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| {{About||other uses of "Celestial"|Celestial (disambiguation)}}
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| In [[astronomy]], a '''celestial coordinate system''' is a system for specifying positions of celestial objects: satellites, planets, stars, galaxies, and so on. [[Coordinate system]]s can specify a position in [[3-dimensional space]], or merely the direction of the object on the [[celestial sphere]], if its distance is not known or not important.
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| The coordinate systems are implemented in either [[spherical coordinates]] or [[Cartesian coordinate system|rectangular coordinates]]. [[Spherical coordinates]], projected on the [[celestial sphere]], are analogous to the [[geographic coordinate system]] used on the surface of the [[Earth]]. These differ in their choice of [[fundamental plane (spherical coordinates)|fundamental plane]], which divides the [[celestial sphere]] into two equal [[sphere|hemisphere]]s along a [[great circle]]. [[Cartesian coordinate system|Rectangular coordinates]], in appropriate [[Units of measurement|units]], are simply the [[Cartesian coordinate system|cartesian]] equivalent of the spherical coordinates, with the same fundamental ({{math|''x,y''}}) plane and primary ({{math|''x''}}-axis) direction. Each coordinate system is named for its choice of fundamental plane. | | The concern is, you only have a very cam recorder and you need it to record if you are driving. 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| {{Infobox
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| |title=Orientation of Astronomical Coordinates
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| |image= [[File:Ecliptic equator galactic anim.gif|thumb]]
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| |caption=A [[star]]'s [[Galactic coordinate system|galactic]] (yellow), [[Ecliptic coordinate system|ecliptic]] (red) and [[Equatorial coordinate system|equatorial]] (blue) coordinates, as projected on the [[celestial sphere]]. Ecliptic and equatorial coordinates share the [[equinox|vernal equinox]] (magenta) as the primary direction, and galactic coordinates are referred to the galactic center (yellow). The origin of coordinates (the "center of the sphere") is ambiguous; see [[celestial sphere]] for more information.
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| }}
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| ==Coordinate systems==
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| The following table lists the common coordinate systems in use by the astronomical community. The [[Fundamental plane (spherical coordinates)|fundamental plane]] divides the [[celestial sphere]] into two equal [[hemisphere]]s and defines the baseline for the vertical coordinates, analogous to the [[equator]] in the [[geographic coordinate system]]. The poles are located at ±90° from the fundamental plane. The primary direction is the starting point of the horizontal coordinates. The origin is the zero distance point, the "center of the celestial sphere", although the definition of [[celestial sphere]] is ambiguous about the definition of its center point.
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| {| class="wikitable"
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| ! Coordinate system <ref>{{cite web|url=http://www.astro.virginia.edu/class/majewski/astr551/lectures/COORDS/coords.html|title=Coordinate Systems|last=Majewski|first=Steve|publisher=UVa Department of Astronomy|accessdate=19 March 2011}}</ref> !! Center point<br>(Origin) !! Fundamental plane<br>(0º vertical) !! Poles !! colspan="2"|Coordinates !! Primary direction<br>(0º horizontal)
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| !!!!!!!!! Vertical !! Horizontal !!
