File:Calculated saros and inex numbers.png

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Summary

Description
English: The graph is like the solar eclipse panorama by Luca Quaglia and John Tilley (compare with w:File:Saros-Inex_panorama.png). The saros and inex numbers of an eclipse in every eclipse season from 11,000 BC to AD 15,000 are calculated from a given approximate date. First an index of the eclipse season is calculated as Index = FLOOR((date+2882.55)*2.1074515+0.5), where "date" is the number of Gregorian years since January 1, 1 BC in the proleptic Gregorian calendar. Then for how many times a five-month period separates two targeted eclipses we use the formula N5 = FLOOR(Index/7.62269+1.071-((Index/2.1074515)/16650)^2 - ((Index/2.1074515)/25000)^3 + 0.064 sin((Index-0.78)/0.335427)). (The sine term attempts to account for the deviation of the sun's longitude from its mean longitude.) The saros number for the eclipse is then 5 Index - 38 N5, and the inex number is 8 Index - 61 N5.


The formulae give the saros and inex number for an eclipse near the input date, checked against the spreadsheet of Quaglia and Tilley. Predicted eclipses will be within three months of "date". Sometimes there will be another eclipse one month before or after an eclipse given by these formulas. These appear in the original panorama of Quaglia and Tilley. If a slightly different formula is used for N5 it may give some of those eclipses instead of the ones given by the above N5 formula.
Though it is possible to make a formula based on the Delaunay arguments given by Simon; et al. (1994), it was found that this did not work well enough outside the date range of validity stated in that paper.


To calculate the saros and inex number for a lunar eclipse near a given date, one can add nine years to the date and find the numbers for the solar eclipse half a saros later, and then subtract 7 from the solar saros number to obtain the lunar saros number, and subtract 13 from the solar inex to obtain the lunar inex. Alternatively, one can subtract nine years, and still subtract 7 from the saros but 12 from the inex number. Usually this will give the same result, but very occasionally they will differ and it could be that only one of the two lunar eclipses predicted actually occurs.
Date
Source Own work
Author Eric Kvaalen

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Captions

Saros and inex number calculated from given date, using formulas, for 11,000 BC to AD 15,000

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25 October 2023

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0044fd0708354359c62ded216aad8602596f074d

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Date/TimeThumbnailDimensionsUserComment
current09:04, 4 August 2024No thumbnail1,286 × 340 (69 KB)commonswiki>Eric KvaalenModified the formula so as to give correct eclipses for the whole range, including in seasons before or after a season with two eclipses.

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