# Moon / Lunar Phase Algorithm

### Question

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.

1
33
3/27/2010 12:51:26 AM

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.

16
9/6/2013 10:38:29 PM

If you're like me, you try to be a careful programmer. So it makes you nervous when you see random code scattered across the internet that purports to solve a complex astronomical problem, but doesn't explain why the solution is correct.

You believe that there must be authoritative sources such as books which contain careful, and complete, solutions. For instance:

Meeus, Jean. Astronomical Algorithms. Richmond: Willmann-Bell, 1991. ISBN 0-943396-35-2.

Duffett-Smith, Peter. Practical Astronomy With Your Calculator. 3rd ed. Cambridge: Cambridge University Press, 1981. ISBN 0-521-28411-2.

You place your trust in widely-used, well-tested, open source libraries which can have their errors corrected (unlike static web pages). Here then, is a Python solution to your question based on the PyEphem library, using the Phases of the Moon interface.

``````#!/usr/bin/python
import datetime
import ephem

def get_phase_on_day(year,month,day):
"""Returns a floating-point number from 0-1. where 0=new, 0.5=full, 1=new"""
#Ephem stores its date numbers as floating points, which the following uses
#to conveniently extract the percent time between one new moon and the next
#This corresponds (somewhat roughly) to the phase of the moon.

#Use Year, Month, Day as arguments
date=ephem.Date(datetime.date(year,month,day))

nnm = ephem.next_new_moon    (date)
pnm = ephem.previous_new_moon(date)

lunation=(date-pnm)/(nnm-pnm)

#Note that there is a ephem.Moon().phase() command, but this returns the
#percentage of the moon which is illuminated. This is not really what we want.

return lunation

def get_moons_in_year(year):
"""Returns a list of the full and new moons in a year. The list contains tuples
of either the form (DATE,'full') or the form (DATE,'new')"""
moons=[]

date=ephem.Date(datetime.date(year,01,01))
while date.datetime().year==year:
date=ephem.next_full_moon(date)
moons.append( (date,'full') )

date=ephem.Date(datetime.date(year,01,01))
while date.datetime().year==year:
date=ephem.next_new_moon(date)
moons.append( (date,'new') )

#Note that previous_first_quarter_moon() and previous_last_quarter_moon()
#are also methods

moons.sort(key=lambda x: x[0])

return moons

print get_phase_on_day(2013,1,1)

print get_moons_in_year(2013)
``````

This returns

``````0.632652265318

[(2013/1/11 19:43:37, 'new'), (2013/1/27 04:38:22, 'full'), (2013/2/10 07:20:06, 'new'), (2013/2/25 20:26:03, 'full'), (2013/3/11 19:51:00, 'new'), (2013/3/27 09:27:18, 'full'), (2013/4/10 09:35:17, 'new'), (2013/4/25 19:57:06, 'full'), (2013/5/10 00:28:22, 'new'), (2013/5/25 04:24:55, 'full'), (2013/6/8 15:56:19, 'new'), (2013/6/23 11:32:15, 'full'), (2013/7/8 07:14:16, 'new'), (2013/7/22 18:15:31, 'full'), (2013/8/6 21:50:40, 'new'), (2013/8/21 01:44:35, 'full'), (2013/9/5 11:36:07, 'new'), (2013/9/19 11:12:49, 'full'), (2013/10/5 00:34:31, 'new'), (2013/10/18 23:37:39, 'full'), (2013/11/3 12:49:57, 'new'), (2013/11/17 15:15:44, 'full'), (2013/12/3 00:22:22, 'new'), (2013/12/17 09:28:05, 'full'), (2014/1/1 11:14:10, 'new'), (2014/1/16 04:52:10, 'full')]
``````