 1627 edition of Tycho 1007, variants 82, Hevelius 1564. The IAU boundary file bound_18.dat has 1565 records. Hipparcos I/239 is loaded at the ReadMe count, 118218 records. Two hundred and sixty-three of them leave the decimal right ascension blank, and those places are read from the sexagesimal columns of the same record.

5 Animations

Six animations are computed: Mars with both readings, the equant construction, Jupiter and Saturn from the Almagest, precession of one catalogue longitude, the elongation of Sirius, and the hippopede drawn with equal radii. Four frames are gaps: Copernicus, Kepler, the nova of 1572, and the Babylonian step functions. A gap frame names the missing source and draws no curve.