--- title: "FromLunationNumber" language: "en" type: "Symbol" summary: "FromLunationNumber[ln] returns the date corresponding to the lunation number ln. FromLunationNumber[scheme, ln] returns the date corresponding to the lunation number in the given counting scheme." keywords: - new moon - full moon - moon phase - lunar count - Meeus lunation number - Brown lunation number - Goldstine lunation number - Hebrew lunation number - Islamic lunation number - Thai lunation number canonical_url: "https://reference.wolfram.com/language/ref/FromLunationNumber.html" source: "Wolfram Language Documentation" related_guides: - title: "Astronomical Computation & Data" link: "https://reference.wolfram.com/language/guide/AstronomicalComputationAndData.en.md" related_functions: - title: "LunationNumber" link: "https://reference.wolfram.com/language/ref/LunationNumber.en.md" - title: "MoonPhaseDate" link: "https://reference.wolfram.com/language/ref/MoonPhaseDate.en.md" - title: "MoonPhase" link: "https://reference.wolfram.com/language/ref/MoonPhase.en.md" - title: "AstroPosition" link: "https://reference.wolfram.com/language/ref/AstroPosition.en.md" - title: "FromJulianDate" link: "https://reference.wolfram.com/language/ref/FromJulianDate.en.md" --- [EXPERIMENTAL] # FromLunationNumber FromLunationNumber[ln] returns the date corresponding to the lunation number ln. FromLunationNumber[scheme, ln] returns the date corresponding to the lunation number in the given counting scheme. ## Details and Options * Lunations are periods between consecutive new moons, also known as synodic months. [image] * ``FromLunationNumber`` is a way to tell time by the motion of the Moon, effectively counting months. * A lunation number 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: | | | | --- | ------------- | | .0 | new moon | | .25 | first quarter | | .5 | full moon | | .75 | last quarter | * The fractional part of a lunation number is proportional to the difference in ecliptic longitudes between the Sun and the Moon. * Possible counting schemes include: | | | | ------------------------- | ----------------------------------------------------- | | Automatic | lunation 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 | * Options of ``FromLunationNumber`` include: | | | | | ---------------- | ---------- | ------------------------------------ | | CalendarType | Automatic | calendar used to return dates | | DateFormat | Automatic | format used to display output dates | | DateGranularity | Automatic | calendar granularity of output dates | | TimeSystem | Automatic | time system of output dates | | TimeZone | \$TimeZone | time zone of output dates | --- ## Examples (12) ### Basic Examples (3) Find the date of lunation number 0: ```wl In[1]:= FromLunationNumber[0] Out[1]= DateObject[{2000, 1, 6, 12, 13, 38.1217}, "Instant", "Gregorian", -6.] ``` --- There will be a solar eclipse at lunation 300: ```wl In[1]:= FromLunationNumber[300] Out[1]= DateObject[{2024, 4, 8, 12, 20, 51.5292}, "Instant", "Gregorian", -6.] ``` --- Lunation number 1 in the Islamic counting scheme was close to the date of Hegira: ```wl In[1]:= FromLunationNumber["IslamicLunationNumber", 1] Out[1]= DateObject[{622, 7, 16, 23, 29, 13.9412}, "Instant", "Gregorian", -6.] ``` ### Scope (2) Find the date corresponding to a lunation number: ```wl In[1]:= FromLunationNumber[300] Out[1]= DateObject[{2024, 4, 8, 12, 20, 51.5292}, "Instant", "Gregorian", -6.] ``` --- Find the date of a lunation number in a non-default scheme: ```wl In[1]:= FromLunationNumber["BrownLunationNumber", 300] Out[1]= DateObject[{1947, 3, 22, 10, 34, 3.42818}, "Instant", "Gregorian", -6.] ``` ### Options (5) #### CalendarType (1) ``FromLunationNumber`` returns dates in the Gregorian calendar by default: ```wl In[1]:= FromLunationNumber[0] Out[1]= DateObject[{2000, 1, 6, 12, 13, 38.1217}, "Instant", "Gregorian", -6.] ``` Return dates in the Jewish calendar: ```wl In[2]:= FromLunationNumber[0, CalendarType -> "Jewish"] Out[2]= DateObject[{5760, 10, 28, 12, 13, 38.1217}, "Instant", "Jewish", -6.] ``` #### DateFormat (1) ``FromLunationNumber`` returns dates in a long format by default: ```wl