Inex cycle
The Inex cycle is an eclipse cycle with the period duration (the Inex period ) of about 29 years less 20 days.
Each individual Inex cycle theoretically contains about 809 solar or lunar eclipses and is theoretically about 23,410 years long. The Dutchman George van den Bergh has rediscovered this previously recognized cycle and named it Inex cycle.
Van den Bergh also created what he called the Saros- Inex-Panorama as an attempt to recognize all imaginable eclipse cycles more easily than with an eclipse canon .
Finding the index period
Continued fraction calculation
The number of eclipses contained in a cycle is greater, the more precisely the eclipse period consisting of synodic months is a whole multiple of half a draconian month . Among the means of continued fraction found -Rechnung number pairs, the pair of 358 synodic months and 777 half drakonitischen months (388.5 drakonitische months) Inexperiode.
Van den Bergh's method
Van den Bergh was not aware of the short texts in older writings about the cycle without a name before him. He also did not use a relatively simple continued fraction calculation, but found the index period through an elaborate evaluation of Theodor Oppolzer's Canon of Eclipses .
Van den Bergh sought out those solar eclipses from the canon that most barely undercut or overcut the eclipse limit assumed to be ± 11 ° . These eclipses follow each other in about 29 years less than 20 days, the index period. He also found that their node distances differ by about 0.0411 ° , the change in node distance in an index cycle.
From the entry ( go IN ) of these found eclipses into the zone for central eclipses located between the eclipse limits and from the exit ( go EX ), van den Bergh formed the name INEX.
Van den Bergh did not regard the found eclipses as part of any series of cycles (which is possible in principle), but as each belonging to a Saros cycle . This approach led directly to his Saros Inex panorama .
Saros-Inex-Panorama
With his Saros-Inex panorama, Van den Bergh wanted to help end the quarrel between the advocates of the Saros and those of the Inex cycle.
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The Canon of the Eclipses from Oppolzer is transferred into the panorama . It is a “frayed” table above and below, the columns of which contain all the eclipses of a Saros cycle; the lines each contain all the eclipses of an inex cycle. Oppolzer's canon was eight times too short to stretch the lines to about 800 eclipses, the length of an Inex cycle. Even with the help of modern eclipse catalogs, this is far from possible.
The numbers of the columns have become the numbers of the individual Saros cycles.
properties
Since the number of half draconian months is odd (777), the eclipses, unlike a Saros cycle, alternate near the ascending or descending lunar node . A cycle consists of two nested rows of eclipses, one of which runs from south to north and the other from north to south.
The change in node distance is positive (+ 0.0411 °). The first of the eclipses taking place near the ascending knot take place in Antarctica , the last in the Arctic , the eclipses at the descending knot migrate in reverse.
The approximately 550 solar eclipses occurring in the middle of the cycle duration are total or total ring-shaped in irregular succession , because the anomalistic month , unlike the Saros cycle, does not fit into the Inex pattern (the earth-moon distance fluctuates during an Inex cycle).
meaning
Like any other cycle, the Inex cycle is a theoretical result from a continued fraction calculation. With average values for the sidereal and draconian months, this leads to the inex period and to the change in the node distance within the inex cycle. In reality, the latter varies considerably compared to the calculated mean value of 0.0411 °. It will decrease in 3000 years from 0.0722 ° to 0.0294 °. The change is more than 100% of the calculated mean value. This disproportionality in a relatively short time and the very large predicted cycle duration do not speak for a significant eclipse cycle, as could be assumed from the theoretical mean values.
The Inex cycle was only of indirect practical importance because van den Bergh introduced the numbering of the individual Saros cycles that is still used today in the Saros Inex Panorama.
Notes and individual references
- ↑ average values, see eclipse cycles
- ↑ George van den Bergh: Periodicity and variation of solar and lunar eclipses , Tjeenk Willink, Haarlem 1955, page 32, above
- ↑ George van den Bergh: Periodicity and variation of solar and lunar eclipses , Tjeenk Willink, Haarlem 1955, page 19
- ^ Theodor Oppolzer: Canon der Darknesses, memoranda of the Imperial Academy of Sciences, mathematical and natural science class, L II.Bd. , Vienna 1887
- ↑ George van den Bergh: Periodicity and variation of solar and lunar eclipses , Tjeenk Willink, Haarlem 1955, pages 15-17
- ↑ George van den Bergh: Periodicity and variation of solar and lunar eclipses , Tjeenk Willink, Haarlem 1955, page 33, below
- ↑ For example, the Five Millennium Canon of Solar Eclipses: −1999 to +3000 is five times too short for that ( online )
- ↑ George van den Bergh: Periodicity and variation of solar and lunar eclipses , Tjeenk Willink, Haarlem 1955, page 35
literature
- George van den Bergh: Periodicity and variation of solar and lunar eclipses , Tjeenk Willink, Haarlem 1955
- Theodor Oppolzer: Canon of the darkness, memoranda of the Imperial Academy of Sciences, mathematical and natural science class, L II.Bd. , Vienna 1887