- by John Hlynialuk
I am sure you have heard the hype about the Jan 31 lunar eclipse, -the super, blue, full Moon turning blood red (or maybe not) and you may be getting tired of sorting the hoopla from reality. Well, gentle readers, there is one more oddity about our Moon that needs some explaining before we are finished. Get set for a shock: there is no full Moon in February!
The Jan 31 full Moon is just 16.5 hours short of falling on Feb 1, but January did not "steal" the full Moon from February. January's 31 days naturally make it long enough to accommodate the time it takes for Moon phases to go through one cycle (29.531 days). Any 30 or 31 day month is long enough to have two of any lunar phase. Any phase can double up, but we like to pick on the full Moon, so a big deal is made about a second full Moon in a month. March also has a second full Moon, so we get two "blue" Moons in three months. If you check the calendar, you will see that October this year has two last quarter Moons but no one cares much about that.
The last time February was short-changed a full Moon was 1999 and previously to that, in 1980. The next two times will be 2037 and 2056 and if you have your math hat on, you will notice there is a consistent interval of 19 years between these dates. This 19-year interval was explained by Greek astronomer Meton of Athens in the fifth century BC, so we refer to this pattern as the Metonic cycle. He discovered that totally by coincidence, 19 solar years (the so-called tropical year) lasting 6,939.602 days, is almost equal to 235 synodic months (one cycle of lunar phases), a duration of 6,939.688 days. The difference is a mere 0.086 days or a shade over 2 hours. So pick a phase on a particular calendar date and 19 years later the Moon has the same phase on the same day.
Thus, if a particular month has, or does not have, a specific phase in a certain month of a certain year, it will happen again 19 years later. A month like February with 28 days is just not long enough (except in leap years) for all the phases to fit and it is the most likely to be short-changed. The next February with no FM will be...(apply the simple math).. in Feb 2037. Note that Feb is always short-changed one of the Moon phases, but only full Moons seem to get special attention.
It is also a fact that lunar eclipses occur only during full Moons (solar eclipses only during new Moons) so applying the Metonic cycle to eclipse prediction, we should expect a lunar eclipse to occur on Jan 31, 2037. And yes, we do get one on that date, and once again we miss out on seeing the entire event! In 2037, the best place to view will be in Pacific Ocean northeast of Australia. There is no need to make reservations yet but it is an additional reason to book a stay on a South Pacific Island 19 years hence.
We know that early astronomers used the Metonic cycle as a starting point for eclipse calculations, but the 2 hours leftover after dividing 19 tropical years into 235 synodic months (review paragraph 4 above, if this went over your head), leads to a slight shift in eclipse seasons over time. In a Metonic cycle only two quantities have to align but for eclipses, there are three, -the positions of Sun, Earth and Moon- so predicting eclipses based on the 19 year Metonic cycle is a good start but not exactly foolproof. There is a story that in one case (at least) it proved fatal.
In early times, eclipses (especially of the Sun) were feared as portents of evil times, the death of rulers, or other catastrophes, so pre-knowledge of these events was important. Before the use of the Metonic cycle, less reliable methods led either to incorrect predictions or totally unannounced eclipses. The Sun all of a sudden disappearing in the middle of the day, understandably caused a panic. There is a story of the Chinese Emperor Chung K'ang, who, not amused by two of his court astrologers' failure to predict a solar eclipse in 2137 B.C., had them beheaded. The story is more than likely an astronomy myth, but mathematicians (astrologers too) do need to keep their heads about them when working the formulas!
