Math problem.

[pauraque_bk]

I need a formula that will tell me, for a given number of days in a year and a given number of days in a month, how many years it will take for the cycles to match up -- in other words, if we start with the new moon on the first day of the year, how many years until the new moon falls on that day again? (Assumption being that a month is shorter than a year.)

This is driving me crazy. Left-brainers, please help!

Comments

Re: More thoughts

[pauraque]

When you "lose" a day in 1000 years, what do you do, add a day to the calendar or subtract one? And what are the "extra months"?

Re: More thoughts

[sedesdraconis.livejournal.com]

If you "lose" a day, you have to add it back in to the calendar. That is, "losing" a day means you're calednar year is slightly shorter than your solar year, and the difference has managed to accumulate up to a day, so that now the solstice (for example) is happening one calendar day too soon. So you add a calendar day, and that fixes it.

"Extra months": so you've set up the # of years in a cycle, and you've set up the approximate number of months in a year. Multiplied together, that'll give you an approximate number of months in a cycle. But if you just use that number, you wouldn't need a cycle, because there'd be an exact number of months (well, offset slighlty, cause of the fudge in year legnth, but not offset enough) in the year, whatever you put in. So you fudge it with the "extra months" cell.

So for example you've got an 11-year cycle, and about 14 months in a year. That makes 154 months in a cycle if there're (nearly) exactly 14 months in a year, but we don't want that. So you put in, say, 4 in the extra months field, so that there are 154+4=158 months in a cycle, or 14 and 4/11 months per year.