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| |-
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| |- style="text-align:center;"
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| | [[Horizontal coordinate system|Horizontal]]<br>(also called Alt/Az or El/Az) || observer || [[horizon]] || [[zenith]] / [[nadir]] || altitude ({{math|''a''}}) or elevation || [[azimuth]] ({{math|''A''}}) || [[north]] or [[south]] point of horizon
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| |- style="text-align:center;"
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| | [[Equatorial coordinate system|Equatorial]] || rowspan="2"|center of the [[Earth]] (geocentric) / center of the [[Sun]] (heliocentric) || [[celestial equator]] || [[celestial pole]]s || [[declination]] ({{math|''δ''}}) || [[right ascension]] ({{math|''α''}}) or [[hour angle]] ({{math|''h''}}) || rowspan="2"|[[equinox|vernal equinox]]
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| |-
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| |- style="text-align:center;"
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| | [[Ecliptic coordinate system|Ecliptic]] || [[ecliptic]] || [[ecliptic pole]]s || [[ecliptic latitude]] ({{math|''β''}}) || [[ecliptic longitude]] ({{math|''λ''}})
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| |-
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| |- style="text-align:center;"
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| | [[Galactic coordinate system|Galactic]] || center of the [[Sun]] || [[galactic plane]] || [[galactic pole]]s || galactic latitude ({{math|''b''}}) || galactic longitude ({{math|''l''}}) || [[galactic center]]
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| |-
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| |- style="text-align:center;"
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| | [[Supergalactic coordinate system|Supergalactic]] || || [[supergalactic plane]] || supergalactic poles || supergalactic latitude ({{math|''SGB''}}) || supergalactic longitude ({{math|''SGL''}}) || intersection of supergalactic plane and galactic plane
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| |}
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| ===Horizontal system===
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| {{Main|Horizontal coordinate system}}
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| The ''horizontal'', or altitude-azimuth, system is based on the position of the observer on Earth, which revolves around its own axis once per [[sidereal day]] (23 hours, 56 minutes and 4.091 seconds) in relation to the "fixed" star background. The positioning of a celestial object by the horizontal system varies with time, but is a useful coordinate system for locating and tracking objects for observers on earth. It is based on the position of stars relative to an observer's ideal horizon.
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| ===Equatorial system===
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| {{Main|Equatorial coordinate system}}
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| [[File:Hipparcos Catalogue equirectangular plot.svg|thumb|300px|Equirectangular plot of [[declination]] vs [[right ascension]] of stars brighter than [[apparent magnitude]] 5 relative to the modern constellations, ecliptic and Milky Way (fuzzy band). To approximate the view of the night sky, right ascension increases from right to left.]]
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| The ''equatorial'' coordinate system is centered at Earth's center, but fixed relative to distant stars and galaxies. The coordinates are based on the location of stars relative to Earth's equator if it were projected out to an infinite distance. The equatorial describes the sky as seen from the solar system, and modern star maps almost exclusively use equatorial coordinates.
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| The ''equatorial'' system is the normal coordinate system for most professional and many amateur astronomers having an equatorial mount that follows the movement of the sky during the night. Celestial objects are found by adjusting the telescope's or other instrument's scales so that they match the equatorial coordinates of the selected object to observe.
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| Popular choices of pole and equator are the older [[B1950]] and the modern [[J2000]] systems, but a pole and equator "of date" can also be used, meaning one appropriate to the date under consideration, such as when a measurement of the position of a planet or spacecraft is made. There are also subdivisions into "mean of date" coordinates, which average out or ignore [[nutation]], and "true of date," which include nutation.
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| ===Ecliptic system===
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| {{Main|Ecliptic coordinate system}}
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| The ecliptic system was the principal coordinate system for ancient astronomy and is still useful for computing the apparent motions of the Sun, Moon, and planets.<ref>[[Asger Aaboe|Aaboe, Asger]]. 2001 ''Episodes from the Early History of Astronomy.'' New York: Springer-Verlag., pp. 17-19.</ref> | |
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| The ecliptic system describes the planets' orbital movement around the sun, and centers on the [[Center_of_mass#Barycenter_in_astrophysics_and_astronomy|barycenter]] of the solar system (i.e. very close to the sun). The fundamental plane is the plane of the Earth's orbit, called the ecliptic plane. The system is primarily used for computing the positions of planets and other solar system bodies, as well as defining their [[orbital elements]].
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| ===Galactic system=== | |
| {{Main|Galactic coordinate system}}
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| The galactic coordinate system uses the approximate plane of our galaxy as its fundamental plane. The solar system is still the center of the coordinate system, and the zero point is defined as the direction towards the galactic center. Galactic latitude resembles the elevation above the galactic plane and galactic longitude determines direction relative to the center of the galaxy.
