Tables of solar eclipse local circumstances include the following data. The calendar date and Dynamical Time of the instant of greatest eclipse[1] are found in the first two columns. Delta T (ΔT) gives the arithmetic difference between Dynamical Time and Universal Time. The lunation number (since 2000 Jan 06) and the Saros series are listed along with the eclipse type (P=Partial, A=Annular, T=Total or H=Hybrid[2]) Gamma is the distance of the shadow axis from Earth's center at greatest eclipse while the eclipse magnitude is defined as the fraction of the Sun's diameter obscured at that instant. The geographic latitude and longitude of the umbra are given for greatest eclipse, along with the Sun's altitude and azimuth, the width of the path (kilometers) and the central line duration of totality or annularity. For both partial and non-central umbral/antumbral eclipses, the latitude and longitude correspond to the point closest to the shadow cone axis at greatest eclipse. The Sun's altitude is always 0° at this location.
The data presented in the catalog are based on the Five Millennium Canon of Solar Eclipses: -1999 to +3000.
[1] Greatest eclipse is defined as the instant when the axis of the Moon's shadow passes closest to Earth's center. For total eclipses, the instant of greatest eclipse is virtually identical to the instants of greatest magnitude and greatest duration. However, for annular eclipses, the instant of greatest duration may occur at either the time of greatest eclipse or near the sunrise and sunset points of the eclipse path.
[2] Hybrid eclipses are also known as annular/total eclipses. They occur when the vertex of the Moon's umbral shadow pierces Earth's surface along the central path of an annular eclipse. The eclipse's character then changes to total along the section of the path where the umbral vertex extends beneath Earth's surface. The central paths of hybrid eclipses usually (but not always) begin and end as annular eclipses, but become total along some middle portion of the path.
Column Heading Definition/Description
1 Seq. Sequential number of the eclipse in the Saros series
Num. (links to global map showing region of visibility).
2 Rel. Relative number of the eclipse in the Saros series
Num. with respect to the eclipse having the minimum absolute
value of gamma (i.e.; closest to the node).
3 Calendar Calendar Date at instant of Greatest Eclipse.
Date Gregorian Calendar is used for dates after 1582 Oct 15.
Julian Calendar is used for dates before 1582 Oct 04.
4 TD of Dynamical Time (TD) of Greatest Eclipse, the instant
Greatest when the axis of the Moon's shadow cone passes closest
Eclipse to Earth's center.
5 ΔT Delta T (ΔT) is the arithmetic difference between
Dynamical Time and Universal Time. It is a measure of
the accumulated clock error due to the variable
rotation period of Earth.
6 Luna Lunation Number is the number of synodic months since
Num New Moon of 2000 Jan 06. The Brown Lunation Number
can be determined by adding 953.
7 Ecl. Eclipse Type where:
Type P = Partial Eclipse.
A = Annular Eclipse.
T = Total Eclipse.
H = Hybrid or Annular/Total Eclipse.
Second character in Eclipse Type:
"m" = Middle eclipse of Saros series.
"n" = Central eclipse with no northern limit.
"s" = Central eclipse with no southern limit.
"+" = Non-central eclipse with no northern limit.
"-" = Non-central eclipse with no southern limit.
"2" = Hybrid path begins total and ends annular.
"3" = Hybrid path begins annular and ends total.
"b" = Saros series begins (first eclipse in series).
"e" = Saros series ends (last eclipse in series).
8 Gamma Distance of the shadow cone axis from the center
of Earth (units of equatorial radii) at the
instant of greatest eclipse.
9 Ecl. Eclipse magnitude is the fraction of the Sun's
Mag. diameter obscured by the Moon. For annular, total and
hybrid eclipses, this value is actually the diameter
ratio of Moon/Sun.
10 Lat Latitude where greatest eclipse is seen.
11 Long Longitude where greatest eclipse is seen.
12 Sun Sun's altitude at greatest eclipse.
Alt
13 Path Width of the path of totality or annularity
Width at greatest eclipse (kilometers).
