--- title: "MoonPosition" language: "en" type: "Symbol" summary: "MoonPosition[] gives the position of the Moon for the current date and location. MoonPosition[datespec] gives the position of the Moon for the specified date. MoonPosition[locationspec] gives the position of the Moon for the specified location. MoonPosition[locationspec, datespec] gives the position of the Moon for the specified date and location. MoonPosition[{{location1, date1}, {location2, date2}, ...}] gives the positions of the Moon for all specified locations on the specified dates. MoonPosition[locationspec, datespec, func] uses func to determine what to return for extended locations." keywords: - moon position - lunar position - moon ephemerides - lunar ephemerides - orbit of the moon canonical_url: "https://reference.wolfram.com/language/ref/MoonPosition.html" source: "Wolfram Language Documentation" related_guides: - title: "Astronomical Computation & Data" link: "https://reference.wolfram.com/language/guide/AstronomicalComputationAndData.en.md" - title: "Date & Time" link: "https://reference.wolfram.com/language/guide/DateAndTime.en.md" - title: "Geodesy" link: "https://reference.wolfram.com/language/guide/Geodesy.en.md" related_functions: - title: "AstroPosition" link: "https://reference.wolfram.com/language/ref/AstroPosition.en.md" - title: "SunPosition" link: "https://reference.wolfram.com/language/ref/SunPosition.en.md" - title: "AstroSubpoint" link: "https://reference.wolfram.com/language/ref/AstroSubpoint.en.md" - title: "PlanetaryMoonData" link: "https://reference.wolfram.com/language/ref/PlanetaryMoonData.en.md" - title: "MoonPhase" link: "https://reference.wolfram.com/language/ref/MoonPhase.en.md" - title: "SolarEclipse" link: "https://reference.wolfram.com/language/ref/SolarEclipse.en.md" - title: "LunarEclipse" link: "https://reference.wolfram.com/language/ref/LunarEclipse.en.md" - title: "TideData" link: "https://reference.wolfram.com/language/ref/TideData.en.md" --- # MoonPosition MoonPosition[] gives the position of the Moon for the current date and location. MoonPosition[datespec] gives the position of the Moon for the specified date. MoonPosition[locationspec] gives the position of the Moon for the specified location. MoonPosition[locationspec, datespec] gives the position of the Moon for the specified date and location. MoonPosition[{{location1, date1}, {location2, date2}, …}] gives the positions of the Moon for all specified locations on the specified dates. MoonPosition[locationspec, datespec, func] uses func to determine what to return for extended locations. ## Details and Options * ``MoonPosition`` returns the coordinates of the Moon on the celestial sphere as observed on any date from any location on Earth. * ``MoonPosition[]`` makes use of ``\$GeoLocation`` and ``\$TimeZone`` to determine your location and time zone. * The default form of the results is in the form ``{azimuth, altitude}``. * Locations can be specified as ``Entity`` objects, assuming they represent objects with geographic coordinates or ``GeoGraphics`` primitives, or they can be latitude/longitude pairs, assuming degrees as units. * ``datespec`` can be a ``DateObject`` expression, a ``TimeObject`` expression, a date string or a ``{y, m, d, h, m, s}`` date list. * ``datespec`` is assumed to be in ``\$TimeZone``, unless it is a ``DateObject`` or ``TimeObject`` expression