The periodicity and recurrence of eclipses is governed by the Saros cycle, a period of approximately 6,585.3 days (18 years 11 days 8 hours). The Saros arises from a natural harmony between three of the Moon's orbital periods:
Synodic Month (New Moon to New Moon) = 29.530589 days = 29d 12h 44m 03s
Anomalistic Month (perigee to perigee) = 27.554550 days = 27d 13h 18m 33s
Draconic Month (node to node) = 27.212221 days = 27d 05h 05m 36s
(above period lengths for 2000 CE)
One Saros is equal to 223 synodic months. However, 239 anomalistic months and 242 draconic months and are also equal to this same period (to within a couple hours)!
223 Synodic Months = 6585.3223 days = 6585d 07h 43m
239 Anomalistic Months = 6585.5375 days = 6585d 12h 54m
242 Draconic Months = 6585.3575 days = 6585d 08h 35m
Two eclipses separated by one Saros cycle share very similar characteristics. They occur with the Moon at nearly the same distance from Earth and at the same time of year. The extra 8 hour displacement means that Earth must rotate an additional ~8 hours or ~120º with each cycle. For solar eclipses, this results in the shifting of each successive eclipse path by ~120º westward. Thus, a Saros series returns to approximately the same geographic region every 3 Saroses (54 years and 34 days).
Another significant eclipse cycle is the Inex, a period of 358 synodic months (29 years minus about 20 days, or nearly 10,752 days). The Inex is useful because it marks the time interval between consecutively numbered Saros series.
A Saros-Inex panorama has been produced by Luca Quaglia and John Tilley in the form of a Microsoft Excel file. It shows 61775 solar eclipses from -11000 to +15000 organised by Saros and Inex Series. The Saros go down the columns and the Inex across the rows. This panorama is based on that of Prof G. van den Bergh in his classic work Periodicity and Variation of Solar (and Lunar) Eclipses.
The most striking feature of the panorama is the pronounced bend - this only became apparent by extending the number of eclipses from the 8000 solar eclipses used by van den Bergh, which was based on Oppolzer's Canon, to 61775 solar eclipses.
The calculation of eclipse dates and Besselian elements was done by Luca Quaglia, using the core of the numerical integrator Solex, which was kindly supplied by Professor Aldo Vitagliano, and was used as the basis of Luca's own integrator. The panorama is used by John and Luca in their program "Solar Eclipse Explorer" and the data was exported as a"CSV" file so that it could be printed using either Open Office (which is free) or Excel.
As most spreadsheets are limited to 256 columns, the panorama is supplied on four worksheets. These can be printed and glued together to form a large display. Before printing - check the column width and row heights. There are 911 Saros across the rows - so at 1mm - the panorama would be around 3 feet across. There is some vertical overlap across the four worksheets - so check the Saros numbers. If you make the first column wider and the first row higher - you can then see the Saros and Inex numbers when printed.
The following link will download Excel file containing the Saros-Inex panorama. This file is about 3.6 MB and may not work with older versions of Excel software.
For questions about the Saros-Inex panorama, contact John Tilley (john@tilley.demon.co.uk) and Luca Quaglia (lqecli@yahoo.fr).
For more information on the Saros and other eclipse cycles, see Periodicity of Solar Eclipses.
