Figuring Out Solstices, Equinoxes, and Lunar Cycles

[Patrick-Leigh]

I'm struggling a bit with the calendar system for one of the Planets in my story setting. I specifically need to determine how to map out the lunar cycle and the time between the Solstices and Equinoxes because there are holidays that are held on the Full Moons of certain months as well as the Solstices and Equinoxes. Thus, when the Full Moon overlaps with a particular Solstice or Equinox, you get a double holiday in certain cultures. I need to figure out how often such double holidays occur as well as put together an almanac of sorts to keep track of the phases of the moon during the stories I'll be writing for this setting, particularly the stories that feature Werewolves and other kinds of Therianthropes that transform during the Full Moons.

My current thinking is that the Planet in question has a year that lasts 375.25 days, so every four years is a Leap Year. I want the Moon of the Planet to have a lunar month of about 30 days. That's about all I have worked out so far, but I'm not sure how to do the math to work out how often the Full Moon would fall on a Solstice or Equinox. Any help you guys can provide on this would be greatly appreciated.

 

[ThinkerX]

I had to contend with something close to this in my 'Empire' series. I simplified it.

12 months of 28 days each. The days are about an hour longer than on Earth.

Four extra days, not part of any of the months, each corresponding to a Solstice or Equinox.

Lunar cycle of 28.3 days, with full moons on the Solstices and Equinoxes.

 

[Patrick-Leigh]

I had to contend with something close to this in my 'Empire' series. I simplified it.

12 months of 28 days each. The days are about an hour longer than on Earth.

Four extra days, not part of any of the months, each corresponding to a Solstice or Equinox.

Lunar cycle of 28.3 days, with full moons on the Solstices and Equinoxes.

That doesn't work for my setting. I need there to be some variation so that it's not too common an occurrence for the Full Moon to fall on a Solstice or Equinox. I also want to have Leap Years so that the extra day in each year is a special event called Fool's Day or Feast of Fools (because it's a day that only shows up once every 4 years, so it's a holiday associated with the Archon of Mischief and Merriment.)

 

[pmmg]

Given your numbers, this will occur every other year.

One year, it will happen on both equinoxes, on the next, on none of them.

The .25 of the 375 days adds some complexity, but full moons last about 3 days, so... it will be approximately close to that.

(Course there could be variation on when the equinoxes occur on the calendar. But...there is really too much to consider to worry over the math. -- Speed of orbit from planet to moon, distance of orbit from planet to moon, speed of obit of planet to sun, distance... tile, shape of obit....on and on.)

What was the math?

275/30 = 12.5 --there are 12.5 full moons in a year. Since it falls on exactly .5, it means it will be back where is started every other year.

275.25/30 = 12.508. That's a very small difference. Using the same math, they would have to adjust by a day, every 12.5 years.

 

[Patrick-Leigh]

Given your numbers, this will occur every other year.

One year, it will happen on both equinoxes, on the next, on none of them.

The .25 of the 375 days adds some complexity, but full moons last about 3 days, so... it will be approximately close to that.

(Course there could be variation on when the equinoxes occur on the calendar. But...there is really too much to consider to worry over the math. -- Speed of orbit from planet to moon, distance of orbit from planet to moon, speed of obit of planet to sun, distance... tile, shape of obit....on and on.)

Would there be some way to have it be less frequent than that, like, perhaps, only on Leap Years?

 

[pmmg]

Yes, have it on a number that does not divide easily by 30.

If the moon had a 60 day cycle, it would happen every four years.

 

[Patrick-Leigh]

Yes, have it on a number that does not divide easily by 30.

If the moon had a 60 day cycle, it would happen every four years.

What about a 28 day cycle?

 

[ThinkerX]

It is just math.

You need to know the length of the year in days.

You need to know the length of the lunar month in days.

You need to know the length of the calendar month in days.

Pick a starting point where the full moon happens on a Solstice or Equinox.

If the lunar month is 25 days and the calendar month is 30 days, they will sync every 150 days. If the year is 360 days, that puts the next sync point 10 days shy of the next Equinox. Each sync point will be 10 days further back in the calendar year. The next point where all three syncs would be 1350 days or 3.75 years.

I'd ignore the leap year aspect for this part of the calculation, as the moon could be deemed 'full' for as much as three days, and the lunar cycle need not be precisely 25 days.

 

[Patrick-Leigh]

It is just math.

You need to know the length of the year in days.

You need to know the length of the lunar month in days.

You need to know the length of the calendar month in days.

Pick a starting point where the full moon happens on a Solstice or Equinox.

If the lunar month is 25 days and the calendar month is 30 days, they will sync every 150 days. If the year is 360 days, that puts the next sync point 10 days shy of the next Equinox. Each sync point will be 10 days further back in the calendar year. The next point where all three syncs would be 1350 days or 3.75 years.

I'd ignore the leap year aspect for this part of the calculation, as the moon could be deemed 'full' for as much as three days, and the lunar cycle need not be precisely 25 days.

Are you saying the lunar cycle is 25 days + 3 full moon days or 25 days total? Because I was proposing we switch it from 30 days to 28 days, not 25.

 

[pmmg]

Maybe this will help:

75/28 = 13.39... that is 13.39 full moons in a year.

How frequently does the .39 return to approx 0. I got 17 years, to get within .02

.39+.39+.39....17 times = 7.02

What reader is going to figure out such math?

 

[Patrick-Leigh]

Maybe this will help:

75/28 = 13.39... that is 13.39 full moons in a year.

How frequently does the .39 return to approx 0. I got 17 years, to get within .02

.39+.39+.39....17 times = 7.02

What reader is going to figure out such math?

I don't need the reader to figure this out, I just need a way to help myself keep track of these things because moon phases, equinoxes, solstices, and the appearances of comets play important roles in certain events.

I think 13 Full Moons is too many. I'd like to keep it to 12, even if it's 12.whatever. If we go with a 29 day lunar cycle, that's 375/29 = 12.93 Full Moons a year. So, how many .93s would we need to get back to 0ish?

 

[pmmg]

At 13 I get, 13.02. The .02 is pretty close to .00, so you could say every 13 years. At 12 years, they are pretty close too.


Though, that also assumes the equinox's are also static. I think they are also approximate.

 

[Patrick-Leigh]

At 13 I get, 13.02. The .02 is pretty close to .00, so you could say every 13 years. At 12 years, they are pretty close too.

So, if we go with a 29 day Lunar Cycle, we get a Full Moon on the Summer Solstice every 12 years?

 

[pmmg]

Every 13 years. 12 will be a close miss.

 

[ThinkerX]

Are you saying the lunar cycle is 25 days + 3 full moon days or 25 days total? Because I was proposing we switch it from 30 days to 28 days, not 25.

I picked those numbers for ease of calculation. What you are doing is choosing numbers for -

- a lunar month,
- a calendar month,
- and an Equinox/Solstice starting point.

You then multiply those out, looking for sync points - numbers that both divide into evenly. With a 28-day lunar month/30-day calendar month, the sync points are 15/14 months apart. You could go decades before a full moon aligned with a solstice/equinox.



Technically, the moon would be full for one day. However, it would be 'close enough to count as full the day before and the day after.

 

[Patrick-Leigh]

I picked those numbers for ease of calculation. What you are doing is choosing numbers for -

- a lunar month,
- a calendar month,
- and an Equinox/Solstice starting point.

You then multiply those out, looking for sync points - numbers that both divide into evenly. With a 28-day lunar month/30-day calendar month, the sync points are 15/14 months apart. You could go decades before a full moon aligned with a solstice/equinox.



Technically, the moon would be full for one day. However, it would be 'close enough to count as full the day before and the day after.

Close enough to count doesn't apply to things like Werewolves, however, unless I have them transform for the 3 nights the moon appears full instead of the one night where it is actually full. And, given that Werewolves are connected to an evil god who logically would have certain ceremonies being held on the solstices and equinoxes, well, you can see how the two events coinciding would be rather significant for certain rituals.

I'm not trying to go overboard with this stuff, of course, but I don't want to just hand wave things, either. I want to make sure things are worked out enough to satisfy any readers that are enthusiastic about astronomy and to ensure I avoid any plot holes because I gave up on doing the math. And I'm pretty terrible when it comes to math like this. My ADHD starts looking at the numbers and goes:

 

[Diana Silver]

I picked those numbers for ease of calculation. What you are doing is choosing numbers for -

- a lunar month,
- a calendar month,
- and an Equinox/Solstice starting point.

You then multiply those out, looking for sync points - numbers that both divide into evenly. With a 28-day lunar month/30-day calendar month, the sync points are 15/14 months apart. You could go decades before a full moon aligned with a solstice/equinox.



Technically, the moon would be full for one day. However, it would be 'close enough to count as full the day before and the day after.

This indeed. I'd say the best thing is to do is to double-study this post and ask about anything that doesn't make sense to you. Cause it's better to understand the math yourself then to just rely on one set of numbers someone calculated for you. If you can use the math yourself, you can go and tweek the exact astronimical details of your world yourself, so they best fit yout story.

 

[Karlin]

I assume you are aware of existing lunisolar calendars. It might help your thinking .

Lunisolar calendar - Wikipedia

en.wikipedia.org

 

[CupofJoe]

This can be a lot of fun to play with:

donjon; Fantasy Calendar Generator

A collection of random generators for Dungeons & Dragons and other tabletop role-playing games

donjon.bin.sh

 

[Rexenm]

Any type of holiday, falls between them, just like day is between night, because there is flux, equidistance. If polarisation gets closer, it is still between, but there is less space.

This is what I get watering the plants, trying to think if it is accurate.