with an explicit ``TimeZone`` option value. * ``locationspec`` and ``datespec`` can be either individual items or lists of individual items. * If ``datespec`` is a list of dates, then the results will contain ``TimeSeries`` objects. * ``datespec`` can be specified as ``{start, end, increment}`` for compatibility with ``DateRange`` specifications. * ``MoonPosition[…, func]`` is used to specify the format of output when locations are specified. * Possible settings for ``func`` include: | | | | ----------------- | ------------------------------------------------- | | Automatic | returns intervals for extended locations only | | Interval | returns intervals for all specified locations | | Mean | returns mean value for extended locations | | Min | returns minimum values for extended locations | | Max | returns maximum values for extended locations | | StandardDeviation | returns standard deviation for extended locations | * ``MoonPosition[CelestialSystem -> "Equatorial"]`` gives the right ascension and declination of the Moon. * ``MoonPosition`` can accept the following options: | | | | | ---------------- | ------------------ | --------------------------------------------------------------------------- | | AltitudeMethod | "ApparentAltitude" | whether to take atmospheric refraction into account when computing altitude | | CelestialSystem | "Horizon" | whether to return azimuth/altitude or right ascension/declination | * Possible settings for ``CelestialSystem`` include: | | | | --- | --- | | "Horizon" | returns results as a pair of azimuth/altitude (az/alt) values | | "Equatorial" | returns results as a pair of right ascension/declination ($\alpha$ / $\delta$) values | [image] * Possible settings for ``AltitudeMethod`` include: | | | | ------------------ | ------------------------------------------------------------------ | | "ApparentAltitude" | take atmospheric refraction into account for altitude computations | | "TrueAltitude" | assume no atmospheric refraction for altitude computations | --- ## Examples (27) ### Basic Examples (5) Compute the current position of the Moon for your location: ```wl In[1]:= MoonPosition[] Out[1]= {Quantity[215.72615657169524, "AngularDegrees"], Quantity[17.86524359439098, "AngularDegrees"]} ``` --- Compute the position of the Moon for a specified date: ```wl In[1]:= MoonPosition[DateObject[{2023, 3, 20, 0, 0}, TimeZone -> -6]] Out[1]= {Quantity[32.709987594884495, "AngularDegrees"], Quantity[-58.78788738377234, "AngularDegrees"]} ``` --- Compute the current position of the Moon for a specified location: ```wl In[1]:= MoonPosition[\[FreeformPrompt]["Chicago"]] Out[1]= {Quantity[215.87653061368366, "AngularDegrees"], Quantity[16.21418270087808, "AngularDegrees"]} ``` --- Compute the position of the Moon for a specified latitude/longitude and date: ```wl In[1]:= MoonPosition[GeoPosition[{50.3, -80.1}], DateObject[{2023, 10, 1, 0, 0}, "Minute", "Gregorian", -6.]] Out[1]= {Quantity[162.95244941649648, "AngularDegrees"], Quantity[51.202933431932564, "AngularDegrees"]} ``` --- Compute the position of the Moon for a specified city and date: ```wl In[1]:= MoonPosition[[image], DateObject[{2023, 10, 1, 0, 0}, "Minute", "Gregorian", -6.]] Out[1]= {Quantity[138.39439588803904, "AngularDegrees"], Quantity[57.98297950728194, "AngularDegrees"]} ``` ### Scope (9) #### Dates (3) Dates can be specified as