MATH GENIOUSES, I NEED HELP
Hello, dear estrangers!
I need a little help.
You know, I’m writing a book, and in this book, basically Christian religion never existed (it’s a whole different universe with different religions, cultures, countries, etc.). This means, Pope Gregory (or whatever his name is in English, here in my country we know him as Papa Gregorio) never existed, and the Gregorian calendar (the one we use, with 30-31 days months and stuff) never existed.
No, in this world, there is a different system. Instead on months, there are “Moons”. A Moon would be some kind of equivalent to the real world months, with 13 of these, and 28 days each one, except for the last one, that has 29 days. The thing is, the story takes place in the year 2124 after… some important event that caused people to start counting the years since then. It’s an equivalent to Jesus’ birth. No spoiler. Leap-years exist, too. Every year is 365 days and 6 minutes, meaning every four years the last Moon last 30 days instead of 29. The first Moon ever counted, in the year 0, started in a full moon, with perfect synchronization. But with leap-years, the 29th – 30th day of the 13th moon the real moon cycles the full moon and the start of a moon don’t synchronize every time.
Considering these facts, every how many years do the moon cycles and the start of a year/Moon synchronize?
(No, I’m not asking help for homework, homework isn’t this fun. This is really, really important. I need to have all the details in my fantasy world, and I’m a disaster with math. I have problems even with the simplest problem. Could you help me, please?)
Comments
An exact year is 365 days, 5 hours, 48 minutes, and 45 or 46 seconds, depending on who you believe. (Years are not really that exact. The orbital time varies slightly.)
The moon phase time (time to get from full moon to full moon, for example) is 29 days, 12 hours, 44 minutes, and 3 seconds. Again, not always perfect.
Time is complicated. To make things a little simpler, we'll say a year is exactly 365 days and 6 hours, and the moon phase time is exactly 29 days and 12 hours.
So in a period of 4 years, including your leap day, 1461 days will have passed, and there will have been 49 full moons, and it would be just a little past the new moon. So the idea of the year starting on a specific moon would already have shifted by quite a bit.
I don't know if you want the math details, but I figured that these would come back into sync perfectly after 86199 years.
Wow, thank you! This saved my life.
Sorry, I goofed. My calculations were actually that they sync up at the start of a year every 86199 days, not years. To get years, we have to divide by 365.25, so it's only a 236 year wait, or 2922 full moons later if you prefer.
Hope your life is still saved.
You're awsome. I love you.