Key to Solar Eclipse Maps
Five Millennium Canon of Solar Eclipses [Espenak and Meeus]
Explanation of Solar Eclipse Maps
Each eclipse is represented on an orthographic projection map of Earth that shows the path of the Moon's penumbral (partial) and umbral/antumbral (total, hybrid, or annular) shadows with respect to the continental coastlines, political boundaries (circa 2000 CE) and the Equator. North is to the top and the daylight terminator is drawn for the instant of greatest eclipse. An "x" symbol marks the sub-solar point or geographic location where the Sun appears directly overhead (zenith) at that time. All salient features of the eclipse maps are identified in Figure 1-1 which serves as a key.
The limits of the Moon's penumbral shadow delineate the region of visibility of a partial solar eclipse. This irregular or saddle shaped region often covers more than half 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 (e.g., 2017 Aug 21). Otherwise, the curves are connected in a distorted figure eight (e.g., 2019 Jul 02). 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 eclipse magnitude is defined as the fraction of the Sun's diameter occulted by the Moon. The curves of eclipse magnitude 0.5 delineate the locus of all points where the local magnitude at maximum eclipse is equal to 0.5. These curves run exclusively between the curves of maximum eclipse at sunrise and sunset. They are approximately parallel to the northern/southern penumbral limits and the umbral/antumbral paths of central eclipses. The northern and southern limits of the penumbra may be thought of as curves of eclipse magnitude of 0.0. For total eclipses, the northern and southern limits of the umbra are curves of eclipse magnitude of 1.0.
Greatest eclipse is the instant when the axis of the Moon's shadow cone 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 negligible. The point on Earth's surface intersected by the axis of the Moon's shadow cone at greatest eclipse is marked by an asterisk symbol "*". For partial eclipses, the shadow axis misses Earth entirely, so the point of greatest eclipse lies on the day/night terminator and the Sun appears on the horizon.
Data relevant to an eclipse appear in the corners of each map. In the top left corner are the eclipse type (total, hybrid, annular, or partial) and the Saros series of the eclipse. To the top right are the Gregorian calendar date (Julian calendar prior to 1582 Oct 14) and the time of greatest eclipse (Terrestrial Dynamical Time). The bottom left corner lists gamma, the minimum distance of the axis of the Moon's shadow cone from Earth's center (in Earth equatorial radii). The Sun's altitude at the geographic position of greatest eclipse is found to the lower right. The content of the final datum depends on the type of eclipse. If the eclipse is partial then the eclipse magnitude is given. If the eclipse is total, hybrid or annular, then the duration of the total or annular phase is given at the position and instant of greatest eclipse. A detailed explanation of each of these items appears in the following sections.
Eclipse Type
There are four basic types of solar eclipses:
- Partial - Moon's penumbral shadow traverses Earth (umbral and antumbral shadows completely miss Earth)
- Annular - Moon's antumbral shadow traverses Earth (Moon is too far from Earth to completely cover the Sun)
- Total - Moon's umbral shadow traverses Earth (Moon is close enough to Earth to completely cover the Sun)
- Hybrid - Moon's umbral and antumbral shadows traverse Earth (eclipse appears annular and total along different sections of its path). Hybrid eclipses are also known as annular-total eclipses. See Five Millennium Catalog of Hybrid Solar Eclipses.
Saros Series Number
Each eclipse belongs to a Saros series using a numbering system first introduced by van den Bergh [1955]. This system has been expanded to include negative values from the past as well as additional series in the future. The eclipses with an odd Saros number take place at the ascending node of the Moon's orbit; those with an even Saros number take place at the descending node.
The Saros is a period of 223 synodic months, or approximately 18 years, 11 days and 8 hours. Eclipses separated by this period belong to the same Saros series and share very similar geometry and characteristics.
Calendar Date
All eclipse dates from 1582 Oct 15 onwards use the modern Gregorian calendar currently found throughout most of the world. The older Julian calendar is used for eclipse dates prior to 1582 Oct 04. Due to the Gregorian Calendar Reform, the day following 1582 Oct 04 (Julian calendar) is 1582 Oct 15 (Gregorian calendar).
The Gregorian calendar was decreed by Pope Gregory XIII in 1582 to correct a problem in a drift of the seasons. It adopts the convention of a year containing 365 days. Every fourth year is a leap year of 366 days if it is divisible by 4 (e.g., 2004, 2008, etc.). However, whole century years (e.g., 1700, 1800, 1900) are excluded from the leap year rule unless they are also divisible by 400 (e.g., 2000). This complicated dating scheme was designed to keep the vernal equinox on or within a day of March 21.
Prior to the Gregorian Calendar Reform in 1582, the Julian calendar was in wide use. It was simpler than the Gregorian in that all years divisible by 4 were counted as 366-day leap years. This simplicity came at a cost. After more that sixteen centuries of use, the Julian calendar date of the vernal equinox had drifted 11 days from March 21. It was this failure of the Julian calendar that resulted in the Gregorian Calendar Reform. See Calendar Dates for more on calendars.
