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This is called its anomaly, and it repeats with its own period; the anomalistic month.
Every third tzolkinex in a series is near an integer number of anomalistic months and so will have similar properties.
It is also close to 239 anomalistic months, which makes the circumstances between two eclipses one saros apart very similar.
The average duration of the anomalistic month is:
The time between one perigee and the next is slightly longer than the sidereal month and known as the anomalistic month.
The orbital period of the Moon from perigee to apogee and back to perigee is called the anomalistic month.
It varies in a period of time called a lunation, also called synodic month; its duration is about 2 days longer than an anomalistic month.
The near integer number of anomalistic months ensures that the apparent diameter of the moon will be nearly the same with each successive eclipse.
The lifetime and form of each Inex series is not simple due to long term period variations: the synodic, draconic and anomalistic months.
An eclipse cycle must comprise close to an integer number of anomalistic months in order to perform well in predicting eclipses.
The full moon cycle is slightly less than 14 synodic months and slightly less than 15 anomalistic months.
The equality of 269 anomalistic months to 251 synodic months was already known to Chaldean astronomers (see Kidinnu).
The saros is based on the recognition that 223 synodic months approximately equal to 242 draconic months and 239 anomalistic months.
Because 223 synodic months is not identical to 239 anomalistic months or 242 draconic months, saros cycles do not endlessly repeat.
The time it takes the Moon to orbit the Earth once and return to the same distance is given by the anomalistic month, which has a period of 27.55 days.
Not a noteworthy eclipse cycle, but Hipparchus constructed it to closely match an integer number of synodic and anomalistic months, years (345), and days.
Because of the non-integer number of anomalistic month each eclipse varies in type, i.e total vs. annular, and greatly varies in length.
Unlike the saros cycle, the inex is not close to an integer number of anomalistic months so successive eclipses are not very similar in their appearance and characteristics.
An anomalistic month is the average time the Moon takes to go from perigee to perigee - the point in the Moon's orbit when it is closest to Earth.
An anomalistic month is longer than a sidereal month because the perigee moves in the same direction as the Moon is orbiting the Earth, one revolution in nine years.
The center of the epicycle moved at a rate corresponding to the mean change in Moon's longitude, while the period of the Moon around the epicycle was an anomalistic month.
This apsidal precession completes one rotation in the same time as the number of sidereal months exceeds the number of anomalistic months by exactly one, after about 3233 days (8.85 years).
A triple inex, with the advantage that it has nearly an integer number of anomalistic months, which makes the circumstances between two eclipses one Triad apart very similar, but at the opposite latitude.
As a consequence, the apparent diameter of a full moon varies, depending on when it occurs in the anomalistic month: larger near the Earth (near perigee); or smaller when more distant (near apogee).
This orbital period is called the anomalistic month, and together with the synodic month causes the so-called "full moon cycle" of about 14 lunations in the timings and appearances of full (and new) Moons.