Key to Solar Eclipse Global Maps (original) (raw)

Fred Espenak

For each solar eclipse, an orthographic projection map of Earth shows the path of penumbral (partial) and umbral (total or annular) eclipse. North is to the top in all cases and the daylight terminator is plotted for the instant of greatest eclipse. The sub-solar point on Earth is indicated by a star shaped symbol.

The limits of the Moon's penumbral shadow delineate the region of visibility of the partial solar eclipse. This irregular or saddle shaped region often covers more than half of the daylight hemisphere of Earth and consists of several distinct zones or limits. At the northern and/or southern boundaries lie the limits of the penumbra's path. Partial eclipses have only one of these limits, as do central eclipses when the Moon's shadow axis falls no closer than about 0.45 radii from Earth's center. Great loops at the western and eastern extremes of the penumbra's path identify the areas where the eclipse begins/ends at sunrise and sunset, respectively. If the penumbra has both a northern and southern limit, the rising and setting curves form two separate, closed loops. Otherwise, the curves are connected in a distorted figure eight. Bisecting the 'eclipse begins/ends at sunrise and sunset' loops is the curve of maximum eclipse at sunrise (western loop) and sunset (eastern loop). The points P1 and P4 mark the coordinates where the penumbral shadow first contacts (partial eclipse begins) and last contacts (partial eclipse ends) Earth's surface. If the penumbral path has both a northern and southern limit, then points P2 and P3 are also plotted. These correspond to the coordinates where the penumbral shadow cone becomes internally tangent to Earth's disk.

A curve of maximum eclipse is the locus of all points where the eclipse is at maximum at a given time. Curves of maximum eclipse are plotted at each half hour Universal Time. They generally run between the penumbral limits in the north/south direction, or from the 'maximum eclipse at sunrise and sunset' curves to one of the limits. If the eclipse is central (i.e. total or annular), the curves of maximum eclipse run through the outlines of the umbral shadow, which are plotted at ten minute intervals. The curves of constant eclipse magnitude delineate the locus of all points where the magnitude at maximum eclipse is constant. These curves run exclusively between the curves of maximum eclipse at sunrise and sunset. Furthermore, they're parallel to the northern/southern penumbral limits and the umbral paths of central eclipses. In fact, the northern and southern limits of the penumbra can be thought of as curves of constant magnitude of 0.0. The adjacent curves are for magnitudes of 0.2, 0.4, 0.6 and 0.8 (i.e. - 20%, 40%, 60% and 80%). For total eclipses, the northern and southern limits of the umbra are curves of constant magnitude of 1.0. Umbral path limits for annular eclipses are curves of maximum eclipse magnitude.

Greatest eclipse is defined as the instant when the axis of the Moon's shadow passes closest to Earth's center. Although greatest eclipse differs slightly from the instants of greatest magnitude and greatest duration (for total eclipses), the differences are usually negligible. The point on Earth's surface nearest to the axis at greatest eclipse is marked by an asterisk symbol. For partial eclipses, the shadow axis misses Earth entirely. Therefore, the point of greatest eclipse lies on the day/night terminator and the Sun appears in the horizon.

Data pertinent to the eclipse appear with each map. At the top are listed the instant of conjunction of the Sun and Moon in right ascension and of the instant of greatest eclipse, expressed as both Universal Times and Julian Dates. The eclipse magnitude is defined as the fraction of the Sun's diameter obscured by the Moon at greatest eclipse. For central eclipses (total or annular), the magnitude is replaced by the geocentric ratio of diameters of the Moon and the Sun. Gamma is the minimum distance of the Moon's shadow axis from Earth's center in Earth radii at greatest eclipse. The Saros series of the eclipse is listed, followed by a pair of numbers. The first number identifies the sequence position of the eclipse in the Saros, while the second is the total number of eclipses in the series.

In the upper left and right corners are the geocentric coordinates of the Sun and the Moon, respectively, at the instant of greatest eclipse. They are:

                  R.A. -  Right Ascension 
                  Dec. -  Declination 
                  S.D. -  Apparent Semi-Diameter 
                  H.P. -  Horizontal Parallax

To the lower left are exterior/interior contact times of the Moon's penumbral shadow with Earth which are defined:

 P1 - Instant of first external tangency of Penumbra with Earth's limb.
      (Partial Eclipse Begins)
 P2 - Instant of first internal tangency of Penumbra with Earth's limb.
 P3 - Instant of last internal tangency of Penumbra with Earth's limb.
 P4 - Instant of last external tangency of Penumbra with Earth's limb.
      (Partial Eclipse Ends)

Not all eclipses have P2 and P3 penumbral contacts. They are only present in cases where the penumbral shadow falls completely within Earth's disk. For central eclipses, the lower right corner lists exterior/interior contact times of the Moon's umbral shadow with Earth's limb which are defined as follows:

 U1 - Instant of first external tangency of Umbra with Earth's limb.
      (Umbral [Total/Annular] Eclipse Begins)
 U2 - Instant of first internal tangency of Umbra with Earth's limb.
 U3 - Instant of last internal tangency of Umbra with Earth's limb.
 U4 - Instant of last external tangency of Umbra with Earth's limb.
      (Umbral [Total/Annular] Eclipse Ends)

At bottom center are the geographic coordinates of the position of greatest eclipse along with the local circumstances at that location (i.e. - Sun altitude, Sun azimuth, path width and duration of totality/annularity). At bottom left are a list of parameters used in the eclipse predictions while bottom right gives the Moon's geocentric libration (optical + physical) at greatest eclipse. The value for ΔT (the difference between Terrestrial Dynamical Time and Universal Time) is extrapolated from pre-1996 observations.

Reproduction of Eclipse Data

The eclipse predictions were generated on a Macintosh iMac using algorithms developed from the Explanatory Supplement [1974] with additional algorithms from Meeus, Grosjean, and Vanderleen [1966]. The solar and lunar ephemerides were generated from Newcomb [1895] and the ILE [1954], respectively. The author uses a smaller value of k (=0.272281) for total and annular calculations than the one adopted by the 1982 IAU General Assembly. This results in a better approximation to the Moon's minimum diameter and consequently a shorter total or longer annular eclipse. The IAU value for k (=0.2725076) is retained for partial phases. All predictions are with respect to the Moon's center of mass; no corrections have been made for the center of figure.

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:

Fifty Year Canon of Solar Eclipses: 1986 - 2035
and
Fifty Year Canon of Lunar Eclipses: 1986 - 2035

Permission is freely granted to reproduce this data when accompanied by an acknowledgment:

"Eclipse Predictions by Fred Espenak, NASA's GSFC"