The Julian calendar does not include the year 0, so the year 1 BCE is followed by the year 1 CE. This is awkward for arithmetic calculations. In this publication, dates are counted using the astronomical numbering system which recognizes the year 0. Historians should note the numerical difference of one year between astronomical dates and BCE dates. Thus, the year 0 corresponds to 1 BCE, and year -100 corresponds to 101 BCE, etc.. (See: BCE/CE Dating Conventions ).
There are a number of ways to write the calendar date through variations in the order of day, month and year. The International Organization for Standardization's ISO 8601 advises a numeric date representation which organizes the elements from the largest to the smallest. The exact format is YYYY-MM-DD where YYYY is the calendar year, MM is the month of the year between 01 (January) and 12 (December), and DD is the day of the month between 01 and 31. For example, the 27th day of April in the year 1943 would then be expressed as 1943-04-27. We support the ISO convention but have replaced the month number with the 3-letter English abbreviation of the month name for additional clarity. From the previous example, we express the date as 1943 Apr 27.
Greatest Eclipse
The instant of greatest eclipse occurs when the distance between the axis of the Moon's shadow cone and the center of Earth reaches a minimum. For partial eclipses, the instant of greatest eclipse differs slightly from the instant of greatest magnitude due to Earth's flattening. For total eclipses, the instant of greatest eclipse differs slightly from the instant of greatest duration, although the differences are quite small.
Solar eclipses occur when the Moon is near one of the nodes of its orbit, and therefore moving at an angle of about five degrees to the ecliptic. Hence, unless the eclipse is perfectly central, the instant of greatest eclipse does not coincide with that of apparent ecliptic conjunction (i.e., New Moon), nor with the time of conjunction in Right Ascension.
Greatest eclipse is given in Terrestrial Dynamical Time which is a time system based on International Atomic Time. As such Terrestrial Dynamical Time (TD) is the atomic time equivalent to its predecessor Ephemeris Time and is used in the theories of motion for bodies in the Solar System. To determine the geographic visibility of an eclipse, Terrestrial Dynamical Time is converted to Universal Time using the parameter ΔT.
Gamma
The quantity gamma is the minimum distance from the axis of the lunar shadow cone to the center of Earth, in units of Earth's equatorial radius. This distance is positive or negative, depending on whether the axis of the shadow cone passes north or south of Earth's center. If gamma is between +0.997 and -0.997, the eclipse is a central one (either total, annular or hybrid). The limiting value 0.997 differs from unity due of the flattening of Earth.
The change in the value of gamma , after one Saros period, is larger when Earth is near its aphelion (June-July) than when it is near perihelion (December-January). Table 1-1 illustrates this point using eclipses from two different Saros series.
Table 1-1 - Variation in Gamma at Aphelion vs. Perihelion
Near Aphelion Near Perihelion
---------------------- ----------------------
Date Gamma Date Gamma
1955 Jun 20 -0.15278 1956 Dec 02 +1.09229
1973 Jun 30 -0.07853 1974 Dec 13 +1.07975
1991 Jul 11 -0.00412 1992 Dec 24 +1.07107
2009 Jul 22 +0.06977 2011 Jan 04 +1.06265
2027 Aug 02 +0.14209 2029 Jan 14 +1.05532
A similar situation exists in the case of lunar eclipses. The explanation can be found in van den Bergh [1955].
Altitude of Sun
The Sun's altitude at the geographic position intersected by the axis of the lunar shadow cone is given at the instant of greatest eclipse. For partial eclipses, the Sun's altitude is always 0° because the shadow axis misses Earth. In this case, the geographic position corresponds to the point closest to the shadow axis.
Duration of Central Eclipse
For central eclipses (total, annular or hybrid), the duration of the total or annular phase (in minutes and seconds) is given at the geographic position intersected by the axis of the lunar shadow cone at the instant of greatest eclipse. In the case of a total or hybrid eclipse, this duration is very nearly, but not exactly the maximum duration of the total phase along the entire umbral path. For an annular eclipse, the duration at greatest eclipse may be near either the minimum or maximum duration of the annular phase along the path. If the annular phase duration exceeds approximately 2.3 minutes, then it corresponds to the near maximum duration along the central line track. However, if the annular phase duration is less, then it corresponds to a near minimum and the annular duration increases towards the ends of the central path.
Eclipse Magnitude
The eclipse magnitude is defined as the fraction of the Sun's diameter occulted by the Moon. For partial eclipses, the eclipse magnitude at the instant of greatest eclipse is given for the geographic position closest to the axis of the Moon's shadow cone. The eclipse magnitude is always less than 1.0 for partial and annular eclipses, but equal to or greater than 1.0 for total and hybrid eclipses.
References
Espenak, F. and Meeus, J., Five Millennium Canon of Solar Eclipses: -1999 to +3000, NASA TP-2006-214141, Greenbelt, MD, 2006.
van den Bergh G., Periodicity and Variation of Solar (and Lunar) Eclipses, Tjeenk Willink, Haarlem, Netherlands, 1955.
Acknowledgments
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)"
