--- title: "SiderealTime" language: "en" type: "Symbol" summary: "SiderealTime[] gives the right ascension of the local meridian for the current date and location. SiderealTime[date] gives the right ascension of the local meridian for the specified date. SiderealTime[loc] gives the right ascension of the local meridian for the specified location. SiderealTime[loc, date] gives the right ascension of the local meridian for the specified location and date. SiderealTime[{{loc1, date1}, {loc2, date2}, ...}] gives the right ascensions of the local meridians for all specified locations on the specified dates. SiderealTime[MeanTime, loc, date] gives the mean sidereal time for the specified location and date. SiderealTime[type, loc, date, func] uses func to determine what to return for extended locations." keywords: - astronomical time - stellar time - telescope time - sidereal day - sidereal rotation period canonical_url: "https://reference.wolfram.com/language/ref/SiderealTime.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" related_functions: - title: "SolarTime" link: "https://reference.wolfram.com/language/ref/SolarTime.en.md" - title: "Sunrise" link: "https://reference.wolfram.com/language/ref/Sunrise.en.md" - title: "Sunset" link: "https://reference.wolfram.com/language/ref/Sunset.en.md" - title: "SunPosition" link: "https://reference.wolfram.com/language/ref/SunPosition.en.md" - title: "DaylightQ" link: "https://reference.wolfram.com/language/ref/DaylightQ.en.md" - title: "JulianDate" link: "https://reference.wolfram.com/language/ref/JulianDate.en.md" - title: "FromJulianDate" link: "https://reference.wolfram.com/language/ref/FromJulianDate.en.md" - title: "StarData" link: "https://reference.wolfram.com/language/ref/StarData.en.md" - title: "PlanetData" link: "https://reference.wolfram.com/language/ref/PlanetData.en.md" - title: "MoonPosition" link: "https://reference.wolfram.com/language/ref/MoonPosition.en.md" - title: "Longitude" link: "https://reference.wolfram.com/language/ref/Longitude.en.md" --- # SiderealTime SiderealTime[] gives the right ascension of the local meridian for the current date and location. SiderealTime[date] gives the right ascension of the local meridian for the specified date. SiderealTime[loc] gives the right ascension of the local meridian for the specified location. SiderealTime[loc, date] gives the right ascension of the local meridian for the specified location and date. SiderealTime[{{loc1, date1}, {loc2, date2}, …}] gives the right ascensions of the local meridians for all specified locations on the specified dates. SiderealTime["MeanTime", loc, date] gives the mean sidereal time for the specified location and date. SiderealTime[type, loc, date, func] uses func to determine what to return for extended locations. ## Details * Sidereal time is typically used to locate celestial objects in the night sky and to decide when and where to point a telescope for optimal observation. * ``SiderealTime`` returns a ``Quantity`` angle expressed in mixed units of hours, minutes and seconds of right ascension, as is traditionally done with angles measured along the celestial equator. * ``SiderealTime[loc, date]``, equivalent to ``SiderealTime["ApparentTime", loc, date]``, computes the local apparent or true sidereal time, based on the apparent equator and equinox of date, hence including the effects of both precession and nutation. * ``SiderealTime["MeanTime", loc, date]`` computes the local mean sidereal time based on the mean equator and equinox of date, including precession but averaging over nutation. * ``SiderealTime[]`` makes use of ``\$GeoLocation`` and ``\$TimeZone`` to determine your location and time zone. * Locations can be specified as ``GeoPosition`` objects, ``{lat, lon}`` pairs in degrees, ``Entity`` geo locations or ``GeoGraphics`` primitives. * ``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. * ``loc`` and ``date`` can be either individual items or lists of them. * 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. * ``SiderealTime[…, func]`` is used to specify the format of output when extended 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 | ## Examples (23) ### Basic Examples (7) Compute the sidereal time for your current location: ```wl In[1]:= SiderealTime[] Out[1]= Quantity[MixedMagnitude[{21, 29, 10.5321}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] ``` --- Compute the sidereal time for a specified date: ```wl In[1]:= SiderealTime[DateObject[{2024, 9, 25, 0, 58, 40.5585}, "Instant", "Gregorian", -5.]] Out[1]= Quantity[MixedMagnitude[{0, 23, 55.2778}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] ``` --- Compute the sidereal time for a specified location: ```wl In[1]:= SiderealTime[Entity["City", {"Chicago", "Illinois", "UnitedStates"}]] Out[1]= Quantity[MixedMagnitude[{21, 31, 24.6032}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] ``` --- Compute the sidereal time for a specified latitude/longitude and date: ```wl In[1]:= SiderealTime[GeoPosition[{50.3, -80.1}], DateObject[{2025, 3, 17, 15, 3, 6.49081}, "Instant", "Gregorian", -5.]] Out[1]= Quantity[MixedMagnitude[{2, 25, 17.7664}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] ``` --- Compute the sidereal time for a specified city and date: ```wl In[1]:= SiderealTime[\[FreeformPrompt]["Saint Louis"], DateObject[{2024, 8, 12, 9, 17, 16.2174}, "Instant", "Gregorian", -5.]] Out[1]= Quantity[MixedMagnitude[{5, 42, 23.3035}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] ``` --- Compute the local mean sidereal time at your geo location for the given date: ```wl In[1]:= SiderealTime["MeanTime", Here, DateObject[{2025, 3, 17, 16, 45, 0}, "Instant", "Gregorian", -5.]] Out[1]= Quantity[MixedMagnitude[{3, 34, 54.3679}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] ``` Compare this to the default apparent local sidereal time: ```wl In[2]:= SiderealTime["ApparentTime", Here, DateObject[{2025, 3, 17, 16, 45, 0}, "Instant", "Gregorian", -5.]] Out[2]= Quantity[MixedMagnitude[{3, 34, 54.4135}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] ``` The difference is known as the equation of equinoxes: ```wl In[3]:= % - %% Out[3]= Quantity[MixedMagnitude[{0, 0, 0.0455746}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] ``` --- Find the mean sidereal time at multiple locations in Illinois for a given date and return their mean value: ```wl In[1]:= SiderealTime["MeanTime", Entity["AdministrativeDivision", {"Illinois", "UnitedStates"}], DateObject[{2025, 3, 17, 16, 45, 0}], Mean] Out[1]= Quantity[MixedMagnitude[{3, 29, 50.8176}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] ``` ### Scope (9) #### Dates (3) Dates can be specified as a ``DateObject`` : ```wl In[1]:= SiderealTime[DateObject[{2023, 9, 13, 0, 0, 0.}, "Instant", "Gregorian", -6.]] Out[1]= Quantity[MixedMagnitude[{23, 34, 56.7477}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] ``` --- Dates can be specified as a date string: ```wl In[1]:= SiderealTime["September 23, 2024 12:00 AM CDT"] Out[1]= Quantity[MixedMagnitude[{23, 17, 11.957}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] ``` --- Generate the sidereal time for a range of dates: ```wl In[1]:= SiderealTime[DateRange[DateObject[{2023, 1, 1, 9, 0}, "Minute", "Gregorian", -6.], DateObject[{2023, 12, 31, 9, 0}, "Minute", "Gregorian", -6.], 10]] Out[1]= TemporalData[TimeSeries, {{QuantityArray[StructuredArray`StructuredData[{37}, {{15.85097563777504, 16.508089030751897, 17.16519741949791, 17.822295664818306, 18.479394669475834, 19.136500425109062, 19.79359375036486, 20.450678493363 ... poralData`DateSpecification[{2023, 1, 1, 10, 0, 0.