Celestial coordinate system

In astronomy, a celestial coordinate system (or celestial reference system) is a system for specifying positions of celestial objects: satellites, planets, stars, galaxies, and so on. Coordinate systems can specify an object's position in three-dimensional space or plot merely its direction on a celestial sphere, if the object's distance is unknown or trivial.

The coordinate systems are implemented in either spherical or rectangular coordinates. Spherical coordinates, projected on the celestial sphere, are analogous to the geographic coordinate system used on the surface of Earth. These differ in their choice of fundamental plane, which divides the celestial sphere into two equal hemispheres along a great circle. Rectangular coordinates, in appropriate units, are simply the cartesian equivalent of the spherical coordinates, with the same fundamental (x, y) plane and primary (x-axis) direction. Each coordinate system is named after its choice of fundamental plane.

Orientation of astronomical coordinates
Ecliptic equator galactic anim
A star's      galactic,      ecliptic, and      equatorial coordinates, as projected on the celestial sphere. Ecliptic and equatorial coordinates share the      vernal equinox as the primary direction, and galactic coordinates are referred to the      galactic center. The origin of coordinates (the "center of the sphere") is ambiguous; see celestial sphere for more information.

Coordinate systems

The following table lists the common coordinate systems in use by the astronomical community. The fundamental plane divides the celestial sphere into two equal hemispheres and defines the baseline for the latitudinal coordinates, similar 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 longitudinal 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.

Coordinate system[1] Center point
(origin)
Fundamental plane
(0° latitude)
Poles Coordinates Primary direction
(0° longitude)
Latitude Longitude
Horizontal (also called alt-az or el-az) Observer Horizon Zenith, nadir Altitude (a) or elevation Azimuth (A) North or south point of horizon
Equatorial Center of the Earth (geocentric), or Sun (heliocentric) Celestial equator Celestial poles Declination (δ) Right ascension (α)
or hour angle (h)
Vernal equinox
Ecliptic Ecliptic Ecliptic poles Ecliptic latitude (β) Ecliptic longitude (λ)
Galactic Center of the Sun Galactic plane Galactic poles Galactic latitude (b) Galactic longitude (l) Galactic center
Supergalactic Supergalactic plane Supergalactic poles Supergalactic latitude (SGB) Supergalactic longitude (SGL) Intersection of supergalactic plane and galactic plane

Horizontal system

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 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.

Equatorial system

The equatorial coordinate system is centered at Earth's center, but fixed relative to the celestial poles and the vernal equinox. 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.

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.

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.

Ecliptic system

The fundamental plane is the plane of the Earth's orbit, called the ecliptic plane. There are two principal variants of the ecliptic coordinate system: geocentric ecliptic coordinates centered on the Earth and heliocentric ecliptic coordinates centered on the center of mass of the solar system.

The geocentric 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.[2]

The heliocentric ecliptic system describes the planets' orbital movement around the Sun, and centers on the barycenter of the solar system (i.e. very close to the center of the Sun). The system is primarily used for computing the positions of planets and other solar system bodies, as well as defining their orbital elements.

Galactic system

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.

Supergalactic system

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.

Converting coordinates

Conversions between the various coordinate systems are given.[3] See the notes before using these equations.

Notation

Hour angle ↔ right ascension

Equatorial ↔ ecliptic

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.[4] The rotation matrix equivalent is given beneath each case.[5] This division is ambiguous because tan has a period of 180° (π) whereas cos and sin have periods of 360° (2π).

Equatorial ↔ horizontal

Note that azimuth (A) is measured from the south point, turning positive to the west.[6] Zenith distance, the angular distance along the great circle from the zenith to a celestial object, is simply the complementary angle of the altitude: 90° − a.[7]

In solving the tan(A) equation for A, in order to avoid the ambiguity of the arctangent, use of the two-argument arctangent, denoted arctan(x,y), is recommended. The two-argument arctangent computes the arctangent of y/x, and accounts for the quadrant in which it is being computed. Thus, consistent with the convention of azimuth being measured from the south and opening positive to the west,

,

where

.

If the above formula produces a negative value for A, it can be rendered positive by simply adding 360°.

