Thirteen months in one year?

After talking about days and hours, this is the turn of the month. Like the day, it corresponds to a natural cycle: the revolution of the moon around the Earth. As we know, seen from the Earth, the moon does not seem to rotate around its axis and always shows us the same face. However, if we take as a reference point a star or the sun, a rotation can be seen. An observer located on the sun would see successively all the points on the surface of the moon, therefore would see it rotating around itself. It could also be observed that its period of rotation is the same as its revolution around the Earth. This is why it always shows the same face towards our planet.

How long does it take for the moon to revolve around us? It depends on the landmark we choose. If we take a star as a reference point, and measure the period of revolution of the moon around the Earth as the time elapsed between two successive alignments of our satellite with the same star, we will obtain a period of slightly more than 27 average solar days (see the attached table). This is the sidereal month, which coincides with the lunar sidereal day. If, on the other hand, we measure the period of the moon as the time elapsed between two successive alignments of our satellite with the sun, we will obtain a cycle of a little over 29 and a half days, the solar month or synodic month, so called because of the solemn proclamations of the beginning of each month performed by priestly councils in ancient civilizations: In fact, the solar month is the cycle of the phases of the moon, which is followed by many calendars.

 

Type of month	Duration (days)		Duration (days, hours, min, seg)
Sidereal month	27.32166		27 days 7 hours 43 min 11.42 seg
Anomalistic month	27.55455		27 days 13 hours 18 min 33.12 seg
Synodic month	29.530588		29 days 12 hours 44 min 2.8032 seg

The solar month was an invention of the Mesopotamian civilization, so that the year could be divided equally. The problem is, the solar year is not an exact multiple of the moon's cycle. Today we know that the solar year lasts 365.2421988 days, while twelve lunar cycles last 12×29.530588 = 354.367 days. So, a year contains twelve complete lunar cycles plus about eleven extra days. Therefore, if a given year begins on the day of the new moon, the next year would begin on the twelfth day of the thirteenth cycle, which corresponds almost to the full moon.

The Sumerians solved the problem by inserting an additional month when the difference of the new moon with the New Year's festival amounted to about fifteen days. It didn't take long for them to realize that in the years with thirteen months there always happened catastrophes somewhere. In the years with twelve months this also happened, but nobody would notice that! Therefore, a twelve-month year was perfect and successful. The thirteen-month year was strange, imperfect, unfortunate. This linked the number thirteen with an unlucky quality that it still retains today. It seems incredible that a legend originated in the structure of the Mesopotamian calendar has persisted for more than two thousand five hundred years, but so it has happened.

Johannes Kepler

Like the Sumerians and Babylonians, the German astronomer Johannes Kepler thought that the Earth-Moon system should have been better designed. The number of days in the year should have been equal to 360, which would happen if the solar day lasted 24 hours and 21 minutes. The number of months in the year should have been equal to 12, which would happen if the lunar month lasted 30 days, rather than a little over 29 and a half. Thus we would have had a single calendar valid for all years, instead of the fourteen calendars we have now (see this post).

The duration of the synodic or solar month is the same as the mean solar day on the surface of the moon, because the position of our satellite with respect to the Earth is fixed (it always shows us the same face). Thus, each of the periods of light and dark last a little over two weeks on the moon.

There is another cycle related to the movement of the moon, which depends on still another point of reference: the anomalistic month, the time elapsed between two successive passages of the moon through the point of its orbit closest to the Earth (the perigee). The orbit of the moon around the Earth revolves with a period of about nine years, so the perigee changes position from month to month and the moon is delayed in reaching it, with respect to the sidereal month.

The same post in Spanish

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Manuel Alfonseca

Happy New Year!