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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Eclipse cycle | 11/12 | https://en.wikipedia.org/wiki/Eclipse_cycle | reference | science, encyclopedia | 2026-05-05T11:12:34.827205+00:00 | kb-cron |
== Eclipse periods == In addition to the eclipse cycles, there are periods in eclipse behavior that do not correspond to an eclipse cycle. As mentioned previously, there is the period of around 565 years in which central eclipses move around the anomalistic year (near to the Tetradia cycles). This is the period of the alternation between times when central eclipses do not move much in date (for example in the 20th century they were in July and are now moving into June) and times when central eclipses move rapidly in date. There is also the period of around 1640 years between times when central eclipses are at perigee (or agogee). In the figure above showing inex versus time of year, this is the time between the successive blue patches when total eclipses are more common than annular ones. The central eclipe at perigee of 1781 (and similar ones around then) will recurr only after this much time, around AD 3420.
There are short periodicities in the sizes of the Sun and Moon at the times of eclipses. Both the angular size of the Moon in the sky at eclipses at the ascending node and the size of the Sun at those eclipses vary in a sort of sine wave. The sizes at the descending node vary in the same way, but 180° out of phase. The Moon is large at an ascending-node eclipse when its perigee is near the ascending node, so the period for the size of the Moon is the time it takes for the angle between the node and the perigee to go through 360°, or
1
1
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period of node
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period of perigee
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1
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18.60
+
1
/
8.85
=
5.997
{\displaystyle {\frac {1}{1/{\text{period of node}}+1/{\text{period of perigee}}}}={\frac {1}{1/18.60+1/8.85}}=5.997}
years (Note that a plus sign is used because the perigee moves eastward whereas the node moves westward.) A maximum of this is in 2024 (September), explaining why the ascending-node solar eclipse of April 8, 2024, is near perigee and total and the descending-node solar eclipse of October 2, 2024, is near apogee and annular. Although this cycle is about a day less than six years, super-moon eclipses actually occur every three years on average, because there are also the ones at the descending node that occur in between the ones at the ascending node. At lunar eclipses the size of the Moon is 180° out of phase with its size at solar eclipses. The Sun is large at an ascending-node eclipse when its perigee (the direction toward the Sun when it is closest to the Earth) is near the ascending node, so the period for the size of the Sun is
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period of node
−
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period of perigee
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1
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18.60
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1
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41
million
=
18.60
{\displaystyle {\frac {1}{1/{\text{period of node}}-1/{\text{period of perigee}}}}={\frac {1}{1/18.60+1/41{\text{ million}}}}=18.60}
years In terms of Delaunay arguments, the Sun is biggest at ascending-node solar eclipses and smallest at descending-node solar eclipses around when l'+D=F (modulo 360°), such as June 2010. It is smallest at descending-node solar eclipses and biggest at ascending-node solar eclipses 9.3 years later, such as September 2019.
== Long-term trends == The lengths of the synodic, draconic, and anomalistic months, the length of the day, and the length of the anomalistic year are all slowly changing. The synodic and draconic months, the day, and the anomalistic year (at least at present) are getting longer, whereas the anomalistic month is getting shorter. The eccentricity of the Earth's orbit is presently decreasing at about one percent per 300 years, thus decreasing the effect of the Sun's anomaly. Formulae for the Delaunay arguments show that the lengthening of the synodic month means that eclipses tend to occur later than they would otherwise proportionally to the square of the time separation from now, by about 0.32 hours per millennium squared. The other Delaunay arguments (mean anomaly of the Moon and of the sun and the argument of latitude) will all be increased because of this, but on the other hand the Delaunay arguments are also affected by the fact that the lengths of the draconic month and anomalistic month and year are changing. The net results are:
the mean argument of latitude is decreased by 0.16° per millennium squared, corresponding to 0.00045 draconic months the mean anomaly of the Moon is increased by 1.1° per millennium squared, corresponding to 0.0030 anomalistic months the mean anomaly of the Sun is decreased by 0.002° per millennium squared, which is fairly negligible. As an example, from the solar eclipse of April 1688 BC, to that of April 1623, is 110 inex plus 7 saros (equivalent to a "Palaea-Horologia" plus a "tritrix", 3310.09 Julian years). According to the table above, the Delaunay arguments should change by:
40941 synodic months, 44429.003 draconic months, 43877.032 anomalistic months, 3310.007 anomalistic years, resp. But because of the changing lengths of these, they actually changed by: