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notes:how_to_make_a_calendar_for_your_world

# How to Make a Calendar for Your World

My planet's name is Gara.

Step 1: Choose a random number of days for your planet to revolve around its host star. I try to keep this number reasonable; between 200 and 800.

Gara Revolution = 531.0568 Earth Days

Step 2: Choose a random number of hours for your planet to rotate around its axis. This I keep between 12 and 48 hours, but there are no rules.

Gara Rotation = 29h 04m 43s (29.07861) Earth Hours
43 Earth Seconds / 60 = 0.7166 Earth Minutes
4.7166 Earth Minutes / 60 = 0.07861 Earth Hours
29.07861 Earth Hours

*Step 3: Calculate the number of rotations per revolution, relative to Earth time (to make it easier to work with later).

(Earth Day = 24 Hours) / (Gara Day = 29.07861 hours) = 0.8253489420574092 Scale Factor
531.0568 Earth Days Per Gara Year * 0.8253489420574092 Scale Factor = 438.3071680523932 Gara Days Per Gara Year
438.307168 Days Per Revolution

Step 4A: Calculate the number of leap days you will need and when. This is hard to do and may require some trial and error. You can over estimate days, then remove them later. Or if you have a more even number, just divide.

438.307168 Days Per Revolution = 438 Days Per Calender Year
0.307168 Remainder

Step 4B: Multiply the remainder by the smallest number that will give you a number greater than 1. Subtract 1.

0.307168 * 4 = 1.228672
1.228672 - 1 = 0.228672
4

Step 4C: Add the remainder to the result until you get over 1 again. The result is the number of times you needed to add.

0.228672 + 0.307168 = 0.53584
0.53584 + 0.307168 = 0.843008
0.843008 + 0.307168 = 1.150176
1.150176 - 1 = 0.150176
3

Step 4D: Repeat step C until you have a number with a leading 0 in the tenths place. Remove 1 again.

0.150176 + 0.307168 = 0.457344
0.457344 + 0.307168 = 0.764512
0.764512 + 0.307168 = 1.7168
1.07168 - 1 = 0.07168
3

4 + 3 + 3 = 10 (This is good.)
3 Leap days per 10 years.
1 leap day on years ending with 4, 7 or 0

Step 4F: Divide the step D remainder into 1. Then round up to the nearest whole number. Multiply by the result of step E.

1 / 0.07168 = 13.9508
14
14 * 10 = 140
1 additional leap day on years divisible by 140

Step 4G: Calculate the remainder of step F, and repeat step F.

0.150176 * 14 = 1.00352
1.00352 - 1 = 0.00352
1 / 0.00352 = 284.0909
285
140 * 285 = 39900
1 additional leap day on years divisible by 39900

Step 4H: You may need to repeat G again if you have a weird year number. Otherwise consolidate.

1 leap day on years ending with 4, 7 or 0
2 leap days on years divisible by 140
3 leap days on years divisible by 39900

Step 5: Calculate the number of days per month with common factors.

Factors of 438 (days)
1,2,3,6,73,146,219,438

This is actually not very good. However we have an option with 12 months and 18 months. Do you see them?

438 * 12 = 36.5 Days Per Month
6 Months with 36 Days, and 6 Months with 37 Days = 36.5 Average

or

438 * 18 = 24.333 Days Per Month
12 Months with 24 Days, and 6 Months with 25 Days = 24.333 Average

I don't want 12 months in my calender because that is not original.

18 Months it is.

Step 6: You don't need to do this but I want a custom time system as well.

Gara has a 29 hour day. Double that is like 60. So that sounds cool. 60 hours each day, each Gara hour about a half an Earth hour long. With 60 minutes in those hours that are faster than regular minutes. Lets calculate the Gara year average in Gara time.

1 Gara Year = 438.307168 Days
0.307168 Days * 60 = 18.43008 Gara Hours
0.43008 Hours * 60 = 25.8048 Gara Minutes
0.8048 Minutes * 60 = 48.288 Gara Seconds
0.288 Seconds * 60 = 17.28 Gara Thirds (one 60th of a Gara Second)
1 Gara Year = 438d.18h.25m.48s.17t

Alright, we know that science now! 