Problem Management — examples
Blue Moons and Leap-Months

Metonic Cycle

The length of the year and the time it takes the Moon to go through all its phases happen to be such that they repeat almost the same pattern every 19 years or 235 lunar months. 19×12 is only 228, so calendar systems that are based on 12 lunar months (the period of time from one new moon to the next) must have a leap-month added 7 times in each cycle in order to stay in sync with the solar seasons.

Seasonal Moons

Within a 12 month year, lunar months can be divided into groups of 3, with each of the 4 groups centered around an equinox or solstice. For instance, the Harvest Moon is the full moon closest to the Autumnal Equinox.

In common use, these names can refer to the full moon specifically, or to the entire lunar month.

Sturgeon Moon Beaver Moon Snow Moon Flower Moon
Autumnal Equinox Winter Solstice Vernal Equinox Summer Solstice
Harvest Moon Cold Moon Worm Moon Strawberry Moon
Hunters Moon Wolf Moon Pink Moon Buck Moon

The 7 unnamed instances are leap-months, and are known as Blue Moons. A Blue Moon occurred between the Hunters Moon and Beaver Moon on 21 November 2010. All Blue Moons occur between, not within, the four sections of the above table.

Note that even though these moon names are subjective and may differ from one geographic or societal area to another (the above list is based on North American native tradition), the Blue Moons will always occur at the same time everywhere on Earth. They are an objective astronomical artifact, not a human invention. (Similar conventions could even be defined on other planets.)

Other Lunar Calendars

Calendars that insert 7 leap-months in every 19 year cycle in order to keep up with the solar seasons are known as lunisolar calendars.

The Roman Church uses a form of the above calendar for some purposes. Easter for instance is defined as the first Sunday after the full Worm Moon. But Rome actually uses approximations rather than actual times, so it doesn't always correspond to this definition, and the Orthodox Church uses even worse approximations (vernal equinox on April 3) so it seldom corresponds to either situation.

The Chinese calendar is another example of this, with month 11 always including the Winter Solstice. Leap-months must contain no zodiac cusp (boundary between signs), and so occur entirely within a single sign of the zodiac.

19   3   6 8   11   14   17 19   3   6 8   11   14   17

The biblical Hebrew calendar is also lunar, though the process is mathematically calculated and not based on current astronomical observations. Leap-months are inserted not where the irregular Blue Moons occur, but consistently just before the last month of years 3, 6, 8, 11, 14, 17, and 19 of each cycle. Interestingly this sequence of leap months maps to the white keys on a musical keyboard, numbering the white keys and the vertical lines between keys.

Strictly lunar calendars, such as the Islamic calendar, do not stay in sync with the solar seasons and have exactly 12 lunar months in each year with no leap-months added. This causes the start of the calendar year to shift by almost 11 days each year with respect to the solar calendar. So for instance, if the month of Ramadan now occurs in the summer, in about 8 years it will be in the spring, and in another 8 years in the winter.

Popular But Incorrect Definition

In 1946, Sky & Telescope magazine published an incorrect article claiming that a Blue Moon is the second moon in a calendar month. They later retracted this false definition (The trendy definition of blue Moon as the second full Moon in a month is a mistake.), but by then it had caught on in popular terminology and is still used by many people today.

That this definition is clearly wrong is illustrated by the Calender Blue Moon that occurred in late 2009 and early 2010, when the Western Hemisphere experienced two full moons in January while most of the Eastern Hemisphere experienced them a month earlier in December. It's even more confusingly silly when New York has a Blue Moon a month before Los Angeles has one.

The fact that designation as a Blue Moon depends upon the location of the observer, politically established timezones, and the arbitrary conventions of the Gregorian calendar gives the concept very little to support it. But it's a lot easier to report in a newspaper and a lot easier for people to (think that they) understand.