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| ===Supergalactic system===
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| {{Main|Supergalactic coordinate system}}
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| The supergalactic coordinate system corresponds to a fundamental plane that contains a higher than average number of local galaxies in the sky as seen from Earth.
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| == Converting coordinates ==
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| {{see also|Euler angles|Rotation matrix}}
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| Conversions between the various coordinate systems are given.<ref>
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| {{cite book
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| | last = Meeus
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| | first = Jean
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| | title = Astronomical Algorithms
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| | publisher = Willmann-Bell, Inc., Richmond, VA
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| | year = 1991
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| |ISBN=0-943396-35-2 }}, chap. 12
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| </ref>
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| See the [[Celestial_coordinates#Notes_on_conversion|notes]] before using these equations.
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| === Notation ===
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| *Horizontal coordinates
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| ** {{math|''A''}} - [[azimuth]]
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| ** {{math|''a''}} - [[Horizontal coordinate system|altitude]]
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| *Equatorial coordinates
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| ** {{math|''α''}} - [[right ascension]]
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| ** {{math|''δ''}} - [[declination]]
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| ** {{math|''h''}} - [[hour angle]]
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| *Ecliptic coordinates
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| ** {{math|''λ''}} - [[ecliptic longitude]]
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| ** {{math|''β''}} - [[ecliptic latitude]]
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| *Galactic coordinates
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| ** {{math|''l''}} - [[galactic longitude]]
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| ** {{math|''b''}} - [[galactic latitude]]
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| *Miscellaneous
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| ** {{math|''λ''<sub>''o''</sub>}} - [[longitude|observer's longitude]]
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| ** {{math|''φ''<sub>''o''</sub>}} - [[latitude|observer's latitude]]
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| ** {{math|''ε''}} - [[Axial_tilt#Obliquity_of_the_ecliptic_.28Earth.27s_axial_tilt.29|obliquity of the ecliptic]]
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| ** {{math|''θ''<sub>''L''</sub>}} - [[sidereal time|local sidereal time]]
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| ** {{math|''θ''<sub>''G''</sub>}} - [[sidereal time|Greenwich sidereal time]]
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| === Hour angle ←→ right ascension === | |
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| :<math>h = \theta_L - \alpha </math> or <math> h = \theta_G - \lambda_o - \alpha</math>
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| :<math>\alpha = \theta_L - h </math> or <math> \alpha = \theta_G - \lambda_o - h</math> | |
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| === Equatorial ←→ ecliptical ===
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| The classical equations, derived from [[spherical trigonometry]], for the longitudinal coordinate are presented to the right of a bracket; simply dividing the first equation by the second gives the convenient tangent equation seen on the left.<ref>
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| {{cite book
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| | last1 = U.S. Naval Observatory
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| | first1=Nautical Almanac Office
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| | last2 = H.M. Nautical Almanac Office
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| | title = Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac
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| | publisher = H.M. Stationery Office, London
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| | year = 1961}}, sec. 2A
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| </ref> The rotation matrix equivalent is given beneath each case.<ref> | |
| {{cite book
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| | last1 = U.S. Naval Observatory
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| | first1=Nautical Almanac Office
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| | editor = P. Kenneth Seidelmann
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| | title = Explanatory Supplement to the Astronomical Almanac
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| | publisher = University Science Books, Mill Valley, CA
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| | year = 1992
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| | isbn = 0-935702-68-7}}, section 11.43
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| </ref> (This division is lossy because the tan has a period of 180° whereas the cos and sin have periods of 360°.)
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| :<math>\tan\lambda = {\sin\alpha \cos\epsilon + \tan\delta \sin\epsilon \over \cos\alpha}; \qquad\qquad \begin{cases} | |
| \cos\beta \sin\lambda = \cos\delta \sin\alpha \cos\epsilon + \sin\delta \sin\epsilon; \\
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| \cos\beta \cos\lambda = \cos\delta \cos\alpha.