a ``DateObject`` : ```wl In[1]:= MoonPosition[DateObject[{2013, 6, 21, 15, 0}, TimeZone -> -6]] Out[1]= {Quantity[93.68047500746182, "AngularDegrees"], Quantity[-28.03977406197851, "AngularDegrees"]} ``` --- Dates can be specified as a date string: ```wl In[1]:= MoonPosition["September 23, 2010 3:00PM CDT"] Out[1]= {Quantity[52.79843763034127, "AngularDegrees"], Quantity[-27.64394033538951, "AngularDegrees"]} ``` --- Generate the Moon's position for a range of dates: ```wl In[1]:= MoonPosition[DateRange[DateObject[{2013, 1, 1, 9, 0}, "Minute", "Gregorian", -6.], DateObject[{2013, 12, 31, 9, 0}, "Minute", "Gregorian", -6.], 10]] Out[1]= TemporalData[TimeSeries, {{QuantityArray[StructuredArray`StructuredData[{37, 2}, {CompressedData["«884»"]\ , "AngularDegrees", {{1}, {2}}}]]}, {TemporalData`DateSpecification[{2013, 1, 1, 10, 0, 0.}, {2013, 12, 27, 10, 0, 0.}, {10, "Day"}]}, 1, {"Continuous", 1}, {"Discrete", 1}, 2, {ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}, ValueDimensions -> 2}}, True, 13.3] ``` #### Locations (6) Locations can be latitude/longitude pairs: ```wl In[1]:= MoonPosition[GeoPosition[{40.1, -88.2}]] Out[1]= {Quantity[215.80284071802302, "AngularDegrees"], Quantity[17.83487485811281, "AngularDegrees"]} ``` --- Cities are treated as single, specific locations: ```wl In[1]:= MoonPosition[[image]] Out[1]= {Quantity[214.34338454976233, "AngularDegrees"], Quantity[19.947450666939506, "AngularDegrees"]} ``` --- Results for extended locations are intervals, by default: ```wl In[1]:= MoonPosition[\[FreeformPrompt]["france"]] Out[1]= {Quantity[Interval[{271.56375002545883, 291.9771050689746}], "AngularDegrees"], Quantity[Interval[{-48.28808914177641, -36.863761655991034}], "AngularDegrees"]} ``` --- The form of the results for extended locations can be overridden: ```wl In[1]:= MoonPosition[\[FreeformPrompt]["france"], Mean] Out[1]= {Quantity[281.13822072677704, "AngularDegrees"], Quantity[-42.08296719872421, "AngularDegrees"]} ``` --- Find the Moon's position for multiple locations: ```wl In[1]:= MoonPosition[{\[FreeformPrompt]["chicago"], [image]}] Out[1]= {{Quantity[215.91834199768667, "AngularDegrees"], Quantity[16.193408935457505, "AngularDegrees"]}, {Quantity[214.34521224571282, "AngularDegrees"], Quantity[19.946550400160586, "AngularDegrees"]}} ``` --- Find the Moon's position for multiple locations on different dates: ```wl In[1]:= MoonPosition[{{Entity["City", {"Chicago", "Illinois", "UnitedStates"}], DateObject[{2025, 1, 1, 12}, TimeZone -> "America/Chicago"]}, {Entity["City", {"Moscow", "Moscow", "Russia"}], DateObject[{2023, 7, 28, 6}, TimeZone -> "Europe/Moscow"]}}] Out[1]= {{Quantity[156.856405390302, "AngularDegrees"], Quantity[20.457411346233126, "AngularDegrees"]}, {Quantity[312.7980953861196, "AngularDegrees"], Quantity[-50.93284479165753, "AngularDegrees"]}} ``` ### Options (2) #### CelestialSystem (1) Find the right ascension and declination of the Moon for your location: ```wl In[1]:= MoonPosition[CelestialSystem -> "Equatorial"] Out[1]= {Quantity[20.994323883610814, "HoursOfRightAscension"], Quantity[-23.20190481021937, "AngularDegrees"]} ``` #### AltitudeMethod (1) The default setting for ``AltitudeMethod`` simulates atmospheric refraction: ```wl In[1]:= MoonPosition[\[FreeformPrompt]["Champaign"], DateObject[{2022, 9, 4, 19, 