Final answer:
A blue moon occurs approximately every 2.7 years. This timeframe is calculated based on the surplus days from the synodic month (29.53 days) not aligning perfectly with the Gregorian calendar year.
Step-by-step explanation:
The average time between two consecutive full moons is 29.53 days, known as the synodic month. A blue moon is the term for the unusual event when there are two full moons within one calendar month. Given that there are about 12 full moons in a year and a full moon occurs every 29.53 days, usually, one month has one full moon.
However, since each calendar year has about 365.25 days, and 12 synodic months sum up to approximately 354.36 days (12*29.53), there’s an excess of about 10.89 days (365.25-354.36) each year. This surplus can add up over time to allow an extra full moon to appear within the same month, which we call a blue moon.
To calculate how frequently blue moons occur, we find how many years it takes for the extra 10.89 days to accumulate to at least 29.53 days (the length of one synodic month). Dividing 29.53 by 10.89 gives approximately 2.71 years. However, because calendar months vary in length and the surplus days do not neatly stack at the end of the calendar year, blue moons occur slightly more frequently, about once every 2.7 years. Therefore, the years between each blue moon, rounded to the nearest tenth, is 2.7 years.