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Here is a definition... A blue moon is a name given to an irregularly timed full moon. Most years have twelve full moons which occur approximately monthly, but each calendar year contains those twelve full lunar cycles plus about eleven days to spare. The extra days accumulate, so that every two or three years there is an extra full moon (this happens every 2.72 years). Different definitions place the extra moon at different times - the extra moon is called a "blue moon".
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Simply, A blue moon is the second of two full moons occouring in the same month. Nothing to do with new moons.
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According to the popular definition, it is the second Full Moon to occur in a single calendar month. The average interval between Full Moons is about 29.5 days, whilst the length of an average month is roughly 30.5 days. This makes it very unlikely that any given month will contain two Full Moons, though it does sometimes happen. On average, there will be 41 months that have two Full Moons in every century, so you could say that once in a Blue Moon actually means once every two-and-a-half years. http://www.obliquity.com/astro/bluemoon.html
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