14 Central Central Line Duration of total or annular phase
Dur. at greatest eclipse.
The coordinates of the Sun used in these predictions are based on the VSOP87 theory [Bretagnon and Francou, 1988]. The Moon's coordinates are based on the ELP-2000/82 theory [Chapront-Touze and Chapront, 1983]. For more information, see: Solar and Lunar Ephemerides. The revised value used for the Moon's secular acceleration is n-dot = -25.858 arc-sec/cy*cy, as deduced from the Apollo lunar laser ranging experiment (Chapront, Chapront-Touze, and Francou, 2002).
The largest uncertainty in the eclipse predictions is caused by fluctuations in Earth's rotation due primarily to tidal friction of the oceans due to the Moon. The resultant drift in apparent clock time is expressed as ΔT and was was determined as follows:
Bretagnon P., Francou G., "Planetary Theories in rectangular and spherical variables: VSOP87 solution", Astron. Astrophys., vol. 202, no. 309 (1988).
Brown, E. W., Tables of the Motion of the Moon, Yale University Press, New Haven, 1919.
Chapront, J., Chapront-Touze, M. and Francou, G., "A new determination of lunar orbital parameters, precession constant and tidal acceleration from LLR measurements", Astron. Astrophys., vol. 387, pp 700-709 (2002).
Chapront-Touze, M and Chapront, J., "The Lunar Ephemeris ELP 2000" , Astron. and Astrophys. vol. 124, no. 1, pp 50-62 (1983).
Eckert, W. J., Jones, R., and Clark, H. K., Improved Lunar Ephemeris 1952-1959, Nautical Almanac Office, U. S. Naval Observatory, Washington, D.C., 1954.
Espenak, F., Fifty Year Canon of Solar Eclipses: 1986Ð2035, NASA RP-1178, Greenbelt, MD, 1987.
Espenak, F. and Meeus, J., Five Millennium Canon of Solar Eclipses: -1999 to +3000, NASA TP-2006-214141, Greenbelt, MD, 2006.
Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac, Her Majesty's Nautical Almanac Office, London, 1974.
Meeus, J., Astronomical Formulae for Calculators, Willmann-Bell, Inc., Richmond, 1982.
Meeus, J., Grosjean, C., and Vanderleen, W., Canon of Solar Eclipses, Pergamon Press, New York, 1966.
Morrison, L. and Stephenson, F. R., "Historical Values of the Earth's Clock Error ΔT and the Calculation of Eclipses", J. Hist. Astron., Vol. 35 Part 3, August 2004, No. 120, pp 327-336 (2004).
Morrison, L.V. and Ward, C. G., "An analysis of the transits of Mercury: 1677-1973", Mon. Not. Roy. Astron. Soc., 173, 183-206, 1975.
Mucke, H., and Meeus, J., Canon of Solar Eclipses -2003 to +2526, Astronomisches Buro, Vienna, 1983.
Newcomb, S., "Tables of the Motion of the Earth on its Axis Around the Sun", Astron. Papers Amer. Eph., Vol. 6, Part I, 1895.
Stephenson F.R and Houlden M.A., Atlas of Historical Eclipse Maps, Cambridge Univ.Press., Cambridge, 1986.
van den Bergh, G., Periodicity and Variation of Solar (and Lunar) Eclipses, Tjeenk Willink, Haarlem, Netherlands, 1955.
Special thanks to Jean Meeus for providing the Besselian elements used in the solar eclipse predictions.
All eclipse calculations are by Fred Espenak, and he assumes full responsibility for their accuracy. Some of the information presented on this web site is based on data originally published in Five Millennium Canon of Solar Eclipses: -1999 to +3000.
Permission is freely granted to reproduce this data when accompanied by an acknowledgment:
"Eclipse Predictions by Fred Espenak and Jean Meeus (NASA's GSFC)"
