SOLAR ECLIPSES on Earth,
1001 BC to AD 2500

revised 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 and to other astronomical phenomena.
In order to facilitate further investigations the presented datafile is proposed.
It includes all solar eclipses visible on Earth during the period 1001 BC to AD 2500.

Several excellent catalogues of Solar Eclipses already exist [1 and 2], but these use Ephemeris Time (or Terrestrial Time).
Our list is based on Universal Time and therefor tends to be directly usable for historical research.


Calendar
Up till October 4th 1582, dates are according to the Julian Calendar.
After that date we changed to the Gregorian Calendar.
Years before AD 1 are given according to the astronomical notation.
This means that year 1 is preceded by year 0, which is preceded by year -1.
So, year 1 = AD 1, year 0 = 1 BC, year -1 = 2 BC, and so on.


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).

In order to derive the local mean solar time for some location on Earth, a correction has to be applied.
If the geographical longitude of the observer's location is taken positive for longitudes West of Greenwich and negative East of Greenwich, the correction to be applied equals:

     correction (hours) = - geographical longitude (degrees) / 15

For a number of major mesoamerican locations corrections are tabulated hereafter:

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
PIEDRAS NEGRAS - 6 h 05 m
QUIRIGUA - 5 h 56 m
TENOCHTITLAN - 6 h 36 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

These corrections have to be added to the tabulated times in order to obtain the mean local time at the considered location.

Example :
     According to our list, a total solar eclipse was at maximum on June 10, AD 1 at 3 h 38 m (UT)
     At that moment the local mean solar time at Tikal was

           3 h 38 m - 5 h 59 m = 21 h 39 m (of the previous day)

     At that time, obviously, the sun was under the horizon at Tital, and therefore the maximum phase of the eclipse was not visible at that location.
     To obtain a list of the solar eclipses that were actually visible in Mesoamerica during the period AD 1 to AD 1600 see our datafile of Solar Eclipses in Mesoamerica.


Method of calculation and Delta T
For the calculations we started from the classical theories [3 to 7], not taking into account very small periodical variations in the solar and lunar orbits.
It should indeed be remembered that, although the astronomical theories used for the calculation of the presented data are more than sufficient to obtain appropriate accuracy with respect to the Earth's centre for the considered period, the irregularities of the Earth's rotation during that same period do not allow to obtain an equally high degree of precision for the exact orientation of the Earth's in space and therefor of Universal Time (or local time) at the instant of a given astronomical event.

To take into account the general slowing down of the Earth's rotation and long-term periodic irregularities of this rotation, this means 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
The datafile lists the solar eclipses that where observable from some point on Earth, with the following details :

Column details
jul.dat julian day number, with decimals, in Universal Time.
dT adopted value for DeltaT (seconds)
year calendar year (astronomical notation)
m calendar month
d calendar day
max(UT) time of maximum eclipse on Earth (universal time)
hem gives an indication on the hemisphere where the eclipse was seen
N = the axis of the Moon's shadow passes north of the Earth's centre
S = the axis of the Moon's shadow passes south of the Earth's centre
type of eclipse type of solar eclipse at maximum.

The following types are indicated:

central total:
At some moment and viewed from some place on Earth the centres of the Sun and the Moon coincided and the Sun was completely obscured by the Moon.

central annular:
At some moment and viewed from some place on Earth the centres of the Sun and the Moon coincided but the Sun was not completely obscured by the Moon, leaving a brilliant 'ring' around the dark moondisk.

central total-annular:
At some moment and viewed from some place on Earth the centres of the Sun and the Moon coincided but due to the varying distances between the Earth, the Moon and the Sun, the eclipse was, at maximum, at some times total and at others annular.

non central eclipse (total or annular):
At no instant did the line joining the centres of the Sun and the Moon coincided with a place on Earth, although the Sun was, at some places on Earth, either completely obscured by the Moon (total eclipse) or the Moon transited fully before the Sun but leaving a brilliant 'ring' around the dark moondisk (annular eclipse).

partial eclipse:
At no instant and nowhere on Earth there was a total or annular eclipse, but in certain areas the Moon obscured the Sun partially.
Our datafile indicates the maximum magnitude (decimal fraction) of these partial eclipses on Earth (1.000 or more = total eclipse, .000 = less than 0.05% obscured).
Saros Number of the Saros series to which the eclipse belongs. [12]
Inex Number of the Inex series to which the eclipse belongs. [12]
wd Weekday (mo, tu, we, th, fr, sa, su)


Downloading the datafile
There are 2 possibilities to download the datafile:


Bibliography
[1] von OPPOLZER Th. - Canon der Finsternisse (Wien, 1887)
[2] MEEUS, GROSJEAN & VANDERLEEN - Canon of Solar Eclipses (Pergamon Press, 1960)
[3] Explanatory Supplement to the Astronomical Ephemeris - (HMSO, London, 1961)
[4] SMART W.M. - Textbook on Spherical Astronomy - (Cambridge University Press, 1977)
[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] VAN DEN BERGH G. - Periodicity and Variation of Solar (and Lunar) eclipses (H.D.Tjeenk Willink & Zoon, Harlem, 1955)


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