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| \end{cases}</math>
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| :<math>\sin\beta = \sin\delta \cos\epsilon - \cos\delta \sin\epsilon \sin\alpha</math>. | |
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|
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| :<math>\begin{bmatrix}
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| \cos\beta\cos\lambda\\
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| \cos\beta\sin\lambda\\
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| \sin\beta
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| \end{bmatrix} = \begin{bmatrix}
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| 1 & 0 & 0 \\
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| 0 & \cos\epsilon & \sin\epsilon\\
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| 0 & -\sin\epsilon & \cos\epsilon
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| \end{bmatrix}\begin{bmatrix}
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| \cos\delta\cos\alpha\\
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| \cos\delta\sin\alpha\\
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| \sin\delta
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| \end{bmatrix}</math>.
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|
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| :<math>\tan\alpha = {\sin\lambda \cos\epsilon - \tan\beta \sin\epsilon \over \cos\lambda} ; \qquad\qquad \begin{cases}
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| \cos\delta \sin\alpha = \cos\beta \sin\lambda \cos\epsilon - \sin\beta \sin\epsilon; \\
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| \cos\delta \cos\alpha = \cos\beta \cos\lambda.
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| \end{cases}</math>
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| :<math>\sin\delta = \sin\beta \cos\epsilon + \cos\beta \sin\epsilon \sin\lambda</math>.
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|
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| :<math>\begin{bmatrix}
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| \cos\delta\cos\alpha\\
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| \cos\delta\sin\alpha\\
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| \sin\delta
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| \end{bmatrix} = \begin{bmatrix}
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| 1 & 0 & 0 \\
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| 0 & \cos\epsilon & -\sin\epsilon\\
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| 0 & \sin\epsilon & \cos\epsilon
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| \end{bmatrix}\begin{bmatrix}
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| \cos\beta\cos\lambda\\
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| \cos\beta\sin\lambda\\
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| \sin\beta
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| \end{bmatrix}</math>.
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| === Equatorial ←→ horizontal === | |
| Note that Azimuth (A) is measured from the South point, turning positive to the West.<ref>
| |
| {{cite book
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| | last1 = Montenbruck
| |
| | first1 = Oliver
| |
| | last2 = Pfleger
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| | first2 = Thomas
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| | title = Astronomy on the Personal Computer
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| | publisher = Springer-Verlag Berlin Heidelberg
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| | year = 2000
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| | ISBN = 978-3-540-67221-0}},pp 35-37</ref>
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| Zenith distance, the angular distance along the [[great circle]] from the [[zenith]] to a celestial object, is simply the [[Complementary angles|complementary angle]] of the altitude: 90° − {{math|''a''}}.<ref>
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| {{cite book
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| | last1 = U.S. Naval Observatory
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| | first1=Nautical Almanac Office
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| | first2 = H.M. Nautical Almanac Office
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| | last2 = U.K. Hydrographic Office
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| | title = The Astronomical Almanac for the Year 2010
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| | publisher = U.S. Govt. Printing Office
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| | year = 2008
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| |ISBN = 978-0160820083
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| |page=M18}}
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| </ref>
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| :<math>\tan A = {\sin h \over \cos h \sin\phi_o - \tan\delta \cos\phi_o} \qquad\qquad \begin{cases}
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| \cos a \sin A = \cos\delta \sin h \\
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| \cos a \cos A = \cos\delta \cos h \sin\phi_o - \sin\delta \cos\phi_o
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| \end{cases}</math>
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|
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| :<math>\sin a = \sin\phi_o \sin\delta + \cos\phi_o \cos\delta \cos h</math>
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| :<math>\begin{bmatrix}