5}, "Minute", "Gregorian", -5.]] Out[1]= {Quantity[168.80962620733223, "AngularDegrees"], Quantity[21.21650995696813, "AngularDegrees"]} ``` Allow for no atmospheric refraction when computing the altitude of the Moon: ```wl In[2]:= MoonPosition[\[FreeformPrompt]["Champaign"], DateObject[{2022, 9, 4, 19, 5}, "Minute", "Gregorian", -5.], AltitudeMethod -> "TrueAltitude"] Out[2]= {Quantity[168.80962620733223, "AngularDegrees"], Quantity[21.1755775733377, "AngularDegrees"]} ``` ### Applications (4) The Moon's orbit is tilted with respect to the Earth's equator: ```wl In[1]:= Graphics[{Red, Point[QuantityMagnitude /@ MoonPosition[DateRange[DateObject[{2023, 1, 1, 0, 0}, "Minute", "Gregorian", -6.], DateObject[{2023, 1, 31, 0, 0}, "Minute", "Gregorian", -6.], 1], CelestialSystem -> "Equatorial"]["Values"]]}, Frame -> True, AspectRatio -> .5] Out[1]= [image] ``` --- Plot the angular distance between the Sun and Moon over a month: ```wl In[1]:= SphereDistance[{ϕ1_, θ1_}, {ϕ2_, θ2_}] := InverseHaversine[Haversine[ϕ1 - ϕ2] + Cos[ϕ1] Cos[ϕ2] Haversine[θ1 - θ2]] In[2]:= sunposequatorial = SunPosition[DateRange[DateObject[{2022, 1, 1, 0, 0, 0}, "Instant", "Gregorian", -6.], DateObject[{2022, 2, 1, 0, 0, 0}, "Instant", "Gregorian", -6.], {1, "Day"}], CelestialSystem -> "Equatorial"]; In[3]:= moonposequatorial = MoonPosition[DateRange[DateObject[{2022, 1, 1, 0, 0, 0}, "Instant", "Gregorian", -6.], DateObject[{2022, 2, 1, 0, 0, 0}, "Instant", "Gregorian", -6.], {1, "Day"}], CelestialSystem -> "Equatorial"]; In[4]:= angdistequatorial = TimeSeriesThread[Quantity[SphereDistance[First[#], Last[#]] / Degree, "AngularDegrees"]&, {sunposequatorial, moonposequatorial}]; In[5]:= DateListPlot[angdistequatorial] Out[5]= [image] ``` --- Reconstruct the Moon's orbital period using the position of the Moon over several months: ```wl In[1]:= moonpos = MoonPosition[DateRange[DateObject[{2014, 1, 1, 0, 0, 0}, "Instant", "Gregorian", -6.], DateObject[{2014, 7, 1, 0, 0, 0}, "Instant", "Gregorian", -6.], {2, "Day"}], CelestialSystem -> "Equatorial"]; ``` Extract the positions where the Moon's right ascension suddenly goes from 24 hours to 0 hours and find the mean period where this transition happens: ```wl In[2]:= Extract[moonpos["Dates"], Position[Differences[N@QuantityMagnitude[Part[moonpos["Values"], All, 1]]], _ ? Negative]]//Differences//Mean//N Out[2]= Quantity[27.333333333333332, "Days"] ``` Compare this to the actual value of the Moon's orbital period: ```wl In[3]:= UnitConvert[EntityValue[\[FreeformPrompt]["the moon"], "OrbitPeriod"], "Day"] Out[3]= Quantity[27.3220000000000000191`5., "Days"] ``` --- Plot the position of the Sun and Moon on the celestial sphere: ```wl In[1]:= EquatorialtoCartesian[ ra_, dec_] := Module[ {x, y, z}, x = Cos[15 ra Degree] Sin[π / 2 - dec Degree]; y = Sin[15ra Degree] Sin[π / 2 - dec Degree]; z = Cos[π / 2 - dec Degree]; {x, y, z} ] In[2]:= Show[ParametricPlot3D[{Cos[t] Sin[p], Sin[t] Sin[p], Cos[p]}, {t, 0, 2 Pi}, {p, 0, Pi}, PlotStyle -> Opacity[.3]], Graphics3D[{Yellow, PointSize[.05], Point[EquatorialtoCartesian@@N@QuantityMagnitude@SunPosition[DateObject[{2017, 8, 20, 9, 0, 0}, "Instant", "Gregorian", -6.], CelestialSystem -> "Equatorial"]], Blue, Point[EquatorialtoCartesian@@N@QuantityMagnitude@MoonPosition[DateObject[{2017, 8, 20, 9, 0, 0}, "Instant", "Gregorian", -6.], CelestialSystem -> "Equatorial"]]}], SphericalRegion -> True] Out[2]= [image] ``` ### Properties & Relations (4) By default, location is specified by ``\$GeoLocation`` and the date is specified by the current date: ```wl In[1]:= MoonPosition[] Out[1]= {Quantity[215.85213267924254, "AngularDegrees"], Quantity[17.801197397392038, "AngularDegrees"]} In[2]:= MoonPosition[$GeoLocation, DateObject[]] Out[2]= {Quantity[215.8523149139171, "AngularDegrees"], Quantity[17.801104546685853, "AngularDegrees"]} ``` --- Results are in the form of a ``TimeSeries`` when a range of dates is specified: ```wl In[1]:= MoonPosition[DateRange[DateObject[{2013, 1, 1, 9, 0}, "Minute", "Gregorian", -6.], DateObject[{2013, 12, 31, 9, 0}, "Minute", "Gregorian", -6.], 10]] Out[1]= TemporalData[TimeSeries, {{QuantityArray[StructuredArray`StructuredData[{37, 2}, {CompressedData["«884»"]\ , "AngularDegrees", {{1}, {2}}}]]}, {TemporalData`DateSpecification[{2013, 1, 1, 10, 0, 0.}, {2013, 12, 27, 10, 0, 0.}, {10, "Day"}]}, 1, {"Continuous", 1}, {"Discrete", 1}, 2, {ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}, ValueDimensions -> 2}}, True, 13.3] ``` --- Results are multivalued for each date specification, so plotting the results using ``DateListPlot`` will result in two curves, one for azimuth and one for altitude: ```wl In[1]:= DateListPlot[MoonPosition[DateRange[DateObject[{2013, 6, 15, 8, 0}, "Minute", "Gregorian", -6.], DateObject[{2013, 6, 15, 16, 0}, "Minute", "Gregorian", -6.], {.5, "Hour"}]], Joined -> True] Out[1]= [image] ``` --- Find the position of the Moon for this location and date: ```wl In[1]:= loc = GeoPosition[{40.11, -88.22}]; date = DateObject[{2023, 7, 16, 12, 36, 0}]; In[2]:= MoonPosition[loc, date] Out[2]= {Quantity[239.89558038726645, "AngularDegrees"], Quantity[68.54951992190334, "AngularDegrees"]} In[3]:= UnitConvert[%, MixedUnit["ArcDMS"]] Out[3]= {Quantity[MixedMagnitude[{239, 53, 44.0894}], MixedUnit[{"AngularDegrees", "Arcminutes", "Arcseconds"}]], Quantity[MixedMagnitude[{68, 32, 58.2717}], MixedUnit[{"AngularDegrees", "Arcminutes", "Arcseconds"}]]} ``` This can also be computed with ``AstroPosition`` : ```wl In[4]:= AstroPosition[Entity["PlanetaryMoon", "Moon"], {"Horizon", loc, date}] Out[4]= AstroPosition[{239.89558038726645, 68.54951992190334, 0.002647154806876779}, {"Horizon", "Date" -> DateObject[{2023, 7, 16, 18, 37, 9.18400000000441}, "Instant", "Gregorian", 0., "TT"], "Location" -> GeoPosition[{40.11, -88.22}]}, "NorthAzAlt"] ``` ### Possible Issues (2) With ``MoonPosition[locationspec, Interval]``, results for specific locations are coerced into intervals: ```wl In[1]:= MoonPosition[GeoPosition[{40.1, -88.2}], Interval] Out[1]= {Quantity[Interval[{215.9710695591466, 215.97106955914666}], "AngularDegrees"], Quantity[Interval[{17.749043742048933, 17.74904374204894}], "AngularDegrees"]} ``` --- Attempting to plot the results of ``MoonPosition`` using ``"Minute"`` granularity or larger can result in artifacts: ```wl In[1]:= Plot[MoonPosition[Entity["City", {"Champaign", "Illinois", "UnitedStates"}], DatePlus[DateObject[{2020, 9, 3, 20, 29}, "Minute", "Gregorian", -5.], {x, "Hour"}]][[2]], {x, 0.1, 1}] Out[1]= [image] ``` One workaround to such issues is to coerce the incoming date so that it has "Instant" granularity: ```wl In[2]:= Plot[MoonPosition[Entity["City", {"Champaign", "Illinois", "UnitedStates"}], DatePlus[DateObject[DateObject[{2020, 9, 3, 20, 29}, "Minute", "Gregorian", -5.], "Instant"], {x, "Hour"}]][[2]], {x, 