About the calculations
How we know where each heavenly body stood
What it covers
How the sky over the Templo Mayor is computed for any date: the ephemerides used, the coordinates, and what the margin of error is.
The full entry is in Spanish, and here is why
What you have read above is this project's own summary of about the calculations. The full entry — the part that rests on the sixteenth-century sources — has not been translated, and that is a decision rather than an omission.
We chose not to touch the primary text. Those sections quote Sahagún, Durán and the codices in their own words, often in sixteenth-century Castilian. A quotation carried across stops being a quotation: it loses the register, the ambiguity and the exact wording someone might want to check against a facsimile.
In Spanish the entry carries:
- Nada está dibujado de antemano
- El cielo de hace siete siglos no es el de hoy
- Desde el Templo Mayor, no desde cualquier sitio
- Cuánto se acerca
- Y contra hechos que no admiten duda
- Calcula, no afirma
- Lo que no hace
- Y una objeción de fondo, que conviene decir
Read the full entry in the original Spanish → Nahuatl names and terms are identical in both versions.
Nothing is drawn in advance
Every time you move the hour, the Sun, the Moon and the five planets are recomputed from scratch. There are no stored tables of positions and no sample sky: the orbits are solved.
For the planets it uses Kepler's equation, which says where a body is on its ellipse. It has no exact solution — you have to approach it step by step — and five iterations are enough to keep the error in tenths of a degree.
It was checked against published positions: on 1 January 2000, Mercury and Mars come out within a tenth of a degree, Jupiter and Saturn within two. And also against a case that does not depend on the date chosen: Mars at opposition must be exactly opposite the Sun.
The sky of seven centuries ago is not today's
The Earth's axis traces a slow circle of some twenty-six thousand years. Between the founding of Tenochtitlan and today the stars have shifted almost ten degrees — twenty full Moons set side by side.
Without correcting for that, the Omeyocan would say it shows 1325 and would be showing this year's sky. It is corrected.
The tilt of the axis changes too: in 1325 it was half a degree greater than now. And the Earth is slowing, so the clocks of then do not read the same as the clocks of now — some seven minutes' difference at the founding. Both are taken into account.
From the Templo Mayor, not from anywhere
Everything is computed for 19.4361° north latitude and 99.1314° west longitude. The latitude matters: at 19 degrees the sky turns almost vertically over the horizon, not tilted as in Europe, and the crescent Moon lies on its back instead of edge-on.
The mountains of the valley cover the first four degrees. A body below that exists but is not visible, as in reality.
How close it gets
All of this can be checked, and was: each body was contrasted with the models the almanacs use — VSOP87 for the planets and the Sun, ELP for the Moon — at seven epochs spread between 1325 and 2100.
How far each one departs, in the worst of those seven cases: the Sun and Venus by a hundredth of a degree; the Moon by a tenth; Jupiter somewhat more; Mercury and Mars close to two tenths; Saturn, the largest, a little under three.
To give a sense of scale: the full Moon is half a degree across. All seven bodies fall below that, and six of them far below. On screen it is less than a finger's width at arm's length.
That margin serves what this app does: show what was in the sky on a given night, each body in its constellation and at its altitude. It does not serve to say at what exact minute something rose, nor to predict an eclipse.
And against facts that admit no doubt
Against two dates that admit no doubt: a solar eclipse happens only at new moon, and a lunar one only at full. The computation came within half a degree of both.
Venus has no such date. It was checked against two facts a crooked computation could not meet by chance.
That it never moves more than some forty-seven degrees from the Sun, and that between two transits in front of it some five hundred and eighty-four days pass. Both hold as well in the fourteenth century as today.
It computes, it does not assert
That the Moon was full on a day in 1519 is arithmetic: it is derived, not inherited from anyone. That somebody looked at it and wrote something down is another matter, and that needs sources.
That is why every line about the sky carries its warning. Confusing the one with the other would be the quickest way to make everything else false.
What it does not do
It does not correct for atmospheric refraction, which lifts bodies by up to half a degree near the horizon, nor for the Moon's parallax, which shifts it by almost a degree depending on where you stand. For looking at the sky these are negligible; for saying at what exact minute, they are not.
It does include how the planets pull on one another, which was the largest correction it lacked. Jupiter makes almost five turns for every two of Saturn, so they always meet in the same regions of the sky and the pull accumulates over eight hundred years.
The background stars are an image, not a live catalogue: they turn with the hour and with precession, but their brightness and position are drawn in. The ones actually computed are the seven that move — the Sun, the Moon and the five planets visible to the naked eye.
How to cite this page
Alma Mexica, «About the calculations», The documents. Revised 2026-09-17. https://almamexica.org/en/document/acerca-de-los-calculos/