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| \cos a \cos A\\
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| \cos a \sin A\\
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| \sin a
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| \end{bmatrix} = \begin{bmatrix}
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| \sin\phi_o & 0 & -\cos\phi_o \\
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| 0 & 1 & 0\\
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| \cos\phi_o & 0 & \sin\phi_o
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| \end{bmatrix}\begin{bmatrix}
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| \cos\delta\cos h\\
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| \cos\delta\sin h\\
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| \sin\delta
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| \end{bmatrix}</math>
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|
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| :<math>\tan h = {\sin A \over \cos A \sin\phi_o + \tan a \cos\phi_o} \qquad\qquad \begin{cases}
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| \cos\delta \sin h = \cos a \sin A \\
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| \cos\delta \cos h = \sin a \cos\phi_o + \cos a \cos A \sin\phi_o
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| \end{cases}</math>
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|
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| :<math>\sin\delta = \sin\phi_o \sin a - \cos\phi_o \cos a \cos A</math><ref> | |
| Depending on the azimuth convention in use, the signs of cos{{math|''A''}} and sin{{math|''A''}} appear in all four different combinations. Karttunen et al., Taff and Roth define {{math|''A''}} clockwise from the south. Lang defines it north through east, Smart north through west. Meeus (1991), p. 89: sin {{math|''δ''}} = sin {{math|''φ''}} sin {{math|''a''}} − cos {{math|''φ''}} cos {{math|''a''}} cos {{math|''A''}}; ''Explanatory Supplement'' (1961), p. 26: sin {{math|''δ''}} = sin {{math|''a''}} sin {{math|''φ''}} + cos {{math|''a''}} cos {{math|''A''}} cos {{math|''φ''}}.
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| </ref> | |
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|
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| :<math> \begin{bmatrix}
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| \cos\delta\cos h\\
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| \cos\delta\sin h\\
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| \sin\delta
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| \end{bmatrix}= \begin{bmatrix}
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| \sin\phi_o & 0 & \cos\phi_o \\
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| 0 & 1 & 0\\
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| -\cos\phi_o & 0 & \sin\phi_o
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| \end{bmatrix}\begin{bmatrix}
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| \cos a \cos A\\
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| \cos a \sin A\\
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| \sin a
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| \end{bmatrix}</math>
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| === Equatorial ←→ galactic ===
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| These equations are for converting equatorial coordinates referred to [[Epoch (astronomy)|B1950.0]]. If the equatorial coordinates are referred to another [[equinox]], they must be [[Axial precession|precessed]] to their place at B1950.0 before applying these formulae.
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| :<math>l = 303^\circ - \arctan\left({\sin(192^\circ.25 - \alpha) \over \cos(192^\circ.25 - \alpha) \sin 27^\circ.4 - \tan\delta \cos 27^\circ.4}\right)</math>
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| :<math>\sin b = \sin\delta \sin 27^\circ.4 + \cos\delta \cos 27^\circ.4 \cos (192^\circ.25 - \alpha)</math>
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| These equations convert to equatorial coordinates referred to [[Epoch (astronomy)|B1950.0]].
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| :<math>\alpha = \arctan\left({\sin(l - 123^\circ) \over \cos(l - 123^\circ) \sin 27^\circ.4 - \tan b \cos 27^\circ.4}\right) + 12^\circ.25</math>
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| :<math>\sin\delta = \sin b \sin 27^\circ.4 + \cos b \cos 27^\circ.4 \cos (l - 123^\circ)</math>
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| === Notes on conversion ===
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| * Angles in the degrees ( ° ), minutes ( ' ), and seconds ( " ) of [[Minute of arc|sexagesimal measure]] must be converted to decimal before calculations are performed. Whether they are converted to decimal [[Degree (angle)|degrees]] or [[radian]]s depends upon the particular calculating machine or program. Negative angles must be carefully handled; −10° 20' 30" must be converted as −10° −20' −30".
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| * Angles in the hours ( <sup>h</sup> ), minutes ( <sup>m</sup> ), and seconds ( <sup>s</sup> ) of time measure must be converted to decimal [[Degree (angle)|degrees]] or [[radian]]s before calculations are performed. 1<sup>h</sup> = 15° 1<sup>m</sup> = 15' 1<sup>s</sup> = 15"
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| * Angles greater than 360° ({{math|2''π''}}) or less than 0° may need to be reduced to the range 0° - 360° (0 - {{math|2''π''}}) depending upon the particular calculating machine or program.
