Periodicity of Solar Eclipses
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Periodicity of Solar Eclipses

The periodicity of solar eclipses is the interval between any two solar eclipses in succession, which will be either 1, 5, or 6 synodic months.[1] It is calculated that the earth will experience a total number of 11,898 solar eclipses between 2000 BCE and 3000 CE. A particular solar eclipse will be repeated approximately after every 18 years 11 days and 8 hours (6,585.32 days) of period, but not in the same geographical region.[2] A particular geographical region will experience a particular solar eclipse in every 54 years 34 days period.[1] Total solar eclipses are rare events, although they occur somewhere on Earth every 18 months on average,[3]

Repetition of solar eclipses

For the repetition of a solar eclipse, the geometric alignment of the Earth, Moon and Sun, as well as some parameters of the lunar orbit should be repeated. The following parameters and criteria must be repeated for the repetition of a solar eclipse:[1]

  1. The Moon must be in new phase.
  2. The longitude of perigee of the Moon must be the same.
  3. The longitude of the ascending node must be the same.
  4. The Earth will be nearly the same distance from the Sun, and tilted to it in nearly the same orientation.

These conditions are related with the three periods of the Moon's orbital motion, viz. the synodic month, anomalistic month and draconic month. In other words, a particular eclipse will be repeated only if the Moon will complete roughly an integer number of synodic, draconic, and anomalistic periods (223, 242, and 239) and the Earth-Sun-Moon geometry will be nearly identical to that eclipse. The Moon will be at the same node and the same distance from the Earth. Gamma changes monotonically throughout any single Saros series. The change in gamma is larger when Earth is near its aphelion (June to July) than when it is near perihelion (December to January). When the Earth is near its average distance (March to April or September to October), the change in gamma is average.[4] The first three conditions can be met after a time equal to the integral multiple of synodic, draconic, and anomalistic periods. The period is approximately equal to 6,585.32 days (18 years 11 days 8 hours).[1]

Eclipses would not occur in every month

If the Earth had a perfectly circular orbit centered around the Sun, and the Moon's orbit was also perfectly circular and centered around the Earth, and both orbits were coplanar (on the same plane) with each other, then two eclipses would happen every lunar month (29.53 days). A lunar eclipse would occur at every full moon, a solar eclipse every new moon, and all solar eclipses would be the same type. In fact the distances between the Earth and Moon and that of the Earth and the Sun vary because both the Earth and the Moon have elliptic orbits. Also, both the orbits are not on the same plane. The Moon's orbit is inclined about 5.14° to Earth's orbit around the Sun. So the Moon's orbit crosses the ecliptic at two points or nodes. If a New Moon takes place within about 17° of a node, then a solar eclipse will be visible from some location on Earth.[4][5][6]

At an average angular velocity of 0.99° per day, the Sun takes 34.5 days to cross the 34° wide eclipse zone centered on each node. Because the Moon's orbit with respect to the Sun has a mean duration of 29.53 days, there will always be one and possibly two solar eclipses during each 34.5-day interval when the Sun passes through the nodal eclipse zones. These time periods are called eclipse seasons.[1] Either two or three eclipses happen each eclipse season. During the eclipse season, the inclination of the Moon's orbit is low, hence the Sun, Moon, and Earth become aligned straight enough (in syzygy) for an eclipse to occur.


  1. ^ a b c d e NASA Periodicity of solar eclipses
  2. ^ van Gent, Robert Harry (8 September 2003). "A Catalogue of Eclipse Cycles".
  3. ^ Solar Eclipses: 2011-2020
  4. ^ a b Littmann, Mark; Fred Espenak; Ken Willcox (2008). Totality: Eclipses of the Sun. Oxford University Press. ISBN 978-0-19-953209-4.Cite error: The named reference "totality" was defined multiple times with different content (see the help page).
  5. ^ Periodicity of Lunar and Solar Eclipses, Fred Espenak
  6. ^ Five Millennium Catalog of Lunar and Solar Eclipses: -1999 to +3000, Fred Espenak and Jean Meeus

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