Lunar Cycle Calculation

[Jahkayhla]

Greetings. I am not entirely sure this is the proper forum for this question, but it seems to me that it would most likely be some sort of algebraic formula that is required. I mostly need help just figuring out which formula I need to use, which I can then use to answer all the questions that I would have. Here's the outline of the primary problem from which the formula would derive.

A planet has eight moons. Each moon has a different orbital period and a different offset. The orbital period is how long it takes for the moon to make one orbit around the planet. The offset is how many days from the first day of the first year of the calendar the orbital period begins. (For example, a moon with an orbital period of ten and an offset of one would start the orbital period on the second day of the first month and end it on the eleventh, with a full moon on the seventh)

The planet's calendar has fifteen months, each month with a different amount of days.

The result I am looking for is the ability to calculate full moons, whether a single moon or multiple moons, without having to essentially draw up a calendar and browse it until I find what I am looking for. The calculation would need to be able to accurately predict a period when all eight moons are full at the same time.

Thank you in advance for reading. If this needs clarification, I am more than happy to explain further and provide all the numbers required if it would be easier.

 

[Ishuda]

Greetings. I am not entirely sure this is the proper forum for this question, but it seems to me that it would most likely be some sort of algebraic formula that is required. I mostly need help just figuring out which formula I need to use, which I can then use to answer all the questions that I would have. Here's the outline of the primary problem from which the formula would derive.

A planet has eight moons. Each moon has a different orbital period and a different offset. The orbital period is how long it takes for the moon to make one orbit around the planet. The offset is how many days from the first day of the first year of the calendar the orbital period begins. (For example, a moon with an orbital period of ten and an offset of one would start the orbital period on the second day of the first month and end it on the eleventh, with a full moon on the seventh)

The planet's calendar has fifteen months, each month with a different amount of days.

The result I am looking for is the ability to calculate full moons, whether a single moon or multiple moons, without having to essentially draw up a calendar and browse it until I find what I am looking for. The calculation would need to be able to accurately predict a period when all eight moons are full at the same time.

Thank you in advance for reading. If this needs clarification, I am more than happy to explain further and provide all the numbers required if it would be easier.

Problems like this for our calendar use a thing called Julian days or something similar. That is, the days are given a number starting at a particular date. Now, if you have an exact number of days in a year in your system and an exact number of days in each month, you could build your own 'Day' calender. For demonstration purpose lets just do 3 months (A, B, and C) with 10, 15, and 17 days in each.
Day 1 = A 1, 1900
Day 7 = A 7, 1900
Day 21 = B 11, 1900
Day 3715:
42 days in a year so = year [3715/42] = 88 years leaving 3715 - 42*88 = 19 days so
Day 3715 = B 9, 1988

Is that easier than looking things up? You have to decide.

EDIT: Oh, and for you full moon. It occurs on
Day = offset + half a period + n times a period, n = 0, 1, 2, ...

 

[Jahkayhla]

So for the first full moon, I simply use the Day = Offset + (period/2) to find the first full moon, and then each full moon after that will occur on the next (period/2). Basically that will give me a number which I can then match to the other full moons and then, on that day, simply use the first calculation to figure out exactly what day it is? If I am understanding you correctly. I am unsure as to what you mean by the "n times a period"

 

[Ishuda]

So for the first full moon, I simply use the Day = Offset + (period/2) to find the first full moon, and then each full moon after that will occur on the next (period/2). Basically that will give me a number which I can then match to the other full moons and then, on that day, simply use the first calculation to figure out exactly what day it is? If I am understanding you correctly. I am unsure as to what you mean by the "n times a period"

Basically, yes. In your example, "For example, a moon with an orbital period of ten and an offset of one would start the orbital period on the second day of the first month and end it on the eleventh, with a full moon on the seventh)", the full moon would appear on the Day 7, Day 17, Day 27, Day 37, ...