0.1, 1}] Out[2]= [image] ``` ### Neat Examples (1) Choose a location and a date: ```wl In[1]:= loc = GeoPosition[{40.1, -88.2}]; date = DateObject[{2017, 7, 5, 16, 0, 0}, TimeZone -> -6]; ``` This is the sidereal time of that location at that time: ```wl In[2]:= sidtime = SiderealTime[loc, date] Out[2]= Quantity[MixedMagnitude[{11, 3, 32.486}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] ``` Take the right ascensions of the Sun, the Moon and the planets: ```wl In[3]:= sunRA = First[SunPosition[date, CelestialSystem -> "Equatorial"]]; moonRA = First[MoonPosition[date, CelestialSystem -> "Equatorial"]]; planetsRA = EntityValue[{Entity["Planet", "Mercury"], Entity["Planet", "Venus"], Entity["Planet", "Mars"], Entity["Planet", "Jupiter"], Entity["Planet", "Saturn"], Entity["Planet", "Uranus"], Entity["Planet", "Neptune"]}, EntityProperty["Planet", "RightAscension", {"Date" -> date}]]; ascensions = Join[{sunRA, moonRA}, planetsRA] Out[3]= {Quantity[7.017206214733577, "HoursOfRightAscension"], Quantity[16.54229460016592, "HoursOfRightAscension"], Quantity[MixedMagnitude[{8, 9, 40.7}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]], Quantit ... itude[{1, 45, 37.44}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]], Quantity[MixedMagnitude[{23, 3, 4.3}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]]} ``` Construct text labels for them: ```wl In[4]:= symbols = {"☼", "☾", "☿", "♀", "♂", "♃", "♄", "♅", "♆"}; colors = {Yellow, White, Orange, Lighter[Blue], Red, Lighter[Purple], Orange, Cyan, Lighter[Blue]}; labels = MapThread[Text[Style[#1, #2, 17], {0, 3.4}.RotationMatrix[#3]]&, {symbols, colors, ascensions}]; ``` Plot the directions of the Sun, the Moon and the planets as viewed from the South Pole, with respect to the fixed stars: ```wl In[5]:= GeoGraphics[{ labels, Thick, Black, Arrow[{{0, 0}, Here}], GeoStyling[Opacity[.5]], NightHemisphere[date], Thickness[.005], Opacity[.5], Line[Pi{{{-1, 0}, {1, 0}}, {{0, -1}, {0, 1}}}] }, GeoRange -> "World", GeoProjection -> {"AzimuthalEquidistant", "Centering" -> {-90, Longitude[loc] - sidtime}}, GeoBackground -> GeoStyling["ReliefMap"], Background -> Black, PlotRange -> 4, PlotLabel -> sidtime, LabelStyle -> White ] Out[5]= [image] ``` ## See Also * [`AstroPosition`](https://reference.wolfram.com/language/ref/AstroPosition.en.md) * [`SunPosition`](https://reference.wolfram.com/language/ref/SunPosition.en.md) * [`AstroSubpoint`](https://reference.wolfram.com/language/ref/AstroSubpoint.en.md) * [`PlanetaryMoonData`](https://reference.wolfram.com/language/ref/PlanetaryMoonData.en.md) * [`MoonPhase`](https://reference.wolfram.com/language/ref/MoonPhase.en.md) * [`SolarEclipse`](https://reference.wolfram.com/language/ref/SolarEclipse.en.md) * [`LunarEclipse`](https://reference.wolfram.com/language/ref/LunarEclipse.en.md) * [`TideData`](https://reference.wolfram.com/language/ref/TideData.en.md) ## Related Guides * [Astronomical Computation & Data](https://reference.wolfram.com/language/guide/AstronomicalComputationAndData.en.md) * [Date & Time](https://reference.wolfram.com/language/guide/DateAndTime.en.md) * [`Geodesy`](https://reference.wolfram.com/language/guide/Geodesy.en.md) ## History * [Introduced in 2014 (10.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn100.en.md) \| [Updated in 2023 (13.3)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn133.en.md)