}, {2023, 12, 27, 10, 0, 0.}, {10, "Day"}]}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}, ValueDimensions -> 1}}, True, 13.3] ``` #### Locations (6) Locations can be latitude/longitude pairs: ```wl In[1]:= SiderealTime[GeoPosition[{40.1, -88.2}]] Out[1]= Quantity[MixedMagnitude[{0, 20, 44.252}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] ``` --- Cities are treated as single, specific locations: ```wl In[1]:= SiderealTime[Entity["City", {"SaintLouis", "Missouri", "UnitedStates"}]] Out[1]= Quantity[MixedMagnitude[{0, 12, 33.6524}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] ``` --- Results for extended locations are intervals, by default: ```wl In[1]:= SiderealTime[Entity["Country", "France"]] Out[1]= Quantity[Interval[{MixedMagnitude[{5, 51, 21.5806}], MixedMagnitude[{6, 54, 46.9563}]}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] ``` --- The form of the results for extended locations can be overridden: ```wl In[1]:= SiderealTime[Entity["Country", "France"], Mean] Out[1]= Quantity[MixedMagnitude[{6, 23, 4.39144}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] ``` --- Generate the sidereal time for multiple locations: ```wl In[1]:= SiderealTime[{Entity["City", {"Chicago", "Illinois", "UnitedStates"}], Entity["City", {"SaintLouis", "Missouri", "UnitedStates"}]}] Out[1]= {Quantity[MixedMagnitude[{0, 22, 49.0984}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]], Quantity[MixedMagnitude[{0, 12, 34.0414}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]]} ``` --- Find the sidereal time for multiple locations on different dates: ```wl In[1]:= SiderealTime[{{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[18.930482339394775, "HoursOfRightAscension"], Quantity[1.8763135101775366, "HoursOfRightAscension"]} ``` ### Applications (2) Plot the equation of time by finding the difference between the Sun's right ascension at noon and the sidereal time at noon: ```wl In[1]:= sunpos = SunPosition[GeoPosition[{0, 0}], DateRange[DateObject[{2021, 1, 1, 12, 0}, "Minute", "Gregorian", 0.], DateObject[{2021, 12, 31, 12, 0}, "Minute", "Gregorian", 0.], 10], CelestialSystem -> "Equatorial"]; In[2]:= stime = SiderealTime[GeoPosition[{0, 0}], DateRange[DateObject[{2021, 1, 1, 12, 0}, "Minute", "Gregorian", 0.], DateObject[{2021, 12, 31, 12, 0}, "Minute", "Gregorian", 0.], 10]]; In[3]:= equationoftime = TimeSeriesThread[With[{diff = First[#][[1]] - Last[#]}, UnitConvert[Mod[diff, Quantity[24, "HoursOfRightAscension"], Quantity[-12, "HoursOfRightAscension"]], "MinutesOfRightAscension"]]&, {sunpos, stime}]; In[4]:= DateListPlot[equationoftime, FrameLabel -> Automatic] Out[4]= [image] ``` --- The difference between apparent and mean sidereal times is called the equation of the equinoxes: ```wl In[1]:= SiderealTime["ApparentTime"] - SiderealTime["MeanTime"] Out[1]= Quantity[MixedMagnitude[{0, 0, 0.0907835}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] ``` Display the equation of the equinoxes over a year: ```wl In[2]:= dates = DateRange[DateObject[{2018, 1, 1, 0, 0, 0}], DateObject[{2018, 12, 31, 0, 0, 0}]]; trueST = SiderealTime[Here, #]& /@ dates; meanST = SiderealTime["MeanTime", Here, #]& /@ dates; In[3]:= ListPlot[UnitConvert[trueST - meanST, "ArcSeconds"]] Out[3]= [image] ``` The same computation over 20 years, which shows the main nutation cycle of 18.6 years: ```wl In[4]:= dates = DateRange[DateObject[{2000, 1, 1, 0, 0, 0}], DateObject[{2020, 12, 31, 0, 0, 0}], "Week"]; trueST = SiderealTime[Here, #]& /@ dates; meanST = SiderealTime["MeanTime", Here, #]& /@ dates; ListPlot[UnitConvert[trueST - meanST, "ArcSeconds"]] Out[4]= [image] ``` The primary period corresponds to an oscillation of 17.2 arc seconds of nutation in longitude: ```wl In[5]:= MinMax[UnitConvert[trueST - meanST, "ArcSeconds"]] Out[5]= {Quantity[-17.3510888095187, "Arcseconds"], Quantity[17.201299858061958, "Arcseconds"]} ``` ### Properties & Relations (3) The output of ``SiderealTime`` is an angle, not a time: ```wl In[1]:= SiderealTime[] Out[1]= Quantity[MixedMagnitude[{8, 9, 43.5369}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] In[2]:= UnitDimensions[%] Out[2]= {{"AngleUnit", 1}} In[3]:= UnitConvert[%%, "AngularDegrees"] Out[3]= Quantity[122.43140380393015, "AngularDegrees"] ``` --- ``SiderealTime`` tracks Earth's rotation with respect to the fixed stars, with a full rotation taking one sidereal day: ```wl In[1]:= With[{now = Now}, {SiderealTime[now], SiderealTime[now + Quantity[1, "SiderealDays"]]}] Out[1]= {Quantity[MixedMagnitude[{8, 9, 43.7605}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]], Quantity[MixedMagnitude[{8, 9, 43.7595}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]]} ``` --- Earth rotates with respect to the fixed stars in less than one day, and it needs to rotate a bit more to complete a full (solar) day: ```wl In[1]:= With[{now = Now}, SiderealTime[now + Quantity[1, "Days"]] - SiderealTime[now]] Out[1]= Quantity[MixedMagnitude[{0, 4, -3.44572}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]] ``` The effect accumulates during one year and hence Earth rotates 366.242 times with respect to the fixed stars in 365.242 days: ```wl In[2]:= Quantity[360, "AngularDegrees"] / % Out[2]= 365.244 ``` Equivalently: ```wl In[3]:= Quantity[1., "SolarYears"] / Quantity[1, "SolarDays"] Out[3]= 365.242 In[4]:= Quantity[1., "SolarYears"] / Quantity[1, "SiderealDays"] Out[4]= 366.242 ``` ### Possible Issues (1) Although it looks like a time-based concept, ``SiderealTime`` is actually an angle: ```wl In[1]:= SiderealTime[]//UnitDimensions Out[1]= {{"AngleUnit", 1}} ``` ### Neat Examples (1) Choose a location and a date: ```wl In[1]:= loc = Here; date = Now; ``` This is the sidereal time of that location at that time: ```wl In[2]:= sidtime = SiderealTime[loc, date] Out[2]= Quantity[MixedMagnitude[{0, 21, 0.537091}], 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[1.5112225258471845, "HoursOfRightAscension"], Quantity[21.021096344541668, "HoursOfRightAscension"], Quantity[MixedMagnitude[{2, 39, 53.44}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]], Qua ... itude[{3, 0, 33.7}], MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]], Quantity[MixedMagnitude[{23, 47, 57.4}], 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 * [`SolarTime`](https://reference.wolfram.com/language/ref/SolarTime.en.md) * [`Sunrise`](https://reference.wolfram.com/language/ref/Sunrise.en.md) * [`Sunset`](https://reference.wolfram.com/language/ref/Sunset.en.md) * [`SunPosition`](https://reference.wolfram.com/language/ref/SunPosition.en.md) * [`DaylightQ`](https://reference.wolfram.com/language/ref/DaylightQ.en.md) * [`JulianDate`](https://reference.wolfram.com/language/ref/JulianDate.en.md) * [`FromJulianDate`](https://reference.wolfram.com/language/ref/FromJulianDate.en.md) * [`StarData`](https://reference.wolfram.com/language/ref/StarData.en.md) * [`PlanetData`](https://reference.wolfram.com/language/ref/PlanetData.en.md) * [`MoonPosition`](https://reference.wolfram.com/language/ref/MoonPosition.en.md) * [`Longitude`](https://reference.wolfram.com/language/ref/Longitude.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) ## History * [Introduced in 2014 (10.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn100.en.md) \| [Updated in 2021 (12.3)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn123.en.md)