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| * [[Inverse trigonometric functions]] arcsine, arccosine and arctangent are [[Quadrant (plane geometry)|quadrant]]-ambiguous, and results should be carefully evaluated. Use of an equation which finds the [[Trigonometric functions|tangent]], followed by the [[Atan2|second arctangent function]] (ATN2 or ATAN2), is recommended when calculating longitude/right ascension/azimuth. An equation which finds the [[Trigonometric functions|sine]], followed by the [[Inverse trigonometric functions|arcsin function]], is recommended when calculating latitude/declination/altitude.
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| * Azimuth ({{math|''A''}}) is referred here to the south point of the [[horizon]], the common astronomical reckoning. An object on the [[Meridian (astronomy)|meridian]] to the south of the observer has {{math|''A''}} = {{math|''h''}} = 0° with this usage. In [[navigation]] and some other disciplines, azimuth is figured from the north.
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| * The equations for altitude ({{math|''a''}}) do not account for [[atmospheric refraction]].
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| * The equations for horizontal coordinates do not account for [[parallax|diurnal parallax]], that is, the small offset in the position of a celestial object caused by the position of the observer on the [[Earth]]'s surface. This effect is significant for the [[Moon]], less so for the [[planet]]s, minute for [[star]]s or more distant objects.
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| * Observer's longitude ({{math|''λ''<sub>''o''</sub>}}) here is measured positively westward from the [[prime meridian]]; this is contrary to current [[International Astronomical Union|IAU]] standards.
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| ==See also==
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| *[[Azimuth]]
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| *[[Celestial sphere]]
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| *[[Orbital elements]]
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| *[[Spherical coordinate system]]
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| ==Notes and references==
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| {{Reflist}}
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| * {{cite book|first1=William Marshall |last1=Smart
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| |title=Text-book on spherical astronomy
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| |publisher=Cambridge University Press
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| |year=1949
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| |bibcode=1965tbsa.book.....S
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| }}
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| * {{cite book| first1= Kenneth R. |last1=Lang
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| |title=Astrophysical Formulae
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| |year=1978
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| |publisher=Springer
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| |isbn=3-540-09064-9
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| |bibcode=1978afcp.book.....L
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| }}
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| *{{cite book|first1=L. G. |last1=Taff
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| |title =Computational spherical astronomy
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| |year=1980
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| |publisher=Wiley
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| |bibcode=1981csa..book.....T
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| }}
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| * {{cite book| first1=H. |last1=Karttunen
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| |first2=P. |last2=Kröger
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| |first3=H. |last3=Oja
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| |first4=M. |last4=Poutanen
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| |first5=H. J. |last5=Donner
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| |title=Fundamental Astronomy
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| |year=2006
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| |isbn=978-3-540-34143-7
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| |bibcode=2003fuas.book.....K
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| }}
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| * {{cite book|first1=G. D. |last1=Roth
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| |title=Handbuch für Sternenfreunde
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| |isbn=3-540-19436-3
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| |publisher=Springer
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| }}
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| ==External links==
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| {{Commons category|Celestial coordinate systems}}
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| * [http://aa.usno.navy.mil/software/novas/novas_info.php NOVAS], the [http://www.usno.navy.mil/USNO/ U.S. Naval Observatory's] Vector Astrometry Software, an integrated package of subroutines and functions for computing various commonly needed quantities in positional astronomy.
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| * [http://www.iausofa.org/ SOFA], the [http://www.iau.org/ IAU's] Standards of Fundamental Astronomy, an accessible and authoritative set of algorithms and procedures that implement standard models used in fundamental astronomy.
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| * ''This article was originally based on Jason Harris' Astroinfo, which comes along with [[KStars]], a [http://edu.kde.org/kstars/ KDE Desktop Planetarium] for [[Linux]]/[[KDE]].''
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| {{Celestial coordinate systems}}
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| [[Category:Celestial coordinate system| ]]
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| {{Link GA|sr}}
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