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Does anyone know an algorithm to either calculate the moon phase or age on a given date or find the dates for new/full moons in a given year?
Googling tells me the answer is in some Astronomy book, but I don't really want to buy a whole book when I only need a single page.
Update:
I should have qualified my statement about googling a little better. I did find solutions that only worked over some subset of time (like the 1900's); and the trig based solutions that would be more computationally expensive than I'd like.
S Lott in his Python book has several algorithms for calculating Easter on a given year, most are less than ten lines of code and some work for all days in the Gregorian calendar. Finding the full moon in March is a key piece of finding Easter so I figured there should be an algorithm that doesn't require trig and works for all dates in the Gregorian calendar.
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The easiest way to calculate the current phase of the moon is to compare it to a known time when it was new, and determine how many cycles it has passed through. We can do this by finding the number of days from a known New Moon and then dividing by the lunar period.
The time interval between a full moon and the next repetition of the same phase, a synodic month, averages about 29.53 days. Therefore, in those lunar calendars in which each month begins on the day of the new moon, the full moon falls on either the 14th or 15th day of the lunar month.
As the Sun sets, the Moon rises with the side that faces Earth fully exposed to sunlight (5). The Moon has phases because it orbits Earth, which causes the portion we see illuminated to change. The Moon takes 27.3 days to orbit Earth, but the lunar phase cycle (from new Moon to new Moon) is 29.5 days.
I ported some code to Python for this a while back. I was going to just link to it, but it turns out that it fell off the web in the meantime, so I had to go dust it off and upload it again. See moon.py which is derived from John Walker's moontool.
I can't find a reference for this for what time spans it's accurate for either, but seems like the authors were pretty rigorous. Which means yes, it does use trig, but I can't imagine what the heck you would be using this for that would make it computationally prohibitive. Python function call overhead is probably more than the cost of the trig operations. Computers are pretty fast at computing.
The algorithms used in the code are drawn from the following sources:
Meeus, Jean. Astronomical Algorithms. Richmond: Willmann-Bell, 1991. ISBN 0-943396-35-2.
A must-have; if you only buy one book, make sure it's this one. Algorithms are presented mathematically, not as computer programs, but source code implementing many of the algorithms in the book can be ordered separately from the publisher in either QuickBasic, Turbo Pascal, or C. Meeus provides many worked examples of calculations which are essential to debugging your code, and frequently presents several algorithms with different tradeoffs among accuracy, speed, complexity, and long-term (century and millennia) validity.
Duffett-Smith, Peter. Practical Astronomy With Your Calculator. 3rd ed. Cambridge: Cambridge University Press, 1981. ISBN 0-521-28411-2.
Despite the word Calculator in the title; this is a valuable reference if you're interested in developing software which calculates planetary positions, orbits, eclipses, and the like. More background information is given than in Meeus, which helps those not already versed in astronomy learn the often-confusing terminology. The algorithms given are simpler and less accurate than those provided by Meeus, but are suitable for most practical work.
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