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LUNAR ECLIPSES in Mesoamerica,
AD 1 to AD 1600

revised November 2003

Please send comments to Felix Verbelen

The presented datafile includes all lunar eclipses visible at Tikal during the period AD 1 to AD 1600.

We have chosen to calculate the local circumstances at Tikal because of its central position in the Maya region.
Although strictly spoken the results are only valid for the ancient city of Tikal (89°,63 West, 17°,22 North), they nervertheless give a very good idea of the circumstances in other parts of Mesoamerica since the magnitude of the eclipse is the same in all the places where the moon is above the local horizon.
Only the elevation angle and the local time of the calculated contacts differ according to the chosen location.
Therefor, the only cases to be examined more precisely are those where the very beginning or ending of the lunar eclipse at Tikal is near the local horizon.
In these critical cases the local circumstances for other locations in Mesoamerica have to be calculated separately.

Calendar
Up till October 4th 1582, dates are according to the Julian Calendar.
After that date we used 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).

In order to derive the local mean solar time for Tikal, 5 h 59 m have to be subtracted from the given times.
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

Example:
     According to our datafile a total lunar eclipse was at maximum on June 18, 1201 AD at 2h 47 m UT.
     At that moment the local mean solar time at Tikal was

           2h47m - 5 h 59 m (+ 24 h) = 20 h 48 m (of the previous day)

Method of calculation - Delta T
For the calculations of the eclipses we started from the classical theories [1 to 7],
not taking into account small periodical variations in the solar and lunar orbits.
To take into account the general deceleration 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 [8], 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

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

The uncertainties with respect to the Earth's rotation do not affect the accuracy of the calculated magnitude of the lunar eclipses.

The Datafile
Eclipses occur when the centres of the Sun, the Earth and the Moon are in a straight line or nearly so.
A lunar eclipse is only possible at Full Moon, when the Earth is located between the Sun and the Moon. At that time, the Earth's shadow cast by the Sun can cover a fraction or the whole Moon.
If the Moon's orbital plane around the Earth coincided with that of the Earth around the Sun, a lunar eclipse would occur at every Full Moon. But the Moon's orbit is inclined at some 5° 9' to the ecliptic (= plane of the Earth's orbit around the Sun), so that a lunar eclipse can only occur when the three bodies happen to be on or near the line of intersection of the two orbital planes (= line of nodes).
There are two zones of shadow produced by the Earth: one where all sunlight is blocked and a second where only part of the sunlight is intercepted.
The first we call umbra, the second penumbra.

The following types of lunar eclipses exist:

A total umbral eclipse occurs when the total surface of the Moon is obscured by the umbra.
This is the most spectacular type of lunar eclipses and can hardly be overlooked by any observer.
The full Moon's brilliant circular surface gradually changes into a decreasing crescent while at the same time its bright colour varies to become dark grey or brown red.
A partial umbral eclipse occurs when only a fraction of the Moon's surface is obscured by the umbra.
This is still a rather spectacular view.
The colour can still vary dramatically, although less dark than in the case of a total umbral eclipse.
A total penumbral eclipse occurs when the Moon fully enters the penumbra, without entering the umbra.
Although still interesting, this type of eclipse is far less spectacular than an umbral one. The brightness of the Moon's surface gradually decreases and also some colour changes can occur. However, under poor weather conditions, such as light fog, high cirrus clouds or the like, or when it occurs near the horizon, penumbral eclipses may not draw the general people's attention. On the other hand, ancient astronomers surely must have noticed them, certainly when atmospheric conditions and elevation of the Moon above the local horizon were favourable.
A partial penumbral eclipse occurs when the Moon only partially enters the penumbra. It is the less spectacular of lunar eclipses. The smaller the section of the Moon's surface entering the penumbra, the more difficult the observation. Skilled observers probably will have noticed these eclipses if the Moon's surface was obscured by the penumbra for some 50% and if other circumstances, such as atmospheric conditions and elevation of the Moon above the horizon were favourable. Smaller partial penumbral eclipses easily may have escaped to the attention of even trained observers.

The Datafile lists the lunar eclipses that where observable at Tikal, with the following details :


Column	details
yyyy	calendar year
mm	calendar month
dd	calendar day
jd (UT)	Julian day number, given with 2 decimals, according to the astronomical notation. The number refers to the time of maximum eclipse. Like all the other time indications, the Julian day number is according to Universal Time.
dT	assumed value for DeltaT (seconds)
lun	Lunation number. The lunation number 0 corresponds to Full Moon of January 15th, 1900 AD. [12] Full moons, - lunations -, are to be counted as positive numbers after that date; before the lunation numbers are negative.
bgpn	Beginning of the penumbral phase (hours.minutes)
em1	Elevation (degrees) of the Moon above the horizon at the beginning of the penumbral phase.
bgum	Beginning of the umbral phase (hours.minutes) If "---": no umbral phase occurs.
em2	Elevation (degrees) of the Moon above the horizon at the beginning of the umbral phase.
bgtl	Beginning of total umbral phase (hours.minutes) If "---": no total umbral phase occurs.
em3	Elevation (degrees) of the Moon above the horizon at the beginning of the total umbral phase.
max	Time of maximum eclipse, either umbral or penumbral (hours.minutes).
em4	Elevation (degrees) of the Moon above the horizon at maximum eclipse.
endtl	End of total umbral phase (hours.minutes) If "---": no total umbral phase occured.
em5	Elevation (degrees) of the Moon above the horizon at the end of the total umbral phase.
endum	End of the umbral phase (hours.minutes) If "---": no umbral phase occured.
em6	Elevation (degrees) of the Moon above the horizon at the end of the umbral phase.
endpn	End of the penumbral phase (hours.minutes)
em7	Elevation (degrees) of the Moon above the horizon at the end of the penumbral phase.
T	Type of eclipse: t = total umbral u = partial umbral p = penumbral (either partial or total)
mxp	Magnitude of the penumbral phase. The given quantity equals the diameter of the penumbral zone entered by the Moon, compared to its own diameter. The eclipse is partial penumbral if the given quantity is between 0.0 and 1.0; else it isat least total penumbral .
mxu	Magnitude of the umbral phase. The given quantity equals the diameter of the umbral zone entered by the Moon, compared to its own diameter. The eclipse is a partial umbral one if the given quantity is less than 1.0. If the given value is greater than 1.0 than the eclipse is total.

Downloading the datafile
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Bibliography
[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] MEEUS Jean and MUCKE Herman - Canon of Lunar Eclipses -2002 to +2526 -- Canon der Mondfinsternisse -2002 bis +2526 - Astron. Büro, Wien, 1979)

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LUNAR ECLIPSES in Mesoamerica, AD 1 to AD 1600

LUNAR ECLIPSES in Mesoamerica,
AD 1 to AD 1600