The irregular calendar month is of little use to astronomers. Instead they use four separate kinds of ‘month’ (note that in the following definitions, a ‘day’ refers to the 24-hour solar day):
- Synodic month
- The time from new moon to new moon. This changes because the Earth’s orbit around the sun is an ellipse (and hence its velocity changes), but averages 29.530589 days.
- Sidereal month
- The time it takes the moon to orbit the earth relative to the stars — 27.321661 days.
- Anomalistic month
- The time between lunar perigees (that is, when the moon is nearest the Earth) — 27.554549 days.
- The draconic month
- The time between two successive lunar crossings (in the same direction) of the plane of the Earth’s orbit around the Sun — 27.212220 days.
The cycle of lunar phases
The length of the synodic month does not divide into the number of days in a year, so the phases of the moon are different on the same day in consecutive years. However, 19 years and 235 synodic months are almost equal lengths (about 6939.7 days), so there is a 19 year cycle after which the phases of the moon are the same. This is called the Metonic cycle, after the 5th century BCE Greek astronomer Meton.
The cycle of solar eclipses
A solar eclipse happens when a new moon coincides with the moon crossing the plane of the Earth’s orbit around the sun. This also follows a cycle, as 223 synodic months and 242 draconic months are almost equal (about 6585 and a third days). Eclipses repeat in this cycle (although the third of a day means they repeat a third of the way further around the world each time). This is called the Saros cycle (‘saros’ means cycle in the language of the Babylonians).