About duo and double-duo solar eclipses and their patterns

Updated: 14 October 2007

A lunation is the period between 2 successive New Moons. On average the length of a lunation is 29.53 day. Two subsequent solar eclipses are separated by 1, 5 or 6 lunations. A duo eclipse is a set of two solar eclipse separated by one lunation. The last time this occurred were the partial eclipses of 1 and 31 July 2000. The next duo pair will be on 1 June 2011 and 1 July 2011.

A double duo consists of two duo pairs separated by 5 lunations. The sequence for a double duo of solar eclipses is:

eclipse - 1 lunation - eclipse - 5 lunations - eclipse - 1 lunation - eclipse

 In this case there are 4 eclipses within a 7 lunation period. The last double duo was in 1935 (5 January / 3 February / 30 June / 30 July), and the next one will be in 2134 (24 April / 23 May / 17 October / 16 November).

It is extremely rare that one of the eclipses of a double duo is total. During the 5 millennia (-2000 / +3000) this has happened only three times.

-1719 Nov  1 P

-1719 Dec  1 P

-1718 Apr 27 T

-1718 May 26 P

 -576 Nov 23 P

 -576 Dec 23 P

 -575 May 19 T

 -575 Jun 18 P

  -26 May 10 P

  -26 Jun  8 T

  -26 Nov  2 P

  -26 Dec  2 P

The graph below shows the total number of solar eclipses per century, as well as number of eclipses that belong to a duo and double duo of eclipses. Again the 585 year period can be seen. It also shows that in some centuries (including the current one) there is no double duo at all. The double duos in the 26th and 27th century are taking place in 2150 and 2691, leaving 181 years without a double duo.

A Saros series consist of 69 to 86 solar eclipse, each separated by 18 year and 10 or 11 and 1/3 days. (10 or 11 depending on the number of leap year in the 18 year period) A Saros series lasts therefore 1226 to 1550 years. Saros series are numbered. Currently eclipses belong to Saros 117 to 155. A new Saros series 156 will begin on 1 July 2011.

The graph below shows the total number of eclipses for Saros series 31 - 144, as well as the number of eclipses of that series that belong to a duo, and the number of eclipses per series that belong to double-duo. Please note that the other eclipse (or three eclipse in case of a double duo) will always belong to different Saros series. As stated, eclipses in the same Saros series are separated by 18 year and 11 days.

The graph also indicates that Saros series with more eclipse seem to have more eclipse that are part of a duo pair or double-duo quartet, and it is remarkable that some Saros series (41-45, 60-63, 79-84, 97-101, 117-120, 135-138) do not have any eclipses at all that a part of a double duo.

Looking at the graph above we see that some Saros series have just as many eclipses belonging to a duo as to a double duo. The double-duo to duo ratio per Saros series is plotted below. For Saros series 37, 49, 57, 67, 95, 104, 122 and 142 this ratio is 100%, meaning that if an eclipse of this series is part of a duo it is also part of a double duo. For series that have no eclipses at all being part of a double duo, this ratio off course will be zero.


The Duo-Saros series

The first (Pb) and last (Pe) eclipse of a Saros series are always part of  a duo. It is interesting that between -2000 and 3000 such duos always that a Pb is the last and a Pe is the first eclipse of the duo. There are no Pe-Pb duos. This means that a P-Pb will be succeeded by another duo one Saros period later, and a Pe-P duo will always have a duo one Saros period earlier. As consequence there will be Saros series of eclipse duos like: P-Pb ... P-P ... ... Pe-P. The question is how many pairs are part of such a series? The answer is 3 up to 22 which means that a duo-Saros series last from just over 36 to almost 379 years. This is shown in the graph below. The duos are always members of Saros n and Saros n+38.

Currently the duo Saros 117-155 is "active". It started with the a rare duo where on of the two eclipses is total (19 May 1928) and the other partial (17 June 1928) and will  end 126 years later in 2054. The next duo-Saros series will start with the eclipse on 1 June (Saros 118) and 1 July 2011 (first of Saros 156). It has 4 duo members and will end 72 years later with a solar eclipse duo on 15 July (last of Saros 118) and 13 August 2083.

A Saros series begins and ends with a minimum of 6 and maximum of 22 partial eclipses. This means that a duo-Saros series with less than 6 members cannot have P-T or T-P pairs.

One lunation in Van der Bergh's formula that 1 = 38I - 61S. On page 124 of Morsels IV, Jean Meeus refers to work that shows that the average number of eclipses per Saros will decrease to just over 61, as compared to more than 73 currently . It is for the reader to argue that this means that the duo-Saros series will become shorter, and that duos in general will happen less frequently. Will this lead to a situation where Pe-Pb duos are possible, or even een situation that some Pb or Pe eclipses are not part of a duo?

The Double-Duo-Saros series

Double duos are often followed by an other double duo one Saros period later. If the Saros number of the first eclipse of a double duo is n, then the Saros numbers of the subsequent eclipses are n+38, n+5 and n+43. Currently (2007), the active Saros numbers range from 117 to 155, which excludes the possibility of double duos. Saros 160 (117+43) will only start after Saros 117 has ended.

However, on 24 October 2098 Saros 164 begins, and on 23 May 2134 Saros 159 will begin, while Saros 121 will end 7 Jun 2206. This leads to a series of 5 double duos with Saros numbers 121-159-126-164 in the period 2134 up to 2206. The last double duo Saros series 111-149-116-154 only had two double duo members in 1916/17 and 1935. The longest double duo Saros (142-180-147-185) will have 9 members and last from 2760 until 2904.

The chart belows shows that the double duo Saros series are grouped. Many combinations, such as above 117-155-122-160 consist of Saros series that do not overlap in time. The graph shows the number of double duos per series.