[8]

Again, in solving the tan(h) equation for h, use of the two-argument arctangent that accounts for the quadrant is recommended. Thus, again consistent with the convention of azimuth being measured from the south and opening positive to the west,

,

where

Equatorial ↔ galactic

These equations[9] are for converting equatorial coordinates to Galactic coordinates.

are the equatorial coordinates of the North Galactic Pole and is the Galactic longitude of the North Celestial Pole. Referred to J2000.0 the values of these quantities are:

If the equatorial coordinates are referred to another equinox, they must be precessed to their place at J2000.0 before applying these formulae.

These equations convert to equatorial coordinates referred to B2000.0.

Notes on conversion

  • Angles in the degrees ( ° ), minutes ( ′ ), and seconds ( ″ ) of sexagesimal measure must be converted to decimal before calculations are performed. Whether they are converted to decimal degrees or radians depends upon the particular calculating machine or program. Negative angles must be carefully handled; –10° 20′ 30″ must be converted as −10° −20′ −30″.
  • Angles in the hours ( h ), minutes ( m ), and seconds ( s ) of time measure must be converted to decimal degrees or radians before calculations are performed. 1h = 15°; 1m = 15′; 1s = 15″
  • Angles greater than 360° (2π) or less than 0° may need to be reduced to the range 0°−360° (0−2π) depending upon the particular calculating machine or program.
  • The cosine of a latitude (declination, ecliptic and Galactic latitude, and altitude) are always positive by definition, since the latitude varies between −90° and +90°.
  • Inverse trigonometric functions arcsine, arccosine and arctangent are quadrant-ambiguous, and results should be carefully evaluated. Use of the second arctangent function (denoted in computing as atn2(y,x) or atan2(y,x), which calculates the arctangent of y/x using the sign of both arguments to determine the right quadrant) is recommended when calculating longitude/right ascension/azimuth. An equation which finds the sine, followed by the arcsin function, is recommended when calculating latitude/declination/altitude.
  • Azimuth (A) is referred here to the south point of the horizon, the common astronomical reckoning. An object on the meridian to the south of the observer has A = h = 0° with this usage. However, n Astropy's AltAz, in the Large Binocular Telescope FITS file convention, and in XEphem for example, the azimuth is East of North. In navigation and some other disciplines, azimuth is figured from the north.
  • The equations for altitude (a) do not account for atmospheric refraction.
  • The equations for horizontal coordinates do not account for 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 planets, minute for stars or more distant objects.
  • Observer's longitude (λo) here is measured positively westward from the prime meridian; this is contrary to current IAU standards.

See also

Notes and references

  1. ^ Majewski, Steve. "Coordinate Systems". UVa Department of Astronomy. Retrieved 19 March 2011.
  2. ^ Aaboe, Asger. 2001 Episodes from the Early History of Astronomy. New York: Springer-Verlag., pp. 17–19.
  3. ^ Meeus, Jean (1991). Astronomical Algorithms. Willmann-Bell, Inc., Richmond, VA. ISBN 0-943396-35-2., chap. 12
  4. ^ U.S. Naval Observatory, Nautical Almanac Office; H.M. Nautical Almanac Office (1961). Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac. H.M. Stationery Office, London., sec. 2A
  5. ^ U.S. Naval Observatory, Nautical Almanac Office (1992). P. Kenneth Seidelmann, ed. Explanatory Supplement to the Astronomical Almanac. University Science Books, Mill Valley, CA. ISBN 0-935702-68-7., section 11.43
  6. ^ Montenbruck, Oliver; Pfleger, Thomas (2000). Astronomy on the Personal Computer. Springer-Verlag Berlin Heidelberg. ISBN 978-3-540-67221-0., pp 35-37
  7. ^ U.S. Naval Observatory, Nautical Almanac Office; U.K. Hydrographic Office, H.M. Nautical Almanac Office (2008). The Astronomical Almanac for the Year 2010. U.S. Govt. Printing Office. p. M18. ISBN 978-0160820083.
  8. ^ Depending on the azimuth convention in use, the signs of cos A and sin A appear in all four different combinations. Karttunen et al., Taff and Roth define A clockwise from the south. Lang defines it north through east, Smart north through west. Meeus (1991), p. 89: sin δ = sin φ sin a − cos φ cos a cos A; Explanatory Supplement (1961), p. 26: sin δ = sin a sin φ + cos a cos A cos φ.
  9. ^ Poleski, Radosław. "Transformation of the equatorial proper motion to the Galactic system" (PDF).

