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SiderealTime
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SiderealTime

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gives the right ascension of the local meridian for the current date and location.

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SiderealTime[date]

gives the right ascension of the local meridian for the specified date.

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gives the right ascension of the local meridian for the specified location.

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SiderealTime[loc,date]

gives the right ascension of the local meridian for the specified date and location.

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SiderealTime[{{loc1,date1},{loc2,date2},…}]

gives the right ascensions of the local meridians for all specified locations on the specified dates.

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SiderealTime[loc,date,func]

uses func to determine what to return for extended locations.

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SiderealTime["MeanTime",loc,date,func]

gives the mean sidereal time for the specified date, location and aggregation function.

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:
  • Automaticreturns intervals for extended locations only
    Intervalreturns intervals for all specified locations
    Meanreturns mean value for extended locations
    Minreturns minimum values for extended locations
    Maxreturns maximum values for extended locations
    StandardDeviationreturns standard deviation for extended locations

Examples

open allclose all

Basic Examples  (5)Summary of the most common use cases

Compute the sidereal time for your current location:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-dnpkjh
Out[1]=1

Compute the sidereal time for a specified date:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-bv5fc0
Out[1]=1

Compute the sidereal time for a specified location:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-frupmt
Out[1]=1

Compute the sidereal time for a specified latitude/longitude and date:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-k5huuj
Out[1]=1

Compute the sidereal time for a specified city and date:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-bild8d
Out[1]=1

Scope  (8)Survey of the scope of standard use cases

Dates  (3)

Dates can be specified as a DateObject:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-t1phag
Out[1]=1

Dates can be specified as a date string:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-zbahi
Out[1]=1

Generate the sidereal time for a range of dates:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-g0c68v
Out[1]=1

Locations  (5)

Locations can be latitude/longitude pairs:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-mmgexd
Out[1]=1

Cities are treated as single, specific locations:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-4kw4q7
Out[1]=1

Results for extended locations are intervals, by default:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-zm0h2h
Out[1]=1

The form of the results for extended locations can be overridden:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-c6w1j1
Out[1]=1

Generate the sidereal time for multiple locations:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-o7x97u
Out[1]=1

Applications  (2)Sample problems that can be solved with this function

Plot the equation of time by finding the difference between the Sun's right ascension at noon and the sidereal time at noon:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-kp2kf
In[2]:=2
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https://wolfram.com/xid/0jz5qcn081c93m-e5gjsa
In[3]:=3
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https://wolfram.com/xid/0jz5qcn081c93m-ewa0e
In[4]:=4
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https://wolfram.com/xid/0jz5qcn081c93m-c20uam
Out[4]=4

The difference between apparent and mean sidereal times is called the equation of the equinoxes:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-5repxo
Out[1]=1

Display the equation of the equinoxes over a year:

In[2]:=2
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https://wolfram.com/xid/0jz5qcn081c93m-tbxomc
In[3]:=3
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https://wolfram.com/xid/0jz5qcn081c93m-hysora
Out[3]=3

The same computation over 20 years, which shows the main nutation cycle of 18.6 years:

In[4]:=4
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https://wolfram.com/xid/0jz5qcn081c93m-47ben
Out[4]=4

The primary period corresponds to an oscillation of 17.2 arc seconds of nutation in longitude:

In[5]:=5
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https://wolfram.com/xid/0jz5qcn081c93m-b3kc07
Out[5]=5

Properties & Relations  (3)Properties of the function, and connections to other functions

The output of SiderealTime is an angle, not a time:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-pbtl98
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0jz5qcn081c93m-ocqi9h
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0jz5qcn081c93m-wj9zbg
Out[3]=3

SiderealTime tracks Earth's rotation with respect to the fixed stars, with a full rotation taking one sidereal day:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-61jdoo
Out[1]=1

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:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-woz3xs
Out[1]=1

The effect accumulates during one year and hence Earth rotates 366.242 times with respect to the fixed stars in 365.242 days:

In[2]:=2
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https://wolfram.com/xid/0jz5qcn081c93m-46nlbi
Out[2]=2

Equivalently:

In[3]:=3
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https://wolfram.com/xid/0jz5qcn081c93m-i969xj
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0jz5qcn081c93m-2q7ym8
Out[4]=4

Possible Issues  (1)Common pitfalls and unexpected behavior

Although it looks like a time-based concept, SiderealTime is actually an angle:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-jhgpqf
Out[1]=1

Neat Examples  (1)Surprising or curious use cases

Choose a location and a date:

In[1]:=1
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https://wolfram.com/xid/0jz5qcn081c93m-i1rhz0

This is the sidereal time of that location at that time:

In[2]:=2
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https://wolfram.com/xid/0jz5qcn081c93m-3elp6y
Out[2]=2

Take the right ascensions of the Sun, the Moon and the planets:

In[3]:=3
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https://wolfram.com/xid/0jz5qcn081c93m-jt3gg0
Out[3]=3

Construct text labels for them:

In[4]:=4
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https://wolfram.com/xid/0jz5qcn081c93m-1aoala

Plot the directions of the Sun, the Moon and the planets as viewed from the South Pole, with respect to the fixed stars:

In[5]:=5
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https://wolfram.com/xid/0jz5qcn081c93m-iqh820
Out[5]=5
Wolfram Research (2014), SiderealTime, Wolfram Language function, https://reference.wolfram.com/language/ref/SiderealTime.html (updated 2021).
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Wolfram Research (2014), SiderealTime, Wolfram Language function, https://reference.wolfram.com/language/ref/SiderealTime.html (updated 2021).

Text

Wolfram Research (2014), SiderealTime, Wolfram Language function, https://reference.wolfram.com/language/ref/SiderealTime.html (updated 2021).

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Wolfram Research (2014), SiderealTime, Wolfram Language function, https://reference.wolfram.com/language/ref/SiderealTime.html (updated 2021).

CMS

Wolfram Language. 2014. "SiderealTime." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/SiderealTime.html.

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Wolfram Language. 2014. "SiderealTime." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/SiderealTime.html.

APA

Wolfram Language. (2014). SiderealTime. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SiderealTime.html

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Wolfram Language. (2014). SiderealTime. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SiderealTime.html

BibTeX

@misc{reference.wolfram_2025_siderealtime, author="Wolfram Research", title="{SiderealTime}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/SiderealTime.html}", note=[Accessed: 27-March-2025 ]}

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@misc{reference.wolfram_2025_siderealtime, author="Wolfram Research", title="{SiderealTime}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/SiderealTime.html}", note=[Accessed: 27-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_siderealtime, organization={Wolfram Research}, title={SiderealTime}, year={2021}, url={https://reference.wolfram.com/language/ref/SiderealTime.html}, note=[Accessed: 27-March-2025 ]}

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@online{reference.wolfram_2025_siderealtime, organization={Wolfram Research}, title={SiderealTime}, year={2021}, url={https://reference.wolfram.com/language/ref/SiderealTime.html}, note=[Accessed: 27-March-2025 ]}