# 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.

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.

Also, pyephem — scientific-grade astronomy routines [PyPI], which is a Python package but has the computational guts in C, and that does say

Precision < 0.05″ from -1369 to +2950.
Uses table lookup techniques to limit calls to trigonometric functions.

I know that you’re looking for Python but if you can understand C# there’s an open source project out there called Chronos XP which does this very well.

If you don’t need high accuracy, you can always (ab)use a lunar (or lunisolar) calendar class (e.g., `HijriCalendar` or `ChineseLunisolarCalendar` in Microsoft .NET) to calculate the (approximate) moon phase of any date, as the calendar’s “day-of-month” property, being a lunar (or lunisolar) calendar day, always corresponds to the moon phase (e.g., day 1 is the new moon, day 15 is the full moon, etc.)

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
from typing import List, Tuple

def get_phase_on_day(year: int, month: int, day: int):
"""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: int) -> List[Tuple[ephem.Date, str]]:
"""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,1,1))
while date.datetime().year==year:
date=ephem.next_full_moon(date)
moons.append( (date,'full') )

date=ephem.Date(datetime.date(year,1,1))
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')]
``````

Pyephem by default uses coordinated universal (UTC) time. I wanted a program that would generate a list of full moons that would be accurate in the pacific time zone. The code below will calculate the full moons for a given year and then adjust that using the ephem.localtime() method to calibrate to the desired time zone. It also appears to properly account for daylight savings time as well. Thank you to Richard, this code is similar to what he had written.

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

# Set time zone to pacific
os.environ['TZ'] = 'US/Pacific'
time.tzset()

print("Time zone calibrated to", os.environ['TZ'])

def get_full_moons_in_year(year):
"""
Generate a list of full moons for a given year calibrated to the local time zone
:param year: year to determine the list of full moons
:return: list of dates as strings in the format YYYY-mm-dd
"""
moons = []

date = ephem.Date(datetime.date(year - 1, 12, 31))
end_date = ephem.Date(datetime.date(year + 1, 1, 1))

while date <= end_date:
date = ephem.next_full_moon(date)

# Convert the moon dates to the local time zone, add to list if moon date still falls in desired year
local_date = ephem.localtime(date)
if local_date.year == year:
# Append the date as a string to the list for easier comparison later
moons.append(local_date.strftime("%Y-%m-%d"))

return moons

moons = get_full_moons_in_year(2015)
print(moons)
``````

The code above will return:

``````Time zone calibrated to US/Pacific
['2015-01-04', '2015-02-03', '2015-03-05', '2015-04-04', '2015-05-03', '2015-06-02', '2015-07-01', '2015-07-31', '2015-08-29', '2015-09-27', '2015-10-27', '2015-11-25', '2015-12-25']
``````

PyEphem is now deprecating – they recommend preferring Skyfield astronomy library over PyEphem for new projects. Its modern design encourages better Python code, and uses NumPy to accelerate its calculations.

The phase of the Moon is defined as the angle between the Moon and the
Sun along the ecliptic. This angle is computed as the difference in
the ecliptic longitude of the Moon and of the Sun.

The result is an angle that is 0° for the New Moon, 90° at the First Quarter, 180° at the Full Moon, and 270° at the Last Quarter.

Code taken from here

``````from skyfield.api import load
from skyfield.framelib import ecliptic_frame

t = ts.utc(2019, 12, 9, 15, 36)

sun, moon, earth = eph['sun'], eph['moon'], eph['earth']

e = earth.at(t)
_, slon, _ = e.observe(sun).apparent().frame_latlon(ecliptic_frame)
_, mlon, _ = e.observe(moon).apparent().frame_latlon(ecliptic_frame)
phase = (mlon.degrees - slon.degrees) % 360.0

print('{0:.1f}'.format(phase))
``````

Output

``````149.4
``````