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Lunar and solar eclipses

• A lunar eclipse can only occur at full moon and a solar eclipse at new moon. There is not an eclipse every month.
• At least two solar eclipse occur every year, and never more than five.
  
• There are at least two lunar eclipses every year and a maximum of five lunar eclipses in a year (three mentioned by Duffett, but perhaps he means only total lunar eclipses).
  
• The lowest number of eclipses is four per year and the highest total number of eclipses in a year, lunar plus solar, is seven.
• Eclipses tend to go in pairs of threes: solar-lunar-solar. A lunar eclipse is always preceded or followed by a solar eclipse (two weeks in between them).
• The pattern of eclipses tend to recur in cycles of 18 years 11 days and 8 hours, the so-called Saros cycle. The pattern is not repeated exactly and here are more patterns. More on periodicy see below.
  
• At the moment of greatest eclipse the sun and moon are either in opposition or conjunction. If the angle between the line of nodes and the sun or the moon is greater than 12°15' a total eclipse is not possible, while if it is less than 9°30' a lunar eclipse must occur (lunar eclipse limit). If the angle is more than 18°31' a solar eclipse cannot happen, while if it is less than 15°31'  a solar eclipse must occur (solar eclipse limit). Two times the angle 18°31' constitute the eclipse season.
  
• In a lunar eclipse, the total phase can last for a maximum of 1 hour 40 minutes, and the umbral phase, partial-total-partial, for a maximum time of 3 hours 40 minutes. The maximum time of a solar eclipse (at the equator) is 7 minutes 40 seconds and an annular eclipse can last at most for 12 minutes and 24 seconds.
• With an annular eclipse (where moon disc is a little smaller than sun disk) does not have a corona visible: like the annular eclipse of May 10^th, 1994.

Eclipses and certain solar and lunar events

• There is in general no seasonal preference for visible/non visible solar/lunar eclipse (pers. comm. Meeus [2008]):
  
  
  
  (0° = spring equinox, 90° = summer solstice, 180° = autumn equinox, 270° = winter solstice)
  
• Because of the above uniformity of solar eclipses over the year, the number of visible solar eclipses around summer will be larger then around winter, because the days are longer in summer.
• Because of the above uniformity of lunar eclipses over the year, the number of visible lunar eclipses around winter will be larger then around summer, because the nights are longer in winter
• At the peak of the lunar perturbation (every 173.31 Days), which happens when the Sun is inline with the lunar nodes (L_s1 of 0° or 180°) the possibility of an eclipse exists at new or full Moon. This is not specifically related to lunar standstill events.
• Near the periods of major/minor lunar standstill limit events we have the minimum amount of solar/lunar eclipses per appr. half year (2 =1 + 1 instead of the average 2.4), but this does not distinguish these event periods significantly from many other comparable periods with 2 eclipses (some 47%).
  The main reasons for these 2 eclipses per period (~91 days before and after the limit) are:
• the major/minor standstill limit events happen only when the lunar nodes are near the spring/autumnal points.
• when the Sun is at its vernal or autumnal point (at equinoxes) and inline with the lunar nodes, this configuration defines the moments of max. lunar declination.
  
• and if the new or full Moon is at its two lunar nodes, eclipses can happen
• around major/minor standstill limit events the eclipses happen in the middle of the eclipse season (31 to 38 days).
  
• one eclipses at each lunar node/equinoxal point happens.
• Yearly solar eclipse occurance periodicy by using Fourier transform (a low pass filter can be used on the occurance data to remove the spurious noise peaks, but that will not remove the major ones).
  
  
  The solar eclipse periodicy. See the two  peaks around 17.4 (close to Saros) &19.0 (Meton) years and half of these two periods (9.3 years),  which looks to be associated with major/minor lunar standstill events.
  (using Eclipse predictions by Fred Espenak and Jean Meeus [NASA's GSFC])
  
• Yearly lunar eclipse occurance periodicy by using Fourier transform (a low pass filter can be used on the occurance data to remove the spurious noise peaks, but that will not remove the major ones).
  
  
  The lunar eclipse periodicy. The two  peaks around Saros&Meton years are not really visible (resolution of the Fourier analysis is lower then for the above solar eclipses), but half of these two periods (9.3 years) is visible,  which looks to be associated with major/minor lunar standstill events.
  (using Eclipse predictions by Fred Espenak and Jean Meeus [NASA's GSFC])
  
• Work is done on mapping the caculated/found periodicy; like ~2.2 [3*Tzolk'in?], ~3.6 [5*Tzolk'in?], ~5.9, ~140 [Tritrix?] and ~580 [Tetradia] years on overviews of known eclipse periods. Interestingly most of these major peaks don't map on mentioned/known periods!
  I know the Tzolk'in is very discussable, I just tried to find a period that migth fit, and Tzolk'in seems to be a relation with predicting eclipses in the Maya trandition.
• The 9.3 periodicy has also its harmonics as smaller peaks at 4.6, 3.1 en 2.3 year. So these are related to Lunar nodal cycle (18.6 years).
  
• The harmonics 5.9 and 2.9-3.0 years might be another series, but this is not an integer number of synodic months! The 580, 293 and 140 years migth be another series.
  
• It would be nice to be able to name the above periodicies, but even better to understand the astronomical reasons. The 9.3, 18 and 19 years cycles are easy to understand astronomically, but what about the other periodicies? Let me know. There must be an astronomical reason otherwise they would not pop up in the Fourier transform.
  
  
  In the above graph the 580 year periodicy is easily spotted.
  (using Eclipse predictions by Fred Espenak and Jean Meeus [NASA's GSFC])
  
• Shorter (smaller then 2 years) periodicies are investigated on this web page.
  
• Eclipses are concentrated around the equinoxes near the epochs when the Moon reaches its major/minor standstill limits, because at those times the nodes of the lunar orbit are close to the equinoxes, and eclipses can only occur near these nodes. In the year of the actual major/minor standstill limit, this is also close to the quarter-ish moon that will have the major/minor declination.
  Around major standstill event (pers. comm. Meeus [2008]):
  lunar    2006, March 14
  solar    2006, March 29
  lunar    2006, Sept.  7
  solar    2006, Sept. 22
  lunar    2007, March  3
  solar    2007, March 19
  and around minor standstill event:
  solar    2015, March 20
  lunar    2015, April  4
  solar    2015, Sept. 13
  lunar    2015, Sept. 28
  solar    2016, March  9
  lunar    2016, March 23
  

Acknowledgments

1. A catelogue of eclipse cycles
2. Eclipse home page
3. Hermit eclipse
   
4. Lunar eclipse intervals seen from a certain location
   

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