SOLAR ECLIPSES in Mesoamerica,
AD 1 to AD 1600

revised and extended November 2003

Please send comments to Felix Verbelen

Several of the Mesoamerican Codices contain elements that are most probably related to solar or lunar eclipses.
Some of these are not fully understood yet.
In order to facilitate further investigations the present list is presented.

Area considered
The list includes the solar eclipses that were theoretically observable from a number of major locations in territories known to have been the cultural area of the Mayas and Aztecs.
In order to get a sufficient geographical and cultural spread, data for the following locations were calculated:

Location western longitude
northern latitude
CHICHEN ITZA 88.60 20.67
CHOLULA 98.30 19.07
COPAN 89.13 14.85
LA VENTA 93.99 18.13
MONTE ALBAN 96.77 17.03
PALENQUE 92.02 17.48
PIEDRAS NEGRAS 91.25 17.13
QUIRIGUA 89.08 15.32
TENOCHTITLAN 99.10 19.45
TEOTIHUACAN 98.87 19.68
TIKAL 89.63 17.22
TULA 99.35 20.05
UXMAL 89.77 20.37
YAXCHILAN 90.97 16.90
These coordinates have been taken from the (U.S.) National Imagery and Mapping Agency and from other sources.

Calendar and period
The list covers the period AD 1 to AD 1600.

Till October 4th 1582, dates are according to the Julian Calendar.
After that date we use to the Gregorian Calendar.

Time indications
All times are expressed in Universal Time (UT).
In a number of countries UT is still referred to as GMT (Greenwich Mean Time).

To derive the local mean solar time, dependent on the location, the following corrections should be added to the given times :

Location correction
(hours and minutes)
CHICHEN ITZA - 5 h 54 m
CHOLULA - 6 h 33 m
COPAN - 5 h 57 m
LA VENTA - 6 h 16 m
MONTE ALBAN - 6 h 27 m
PALENQUE - 6 h 08 m
QUIRIGUA - 5 h 56 m
TEOTIHUACAN - 6 h 35 m
TIKAL - 5 h 59 m
TULA - 6 h 37 m
UXMAL - 5 h 59 m
YAXCHILAN - 6 h 04m

      According to our list, a partial solar eclipse occurred at Tikal on April 13th, AD 804.
     Maximum eclipse at Tikal was reached at 22 h 23 m (UT).
     At that moment local mean solar time at Tikal was

           22 h 23 m - 5 h 59 m = 16 h 24 m

Method of calculation and accuracy
To obtain the solar and lunar coordinates, Besselian elements and local circumstances we started from the classical theories [1 to 7], not taking into account the smallest periodical variations.
We neglected these small periodical variations because it is fairly irrelevant to perform lengthy calculations in view to obtain very precise results with respect to the positions of the Sun and the Moon, if at the same time the uncertainties with respect to the Earth's rotation are rather important.
It should indeed be noted that, although the present astronomical theories for the calculation of the presented data are sufficient to obtain high accuracy with respect to the Earth's centre, at the same time the irregularities of the Earth's rotation (DeltaT) prevent a precise calculation for a given location on the Earth's surface, since these irregularities are still insufficiently known for the historical period we considered.

To take into account the general slowing down of the Earth's rotation and longterm periodic irregularities of this rotation, i.e. to convert Terrestrial Time (TT) to Universal Time (UT), several equations have been proposed, among others by Spencer Jones [7], L. V. Morrison and F. R. Stephenson [8], F. R. Stephenson and L. V. Morrison [9], F. R. Stephenson and M. A. Houlden [10], and F. R. Stephenson [11].

We used the following equations  [10] :

     till AD 948:
     DeltaT = 1830 - 405*E +46.5*E^2
     where E = Julian centuries since AD 948

     AD 948 to AD1600:
     DeltaT = 22.5 t^2
     where t = Julian centuries since AD 1850

The Datafile lists the solar eclipses that where observable from the different locations indicated above, per calendar date and per location, with the following details :
Column details
year calendar year
m calendar month
d calendar day
JD julian day number (with 2 decimals)
Like all other time indications, JD is according to Universal Time.
dT assumed value for DeltaT (seconds)
h1.m1 time of first contact;
This is the moment at which the limbs of Sun and Moon touch for the first time.
It is the beginning of the (partial phase of the) eclipse.
se1 elevation of the centre of the solar disk above the horizon at the time of first contact (h1.m1) . time of maximum eclipse at the observer's location
sem elevation of the centre of the solar disk above the horizon at the time of maximum eclipse (
t type of solar eclipse at the considered location, at the time of maximum eclipse:
T = total eclipse
A = annular eclipse
p = partial eclipse
magn maximum size of the eclipse, this means the fraction of solar diameter eclipsed by the Moon at the time of maximum ( eclipse.
If "magn" is equal or greater than 1, the eclipse is total.
h4.m4 time of last contact between the lunar and solar limbs. It is the end of the eclipse at the considered location.
se4 elevation of the centre of the solar disk above the horizon at the time of last contact (h4.m4) right ascension of the Sun at the time of maximum eclipse (expressed in hours and minutes)
dd.dd declination of the Sun at the time of maximum eclipse (expressed in degrees.decimals)
obs location for which the eclipse was calculated. (first 3 characters)

     Remarks Downloading the datafile
There are 2 ways to download the datafile:

[1] Improved Lunar Ephemeris - (Washington, 1954)
[2] Explanatory Supplement to the Astronomical Ephemeris - (HMSO, London, 1961)
[3] SMART W.M. - Textbook on Spherical Astronomy - (Cambridge University Press, 1977)
[4] MEEUS Jean - Tables of Moon and Sun (Kessel-Lo, 1962)
[5] MEEUS Jean - Astronomical Formulae for Calculators - (Urania, Hove / VVS, Brussel, 1978)
[6] Mc NALLY D. - Positional Astronomy (Muller, 1974)
[7] DANJON A. - Astronomie Générale (Blanchart, 1980)
[8] MORRISON L.V. and STEPHENSON F.R. - Sun and Planetary Systems - Vol.96 (Reidel, 1982)
[9] STEPHENSON F.R and MORRISON L.V - Long-Term changes in the rotation of the Earth
           - Phil.Trans.Royal Soc. - Vol.313 (1984)
[10] STEPHENSON F.R and HOULDEN M.A. - Atlas of Historical Eclipse Maps - Cambridge Univ.Press. (1986)
[11] STEPHENSON F.R. - Historical Eclipses and Earth's Rotation - Cambridge Univ. Press. (1997)
[12] Explanatory Supplement to the Astronomical Almanac - (U.S. Naval Observatory, 1992)