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LunationNumber[]

returns the number of new moons since the first new moon of the year 2000.

LunationNumber[date]

returns the number of new moons since the given date.

LunationNumber[scheme,date]

returns the number of new moons since the zeroth new moon of the given counting scheme.

Details
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Examples  
Basic Examples  
Scope  
Properties & Relations  
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LunationNumber

LunationNumber[]

returns the number of new moons since the first new moon of the year 2000.

LunationNumber[date]

returns the number of new moons since the given date.

LunationNumber[scheme,date]

returns the number of new moons since the zeroth new moon of the given counting scheme.

Details

  • Lunations are periods between a new moon and a new moon, and are also known as synodic months.
  • LunationNumber is a way to tell time by the motion of the Moon, effectively counting months.
  • The result of LunationNumber is a real number. The integer part gives the number of new moons since the first new moon on January 6, 2000. The fractional part of a lunation number gives the phase of the Moon:
  • .0new moon
    .25first quarter
    .5full moon
    .75last quarter
  • The result of LunationNumber is proportional to the difference in ecliptic longitudes between the Sun and the Moon.
  • Possible counting schemes include:
  • Automaticlunation 0 on January 6, 2000
    "BrownLunationNumber"lunation 1 on January 17, 1923
    "GoldstineLunationNumber"lunation 0 on January 1, –1001, proleptic Gregorian
    "HebrewLunationNumber"lunation 1 on September 6, –3761, proleptic Gregorian
    "IslamicLunationNumber"lunation 1 on July 17, 622, proleptic Gregorian
    "ThaiLunationNumber"lunation 0 on March 24, 638, proleptic Gregorian

Examples

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Basic Examples  (3)

Find the current lunation number:

Find the lunation number of the beginning of the year 2020:

Find the current lunation number in the Islamic counting scheme:

Scope  (2)

Find the lunation number of a given date:

Find the lunation number of a date in a non-default scheme:

Properties & Relations  (4)

LunationNumber and FromLunationNumber are inverse functions:

New moons correspond to integer lunation numbers:

Full moons correspond to semi-integer lunation numbers:

Every solar eclipse happens within a few minutes of a new moon. Hence solar eclipses have an associated lunation number:

It is very close to the lunation number of the instant of maximum eclipse:

Wolfram Research (2024), LunationNumber, Wolfram Language function, https://reference.wolfram.com/language/ref/LunationNumber.html.

Text

Wolfram Research (2024), LunationNumber, Wolfram Language function, https://reference.wolfram.com/language/ref/LunationNumber.html.

CMS

Wolfram Language. 2024. "LunationNumber." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LunationNumber.html.

APA

Wolfram Language. (2024). LunationNumber. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LunationNumber.html

BibTeX

@misc{reference.wolfram_2025_lunationnumber, author="Wolfram Research", title="{LunationNumber}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/LunationNumber.html}", note=[Accessed: 16-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_lunationnumber, organization={Wolfram Research}, title={LunationNumber}, year={2024}, url={https://reference.wolfram.com/language/ref/LunationNumber.html}, note=[Accessed: 16-August-2025]}