Blue Moon??

Mark,

Thanks for the neat calculation!

However, I have a problem: this shows that for a paricular month with a blue moon, we will have a repeat in 2.716 years but other blue moons during the intervening period of 2.716 years will also recycle in 2.716 years.

To this end, we can have multiple blue moons during any given time period and whose average will be less than 2.716 years. Put another way, the maximum interval between blue moons is 2.716 years as per your calculations and which I can accept but I think your calculations represents the maximum possible average.

What have I missed?

Anthony.

Mark,

Let's take a slightly different approach since the repeatability of 2.716 yrs does not necessarily mean another blue moon.

Since the synodic period is 29.531 days, a blue moon can only occur during months which have 30 or 31 days (obviously). Furthermore, the first full moon must occur early on the first of the month for months which have 30 days and on the first or early on the second of the month for months which have 31 days.

Without doing the math, it would seem very low probabilities are involved given that we only have 12 (or 13) full moons during a calendar year.

Anthony.

There were two blue moons in 1999 that were 3 months apart.

2.716 years seems to be a maximum. I guess that this is because our "months" have arbitrary days in them. There would also the factor of your geographical location. The last full moon here in Ireland was in fact the first full moon of January 2010 down-under. So their blue moon appears at the end of this month...

Dave,

Given how arbitrary the months are, it sounds more like an empirical problem than anything else.

I also like your comment about the geographical bias and this is certainly true!

Anthony.

Anthony - Thanks for the feedback on that. Strictly speaking the only interpretation that can be made from my calculation is that it defines the frequency in years in which there are 13 full moons.

For that to happen one and only one 1/12 period (and there lies the conflict) - a nominal month in such a year must have two full moons (as there are only 12 such periods in a year).
So it can only be interpreted as an average due to the irregular size of the calendar months. You are quite correct in spotting that it shouldn't be taken as a hard reality.

Mark