In[1]:= FromLunationNumber[0] Out[1]= DateObject[{2000, 1, 6, 12, 13, 38.1217}, "Instant", "Gregorian", -6.] ``` Specify your own format: ```wl In[2]:= FromLunationNumber[0, DateFormat -> {"Day", "/", "Month", "/", "Year"}] Out[2]= DateObject[{2000, 1, 6, 12, 13, 38.1217}, "Instant", "Gregorian", -6., "SmearedUTC", {"Day", "/", "Month", "/", "Year"}] ``` #### DateGranularity (1) ``FromLunationNumber`` returns dates with granularity ``"Instant"`` by default: ```wl In[1]:= FromLunationNumber[0] Out[1]= DateObject[{2000, 1, 6, 12, 13, 38.1217}, "Instant", "Gregorian", -6.] ``` Return dates with ``"Day"`` granularity: ```wl In[2]:= FromLunationNumber[0, DateGranularity -> "Day"] Out[2]= DateObject[{2000, 1, 6}, "Day", "Gregorian", -6.] ``` #### TimeSystem (1) ``FromLunationNumber`` returns dates in universal time by default: ```wl In[1]:= FromLunationNumber[0] Out[1]= DateObject[{2000, 1, 6, 12, 13, 38.1217}, "Instant", "Gregorian", -6.] ``` Return dates in ``"TT"`` time instead: ```wl In[2]:= FromLunationNumber[0, TimeSystem -> "TT"] Out[2]= DateObject[{2000, 1, 6, 12, 14, 42.3057}, "Instant", "Gregorian", -6., "TT"] ``` #### TimeZone (1) ``FromLunationNumber`` returns dates in your local time zone by default: ```wl In[1]:= FromLunationNumber[0] Out[1]= DateObject[{2000, 1, 6, 12, 13, 38.1217}, "Instant", "Gregorian", -6.] ``` Return dates in the GMT time zone: ```wl In[2]:= FromLunationNumber[0, TimeZone -> "GMT"] Out[2]= DateObject[{2000, 1, 6, 18, 13, 38.1217}, "Instant", "Gregorian", "GMT"] ``` ### Properties & Relations (2) ``LunationNumber`` and ``FromLunationNumber`` are inverse functions: ```wl In[1]:= LunationNumber[DateObject[{2023, 9, 28, 12, 0, 0}]] Out[1]= 293.474 In[2]:= FromLunationNumber[%] Out[2]= DateObject[{2023, 9, 28, 12, 0, 6.67572021484375`*^-6}, "Instant", "Gregorian", -6.] ``` --- Take all dates of lunations between 200 and 300: ```wl In[1]:= dates = FromLunationNumber /@ Range[200, 300]; In[2]:= {First[dates], Last[dates]} Out[2]= {DateObject[{2016, 3, 8, 19, 54, 29.3693}, "Instant", "Gregorian", -6.], DateObject[{2024, 4, 8, 12, 20, 51.5292}, "Instant", "Gregorian", -6.]} ``` In a solar calendar like the default Gregorian calendar, new moons can be on any day of the month: ```wl In[3]:= DateValue[dates, "Day"] Out[3]= {8, 7, 6, 4, 4, 2, 1, 30, 30, 29, 29, 27, 26, 27, 26, 25, 23, 23, 21, 19, 19, 18, 18, 16, 15, 17, 15, 15, 13, 12, 11, 9, 8, 7, 7, 5, 4, 6, 5, 4, 3, 2, 31, 30, 28, 27, 26, 25, 24, 23, 24, 22, 22, 21, 20, 18, 17, 16, 14, 14, 12, 11, 13, 11, 11, 10, 9, 8, 6, 6, 4, 4, 2, 31, 2, 1, 30, 30, 28, 28, 27, 25, 25, 23, 23, 21, 20, 21, 19, 19, 17, 17, 16, 14, 14, 13, 12, 11, 9, 10, 8} ``` In a lunisolar calendar like the Jewish calendar, new moons fall on days near the change of month: ```wl In[4]:= DateValue[CalendarConvert[dates, "Jewish"], "Day"] Out[4]= {28, 28, 28, 27, 28, 27, 28, 27, 28, 28, 29, 29, 30, 29, 30, 29, 29, 29, 29, 28, 29, 29, 30, 29, 30, 1, 30, 1, 30, 29, 30, 29, 29, 29, 29, 28, 29, 29, 29, 29, 29, 29, 28, 29, 28, 28, 28, 27, 27, 28, 28, 28, 28, 29, 28, 28, 28, 28, 27, 28, 28, 29, 29, 29, 29, 30, 29, 30, 29, 30, 29, 30, 29, 29, 29, 29, 29, 29, 29, 29, 30, 29, 30, 29, 29, 28, 29, 28, 28, 28, 28, 28, 29, 28, 29, 29, 29, 1, 30, 30, 29} ``` Perform the analysis with 5000 lunar months: ```wl In[5]:= dates = FromLunationNumber /@ Range[0, 5000]; In[6]:= Histogram[DateValue[dates, "Day"], 30] Out[6]= [image] In[7]:= Histogram[DateValue[CalendarConvert[dates, "Jewish"], "Day"], 30] Out[7]= [image] ``` ## See Also * [`LunationNumber`](https://reference.wolfram.com/language/ref/LunationNumber.en.md) * [`MoonPhaseDate`](https://reference.wolfram.com/language/ref/MoonPhaseDate.en.md) * [`MoonPhase`](https://reference.wolfram.com/language/ref/MoonPhase.en.md) * [`AstroPosition`](https://reference.wolfram.com/language/ref/AstroPosition.en.md) * [`FromJulianDate`](https://reference.wolfram.com/language/ref/FromJulianDate.en.md) ## Related Guides * [Astronomical Computation & Data](https://reference.wolfram.com/language/guide/AstronomicalComputationAndData.en.md) ## History * [Introduced in 2024 (14.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn140.en.md)