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By popular definition, the Blue Moon is the second full moon to occur in any calendar month. The term "Blue Moon" has been used in the English language for over 400 years but there seems to be no reference as to why the second full moon should be referred to as blue. It certainly does not turn blue in colour. An average month is around 30.5 days and the average interval between full moons is 29.5 days so it makes the incidence of two full moons in the one calendar month a rarity. Every century there is an average of 41 months that contain two full moons which makes an average of two-and-a-half years between Blue Moons. So we have the term "Once in a Blue Moon" used today to indicate that something occurs "not very often". At the other extreme February is the only month that can miss out on having a full moon and this only occurs four or five times every century.
The Sun is 400 times larger than the Moon but because it lies 400 times further away they appear to be the same angular size in the sky (about 1/2degree), so that it is possible for the Moon to totally cover the Sun's disc. If the Sun, Moon and Earth lie directly in a straight line then a total or annular eclipse will occur. If the Moon's orbit around the Earth was to lie in the same plane as Earth's orbit around the Sun there would be a solar eclipse every new moon and a total lunar eclipse every full moon. The two planes are however inclined at an angle of 5 degrees, intersecting only at the nodes of the Moon's orbit and this is when the eclipses can occur.
WARNING:- Under no circumstances should you try to observe the Sun without the correct solar filters... or serious eye damage will occur.