External links

  • NOVAS, the U.S. Naval Observatory's Vector Astrometry Software, an integrated package of subroutines and functions for computing various commonly needed quantities in positional astronomy.
  • SOFA, the IAU's Standards of Fundamental Astronomy, an accessible and authoritative set of algorithms and procedures that implement standard models used in fundamental astronomy.
  • This article was originally based on Jason Harris' Astroinfo, which comes along with KStars, a KDE Desktop Planetarium for Linux/KDE.
Almucantar

An almucantar (also spelled almucantarat or almacantara) is a circle on the celestial sphere parallel to the horizon. Two stars that lie on the same almucantar have the same altitude.

The term was introduced into European astronomy by monastic astronomer Hermann Contractus of Reichenau, Latinized from the Arabic word al-muqanṭarah ("the almucantar, sundial", plural: al-muqanṭarāt), derived from qanṭarah ("arch, bridge")

Celestial equator

The celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. This plane of reference bases the equatorial coordinate system. In other words, the celestial equator is an abstract projection of the terrestrial equator into outer space. Due to Earth's axial tilt, the celestial equator is currently inclined by about 23.44° with respect to the ecliptic (the plane of Earth's orbit).

An observer standing on Earth's equator visualizes the celestial equator as a semicircle passing through the zenith, the point directly overhead. As the observer moves north (or south), the celestial equator tilts towards the opposite horizon. The celestial equator is defined to be infinitely distant (since it is on the celestial sphere); thus, the ends of the semicircle always intersect the horizon due east and due west, regardless of the observer's position on Earth. (At the poles, the celestial equator coincides with the astronomical horizon.) At all latitudes, the celestial equator is a uniform arc or circle because the observer is only finitely far from the plane of the celestial equator, but infinitely far from the celestial equator itself.Astronomical objects near the celestial equator appear above the horizon from most places on earth, but they culminate (reach the meridian) highest near the equator. The celestial equator currently passes through these constellations:

These, by definition, are the most globally visible constellations.

Celestial bodies other than Earth also have similarly defined celestial equators.

Celestial sphere

In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, which may be centered on Earth or the observer. If centered on the observer, half of the sphere would resemble a hemispherical screen over the observing location.

The celestial sphere is a practical tool for spherical astronomy, allowing astronomers to specify the apparent positions of objects in the sky if their distances are unknown or irrelevant. In the equatorial coordinate system, the celestial equator divides the celestial sphere into two halves: the northern and southern celestial hemispheres.

Declination

In astronomy, declination (abbreviated dec; symbol δ) is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. Declination's angle is measured north or south of the celestial equator, along the hour circle passing through the point in question.

The root of the word declination (Latin, declinatio) means "a bending away" or "a bending down". It comes from the same root as the words incline ("bend toward") and recline ("bend backward").In some 18th and 19th century astronomical texts, declination is given as North Pole Distance (N.P.D.), which is equivalent to 90 - (declination). For instance an object marked as declination -5 would have a NPD of 95, and a declination of -90 (the south celestial pole) would have a NPD of 180.

Ecliptic coordinate system

The ecliptic coordinate system is a celestial coordinate system commonly used for representing the apparent positions and orbits of Solar System objects. Because most planets (except Mercury) and many small Solar System bodies have orbits with slight inclinations to the ecliptic, using it as the fundamental plane is convenient. The system's origin can be the center of either the Sun or Earth, its primary direction is towards the vernal (northward) equinox, and it has a right-hand convention. It may be implemented in spherical or rectangular coordinates.

Equatorial coordinate system

The equatorial coordinate system is a celestial coordinate system widely used to specify the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the centre of Earth, a fundamental plane consisting of the projection of Earth's equator onto the celestial sphere (forming the celestial equator), a primary direction towards the vernal equinox, and a right-handed convention.The origin at the center of Earth means the coordinates are geocentric, that is, as seen from the centre of Earth as if it were transparent. The fundamental plane and the primary direction mean that the coordinate system, while aligned with Earth's equator and pole, does not rotate with the Earth, but remains relatively fixed against the background stars. A right-handed convention means that coordinates increase northward from and eastward around the fundamental plane.

