How Long Is a Month Really? Four Different Answers

Defining a month means choosing what the moon should return to, and different choices give different answers. Returning to the same position against the background stars is one orbit and takes about twenty seven and a third days. Returning to the same phase takes longer, about twenty nine and a half days, because the earth has moved around the sun during that orbit so the moon must travel further to bring the sun, earth and moon back into the same alignment. That difference of roughly two days is the source of most confusion about lunar periods. Two further definitions exist, based on the moon's closest approach and on the crossing points of its orbit, and both matter for predicting eclipses and tides.

Each is measured against a different reference and each has its uses:

• •The sidereal month, about 27.3 days, one orbit measured against the stars
• •The synodic month, about 29.5 days, from new moon to new moon, which is what calendars use
• •The anomalistic month, about 27.55 days, between closest approaches, which governs apparent size
• •The draconic month, about 27.2 days, between crossings of the earth's orbital plane, which governs eclipses
• •The tropical month, about 27.3 days, measured against the equinox
• •None of them divides evenly into a year, which is why calendars are complicated

Predicting eclipses requires two periods to coincide, which is why they do not happen monthly. An eclipse needs the moon to be at the right phase, which the synodic period governs, and simultaneously to be crossing the plane of the earth's orbit, which the draconic period governs, since the moon's orbit is tilted by about five degrees and it passes above or below the line most months. The two periods come back into step after a little over eighteen years, a cycle known since antiquity and used to predict eclipses, and knowing it lets somebody forecast an eclipse without understanding why one occurs. Adding the third period, which determines how far away the moon is and therefore whether an eclipse is total or annular, improves the prediction further.

Several features of what the moon appears to do puzzle people and have straightforward explanations. The lit portion always faces the sun, so the orientation of a crescent depends on where the sun is relative to the horizon and changes through the night and with latitude, which is why the crescent appears to lie on its back near the equator and stand upright further north. The moon is visible in daylight for much of the month, and most people simply never look. A full moon rises at sunset by definition, so anybody seeing a full moon high in the sky at midday has misidentified it. And the apparent enlargement near the horizon is an illusion of perception rather than an optical effect, since photographs show no change in size.

The calendar month is not a lunar period at all and its lengths record a political history. Roman calendars were lunar in origin, and the reform attributed to Julius Caesar in 46 before the common era abandoned the moon in favour of fitting twelve months into a solar year, which required lengths of thirty and thirty one days with one short month absorbing the remainder. The names preserve an earlier arrangement where the year began in March, which is why the ninth through twelfth months carry names meaning seventh through tenth. Two months were renamed after emperors. None of this has any astronomical meaning, and the persistent story that a day was moved between two months to satisfy an emperor's vanity is a sixteenth century invention with no ancient source.

One orbit against the stars takes about 27.3 days while returning to the same phase takes about 29.5, because the earth moves round the sun meanwhile. Two further periods govern apparent size and eclipse geometry. Eclipses need the phase and the orbital crossing to coincide, which happens on a cycle of a little over eighteen years that was known in antiquity.