Yora

2014-05-22, 03:32 PM

I am working on a calendar for a fantasy world, and it's pretty simple:

The new year begins at dawn on the morning after the first moon after midwinter night. No weekdays, no standard month length to worry about.

Now I made up some numbers for the orbits of the planet around the sun and for the moon around the planet, just by picking numbers that "look nice".

A solar year is very close to 372.35 days, which means that there will be a leap year every three years. Except that there is only a single regular year between the 6th and 7th leap year of every circle. That seems to be entirely the result of of the .35 and I like this particular effect on the calendar.

I also picked the duration for a lunar month to be close to 29.2 days. That means you get 4 months of 29 days and every 5th month with 30 days. Also neat.

Now here's the million dollar question: How often will the midwinter night be a night of a new moon?

Or to put it more mathmatical, how often will a 372,35 cycle and a 29,2 cycle match up exactly? I think it has to be a pretty basic calculation, but I'm not quite sure how to do it. I tried 372.35 times 29.2 and multiplied that by 100 to get rid of the decimal points, which results in 2,920 years.

But as further complication, I think that's the the number of nights between "perfect alignments at midnight". But the calendar is not calibrated to midnight, but to the dawn after midwinter night. If the "perfect new moon alignment" happens at 4:48 PM or 7:12 AM, that still counts.

So, do I just have to divide the 2.920 years by 3?

That gets me 973.3333 years. Which in turn would mean two cyles of 973 years followed by one cycle of 974 years.

Is this math correct?

The new year begins at dawn on the morning after the first moon after midwinter night. No weekdays, no standard month length to worry about.

Now I made up some numbers for the orbits of the planet around the sun and for the moon around the planet, just by picking numbers that "look nice".

A solar year is very close to 372.35 days, which means that there will be a leap year every three years. Except that there is only a single regular year between the 6th and 7th leap year of every circle. That seems to be entirely the result of of the .35 and I like this particular effect on the calendar.

I also picked the duration for a lunar month to be close to 29.2 days. That means you get 4 months of 29 days and every 5th month with 30 days. Also neat.

Now here's the million dollar question: How often will the midwinter night be a night of a new moon?

Or to put it more mathmatical, how often will a 372,35 cycle and a 29,2 cycle match up exactly? I think it has to be a pretty basic calculation, but I'm not quite sure how to do it. I tried 372.35 times 29.2 and multiplied that by 100 to get rid of the decimal points, which results in 2,920 years.

But as further complication, I think that's the the number of nights between "perfect alignments at midnight". But the calendar is not calibrated to midnight, but to the dawn after midwinter night. If the "perfect new moon alignment" happens at 4:48 PM or 7:12 AM, that still counts.

So, do I just have to divide the 2.920 years by 3?

That gets me 973.3333 years. Which in turn would mean two cyles of 973 years followed by one cycle of 974 years.

Is this math correct?