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ReferenceAltitude: Reference altitude angle for sunrise and sunset twilight—Wolfram Documentation

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ReferenceAltitude

is an option of Sunrise, AstroRiseSet and related functions that specifies how to define the instant of rise or set of an astronomical body or point on the celestial sphere.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Solar Twilight  
Choice of Reference Altitude Angle  
Choice of Astronomical Body Limb  
Properties & Relations  
See Also
Related Guides
History
Cite this Page

ReferenceAltitude

ReferenceAltitude

is an option of Sunrise, AstroRiseSet and related functions that specifies how to define the instant of rise or set of an astronomical body or point on the celestial sphere.

Details

  • ReferenceAltitude can be used to define the instants of beginning and end of civil, nautical or astronomical twilight, as well as different definitions of rise and set of an astronomical object.
  • Possible values of the ReferenceAltitude option include:
  • Automaticupper limb of the body crosses zero altitude
    altcenter of the body crosses numeric altitude alt
    {alt,limb}the given limb of the body crosses numeric altitude alt
  • The reference altitude angle alt can be given as a Quantity angle or as a numeric expression interpreted in angular degrees. For the particular case of the Sun, these are the traditional values of reference altitude:
  • "Civil"the center of the Sun has altitude –6 degrees
    "Nautical"the center of the Sun has altitude –12 degrees
    "Astronomical"the center of the Sun has altitude –18 degrees
  • Possible values for the limb of the body include:
  • "UpperLimb"upper limb of the body
    "Center"central point of the body
    "LowerLimb"lower limb of the body
    limbnumeric value between –1 (lower limb) and 1 (upper limb)

Examples

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Basic Examples  (3)

Find the next instant of the beginning of civil twilight in the morning, for your current geo location:

Wolfram Language code: Sunrise[ReferenceAltitude -> "Civil"]

Find the next instant of the ending of nautical twilight in the evening, for your current geo location:

Wolfram Language code: Sunset[ReferenceAltitude -> "Nautical"]

Find the next two events of Mars crossing altitude 10° on its way up and down in the sky:

Wolfram Language code: AstroRiseSet["Mars", {"Rise", "Set"}, ReferenceAltitude -> Quantity[10, "AngularDegrees"]]

Scope  (5)

Solar Twilight  (2)

Compare the instant of sunrise to the standard definitions of civil, nautical and astronomical twilight:

Wolfram Language code: loc = GeoPosition[{40, -90}]; date = DateObject[{2024, 6, 1}];
Wolfram Language code: rise0 = Sunrise[loc, date]
Wolfram Language code: rise6 = Sunrise[loc, date, ReferenceAltitude -> "Civil"]
Wolfram Language code: rise12 = Sunrise[loc, date, ReferenceAltitude -> "Nautical"]
Wolfram Language code: rise18 = Sunrise[loc, date, ReferenceAltitude -> "Astronomical"]
Wolfram Language code: Differences[{rise18, rise12, rise6, rise0}]

Compare the instant of sunset to the standard definitions of civil, nautical and astronomical twilight:

Wolfram Language code: loc = GeoPosition[{40, -90}]; date = DateObject[{2024, 6, 1}];
Wolfram Language code: set0 = Sunset[loc, date]
Wolfram Language code: set6 = Sunset[loc, date, ReferenceAltitude -> "Civil"]
Wolfram Language code: set12 = Sunset[loc, date, ReferenceAltitude -> "Nautical"]
Wolfram Language code: set18 = Sunset[loc, date, ReferenceAltitude -> "Astronomical"]
Wolfram Language code: Differences[{set0, set6, set12, set18}]

Choice of Reference Altitude Angle  (1)

Compare the instants for which the Moon crosses different levels of altitude when rising:

Wolfram Language code: riseM10 = AstroRiseSet["Moon", "Rise", ReferenceAltitude -> Quantity[-10, "AngularDegrees"]]
Wolfram Language code: rise0 = AstroRiseSet["Moon", "Rise", ReferenceAltitude -> Quantity[0, "AngularDegrees"]]
Wolfram Language code: rise10 = AstroRiseSet["Moon", "Rise", ReferenceAltitude -> Quantity[10, "AngularDegrees"]]
Wolfram Language code: Differences[{riseM10, rise0, rise10}]

Choice of Astronomical Body Limb  (2)

Compare the instants for which different parts of the Moon cross the local horizon when rising:

Wolfram Language code: upper = AstroRiseSet["Moon", "Rise", ReferenceAltitude -> "UpperLimb"]
Wolfram Language code: center = AstroRiseSet["Moon", "Rise", ReferenceAltitude -> "Center"]
Wolfram Language code: lower = AstroRiseSet["Moon", "Rise", ReferenceAltitude -> "LowerLimb"]
Wolfram Language code: Differences[{upper, center, lower}]

Compare the instants for which different parts of the Moon cross the local horizon when setting:

Wolfram Language code: lower = AstroRiseSet["Moon", "Set", ReferenceAltitude -> "LowerLimb"]
Wolfram Language code: center = AstroRiseSet["Moon", "Set", ReferenceAltitude -> "Center"]
Wolfram Language code: upper = AstroRiseSet["Moon", "Set", ReferenceAltitude -> "UpperLimb"]
Wolfram Language code: Differences[{lower, center, upper}]

Properties & Relations  (1)

Sunrise is defined as the instant when the upper limb of the Sun crosses altitude 0 in the morning:

Wolfram Language code: Sunrise[]
Wolfram Language code: Sunrise[ReferenceAltitude -> {Quantity[0, "AngularDegrees"], "UpperLimb"}]

At that moment, the altitude of the center is negative, corresponding to half the angular size of the Sun:

Wolfram Language code: AstroPosition["Sun", %]

A few minutes later, the center of the Sun crosses the local horizon:

Wolfram Language code: Sunrise[ReferenceAltitude -> {Quantity[0, "AngularDegrees"], "Center"}]

At that moment, the altitude of the center is zero:

Wolfram Language code: AstroPosition["Sun", %]
Wolfram Research (2024), ReferenceAltitude, Wolfram Language function, https://reference.wolfram.com/language/ref/ReferenceAltitude.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_referencealtitude, author="Wolfram Research", title="{ReferenceAltitude}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/ReferenceAltitude.html}", note=[Accessed: 14-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_referencealtitude, organization={Wolfram Research}, title={ReferenceAltitude}, year={2024}, url={https://reference.wolfram.com/language/ref/ReferenceAltitude.html}, note=[Accessed: 14-November-2026]}