Editing Lunar phase (section)

==Calculating phase==
[[File:BethinAZ - 10-13.002 (by).jpg|thumb|right|220px|A crescent Moon over [[Kingman, Arizona]]]]

Each of the four intermediate phases lasts approximately seven days (7.38 days on average), but varies ±11.25% due to lunar [[apsis|apogee and perigee]].

The number of days counted from the time of the [[new moon]] is the Moon's "age". Each complete cycle of phases is called a "[[lunation]]".<ref>{{cite web |url=http://aa.usno.navy.mil/faq/docs/moon_phases.php |title=Phases of the Moon and Percent of the Moon Illuminated |website=aa.usno.navy.mil |language=en |access-date=2018-02-12 |archive-date=2018-02-06 |archive-url=https://web.archive.org/web/20180206063503/http://aa.usno.navy.mil/faq/docs/moon_phases.php |url-status=dead }}</ref>

The approximate age of the Moon, and hence the approximate phase, can be calculated for any date by calculating the number of days since a known new moon (such as 1 January 1900 or 11 August 1999) and reducing this [[modulo operation|modulo]] 29.53059 days (the mean length of a [[synodic month]]).{{sfn|Seidelmann|1992|p=577}}{{efn|Lunar months vary in length about the mean by up to seven hours in any given year. In 2001, the synodic months varied from 29d 19h 14m in January to 29d 07h 11m in July.<ref>{{cite web | title=Length of the Synodic Month: 2001 to 2100 | website=astropixels.com |date=8 November 2019 |url=http://astropixels.com/ephemeris/moon/synodicmonth2001.html}}</ref>}} The difference between two dates can be calculated by subtracting the [[Julian day|Julian day number]] of one from that of the other, or there are simpler formulae giving (for instance) the number of days since 31 December 1899. However, this calculation assumes a perfectly [[circular orbit]] and makes no allowance for the time of day at which the new moon occurred and therefore may be incorrect by several hours. (It also becomes less accurate the larger the difference between the required date and the reference date.) It is accurate enough to use in a novelty clock application showing lunar phase, but specialist usage taking account of lunar apogee and perigee requires a more elaborate calculation. Also, due to [[lunar libration]] it is not uncommon to see up to 101% of the full moon  or even up to 5% of the lunar backside.

===Calculating phase size===
The phase is equal to the area of the visible lunar sphere that is illuminated by the Sun. This area or ''degree of illumination'' is given by <math>(1-\cos e)/2=\sin^2(e/2)</math>, where <math>e</math> is the [[elongation (astronomy)|elongation]] (i.e., the angle between Moon, the observer on Earth, and the Sun).