Figure 1 is an orthographic projection map of Earth showing the path of penumbral (partial) and umbral (either total or annular) eclipse. The daylight terminator is plotted for the instant of greatest eclipse with north at the top. The orientation of the map is centered over the point of greatest eclipse and is indicated with an asterisk symbol. The sub-solar point (Sun in zenith) at that instant is also shown.
The limits of the Moon's penumbral shadow define the region of visibility of the partial 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 exterior tangency 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. The path of the umbral shadow bisects the penumbral path from west to east and is colored dark blue.
A curve of maximum eclipse is the locus of all points where the eclipse is at maximum at a given time. They are plotted at each half hour Universal Time and 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 magnitude1 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 (i.e. - 100%). 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.
At the top of Figure 1, the Universal Time of geocentric conjunction between the Moon and Sun is given followed by the instant of greatest eclipse. The eclipse magnitude is given for greatest eclipse. For central eclipses (both total and annular), it is equivalent to the geocentric ratio of diameters of the Moon and Sun. Gamma is the minimum distance of the Moon's shadow axis from Earth's center in units of equatorial Earth radii. The shadow axis passes south of Earth's geocenter for negative values of Gamma. Finally, the Saros series number is given along with the eclipse's relative sequence 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 T (the difference between Terrestrial Dynamical Time and Universal Time) is extrapolated from pre-2007 observations.
1 Eclipse magnitude is defined as the fraction of the Sun's diameter occulted by the Moon. It is strictly a ratio of diameters and should not be confused with eclipse obscuration, which is a measure of the Sun's surface area occulted by the Moon. Eclipse magnitude may be expressed as either a percentage or a decimal fraction (e.g.: 50% or 0.50).
All eclipse calculations are by Fred Espenak, and he assumes full responsibility for their accuracy. Permission is freely granted to reproduce this data when accompanied by an acknowledgment:
"Eclipse Predictions by Fred Espenak, NASA's GSFC"
For more information, see: NASA Copyright Information