Equinox (celestial coordinates)

In astronomy, equinox is either of two places on the celestial sphere at which the ecliptic intersects the celestial equator. Although there are two intersections of the ecliptic with the celestial equator, by convention the equinox associated with the sun's ascending node is used as the origin of celestial coordinate systems and referred to simply as the equinox. In contrast to the common usage of spring and fall, or vernal and autumnal, equinoxes, the celestial coordinate system equinox is a direction in space rather than a moment in time.

The equinox moves because of perturbing forces, therefore in order to define a coordinate system it is necessary to specify the date for which the equinox is chosen. This date should not be confused with the epoch. Astronomical objects show real movements such as orbital and proper motions, and the epoch defines the date for which the position of an object applies. Therefore a complete specification of the coordinates for an astronomical objects requires both the date of the equinox and of the epoch.The currently used standard equinox and epoch is J2000.0, which is January 1, 2000 at 12:00 TT. The prefix "J" indicates that it is a Julian epoch. The previous standard equinox and epoch was B1950.0, with the prefix "B" indicating it was a Besselian epoch. Before 1984 Besselian equinoxes and epochs were used. Since that time Julian equinoxes and epochs have been used.

Galactic coordinate system

The galactic coordinate system is a celestial coordinate system in spherical coordinates, with the Sun as its center, the primary direction aligned with the approximate center of the Milky Way galaxy, and the fundamental plane parallel to an approximation of the galactic plane but offset to its north. It uses the right-handed convention, meaning that coordinates are positive toward the north and toward the east in the fundamental plane.

Galactic quadrant

A galactic quadrant, or quadrant of the Galaxy, is one of four circular sectors in the division of the Milky Way Galaxy.

Horizontal coordinate system

The horizontal coordinate system, also known as topocentric coordinate system, is a celestial coordinate system that uses the observer's local horizon as the fundamental plane. Coordinates of an object in the sky are expressed in terms of altitude (or elevation) angle and azimuth.

International Celestial Reference System

The International Celestial Reference System (ICRS) is the current standard celestial reference system adopted by the International Astronomical Union (IAU). Its origin is at the barycenter of the Solar System, with axes that are intended to be "fixed" with respect to space. ICRS coordinates are approximately the same as equatorial coordinates: the mean pole at J2000.0 in the ICRS lies at 17.3±0.2 mas in the direction 12 h and 5.1±0.2 mas in the direction 18 h. The mean equinox of J2000.0 is shifted from the ICRS right ascension origin by 78±10 mas (direct rotation around the polar axis).

The defining extragalactic reference frame of the ICRS is the International Celestial Reference Frame (currently ICRF2) based on hundreds of extra-galactic radio sources, mostly quasars, distributed around the entire sky. Because they are so distant, they are apparently stationary to our current technology, yet their positions can be measured with the utmost accuracy by Very Long Baseline Interferometry (VLBI). The positions of most are known to 0.001 arcsecond or better, which is orders of magnitude more precise than the best optical measurements. At optical wavelengths, the ICRS is currently realized by the Hipparcos Celestial Reference Frame (HCRF), a subset of about 100,000 stars in the Hipparcos Catalogue. A more accurate optical realization of the ICRS (Gaia-CRF2), based on the observation by the Gaia spacecraft of almost 500,000 extragalactic objects believed to be quasars, is under preparation.

Meridian (astronomy)

In astronomy, the meridian is the great circle passing through the celestial poles, as well as the zenith and nadir of an observer's location. Consequently, it contains also the north and south points on the horizon, and it is perpendicular to the celestial equator and horizon. A celestial meridian is coplanar with the analogous terrestrial meridian projected onto the celestial sphere. Hence, the number of celestial meridians is also infinite.

The celestial meridian is undefined when the observer is at the geographical poles, since at these two points, the zenith and nadir are on the celestial poles, and any great circle passing through the celestial poles also passes through the zenith and nadir.

There are several ways to divide the meridian into semicircles. In the horizontal coordinate system, the observer's meridian is divided into halves terminated by the horizon's north and south points. The observer's upper meridian passes through the zenith while the lower meridian passes through the nadir. Another way, the meridian is divided into the local meridian, the semicircle that contains the observer's zenith and both celestial poles, and the opposite semicircle, which contains the nadir and both poles.

On any given (sidereal) day/night, a celestial object will appear to drift across, or transit, the observer's upper meridian as Earth rotates, since the meridian is fixed to the local horizon. At culmination, the object contacts the upper meridian and reaches its highest point in the sky. An object's right ascension and the local sidereal time can be used to determine the time of its culmination (see hour angle).

The term meridian comes from the Latin meridies, which means both "midday" and "south", as the celestial equator appears to tilt southward from the Northern Hemisphere.

Nadir

The nadir (UK: , US: ; from Arabic: نظير‎ / ALA-LC: naẓīr, meaning "counterpart") is the direction pointing directly below a particular location; that is, it is one of two vertical directions at a specified location, orthogonal to a horizontal flat surface there. Since the concept of being below is itself somewhat vague, scientists define the nadir in more rigorous terms. Specifically, in astronomy, geophysics and related sciences (e.g., meteorology), the nadir at a given point is the local vertical direction pointing in the direction of the force of gravity at that location. The direction opposite the nadir is the zenith.

Northern celestial hemisphere

The northern celestial hemisphere, also called the Northern Sky, is the northern half of the celestial sphere; that is, it lies north of the celestial equator. This arbitrary sphere appears to rotate westward around a polar axis due to Earth's rotation.

At any given time, the entire Northern Sky is visible from the geographic North Pole, while less of this hemisphere is visible the further south the observer is located. The southern counterpart is the southern celestial hemisphere.

Poles of astronomical bodies

The poles of astronomical bodies are determined based on their axis of rotation in relation to the celestial poles of the celestial sphere. Astronomical bodies include stars, planets, dwarf planets and small Solar System bodies such as comets and minor planets (i.e. asteroids), as well as natural satellites and minor-planet moons.

Right ascension

Right ascension (abbreviated RA; symbol α) is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the (hour circle of the) point above the earth in question.

When paired with declination, these astronomical coordinates specify the direction of a point on the celestial sphere in the equatorial coordinate system.

An old term, right ascension (Latin: ascensio recta) refers to the ascension, or the point on the celestial equator that rises with any celestial object as seen from Earth's equator, where the celestial equator intersects the horizon at a right angle. It contrasts with oblique ascension, the point on the celestial equator that rises with any celestial object as seen from most latitudes on Earth, where the celestial equator intersects the horizon at an oblique angle.

Sidereal year

A sidereal year (from Latin sidus "asterism, star") is the time taken by the Earth to orbit the Sun once with respect to the fixed stars. Hence, it is also the time taken for the Sun to return to the same position with respect to the fixed stars after apparently travelling once around the ecliptic.

It equals 365.256 363 004 SI days for the J2000.0 epoch.The sidereal year differs from the tropical year, "the period of time required for the ecliptic longitude of the sun to increase 360 degrees", due to the precession of the equinoxes.

The sidereal year is 20 min 24.5 s longer than the mean tropical year at J2000.0 (365.242 190 402 SI days).Before the discovery of the precession of the equinoxes by Hipparchus in the Hellenistic period, the difference between sidereal and tropical year was unknown. For naked-eye observation, the shift of the constellations relative to the equinoxes only becomes apparent over centuries or "ages", and pre-modern calendars such as Hesiod's Works and Days would give the times of the year for sowing, harvest, and so on by reference to the first visibility of stars, effectively using the sidereal year.

Southern celestial hemisphere

The southern celestial hemisphere, also called the Southern Sky, is the southern half of the celestial sphere; that is, it lies south of the celestial equator. This arbitrary sphere, on which seemingly fixed stars form constellations, appears to rotate westward around a polar axis due to Earth's rotation.

At any given time, the entire Southern Sky is visible from the geographic South Pole, while less of this hemisphere is visible the further north the observer is located. The northern counterpart is the northern celestial hemisphere.

Zenith

The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e. the direction in which gravity pulls, is toward the nadir. The zenith is the "highest" point on the celestial sphere.

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