Astronomical coordinate systems are organized arrangements for specifying positions of
satellites
A satellite or artificial satellite is an object intentionally placed into orbit in outer space. Except for passive satellites, most satellites have an electricity generation system for equipment on board, such as solar panels or radioisotop ...
,
planet
A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a ...
s,
star
A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night, but their immense distances from Earth make ...
s,
galaxies, and other celestial objects relative to physical reference points available to a situated observer (e.g. the true
horizon and north
cardinal direction
The four cardinal directions, or cardinal points, are the four main compass directions: north, east, south, and west, commonly denoted by their initials N, E, S, and W respectively. Relative to north, the directions east, south, and west are a ...
to an observer situated on the Earth's surface).
Coordinate systems in
astronomy
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
can specify an object's position in
three-dimensional space
Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position of an element (i.e., point). This is the informal ...
or
plot
Plot or Plotting may refer to:
Art, media and entertainment
* Plot (narrative), the story of a piece of fiction
Music
* ''The Plot'' (album), a 1976 album by jazz trumpeter Enrico Rava
* The Plot (band), a band formed in 2003
Other
* ''Plot ...
merely its direction on a
celestial sphere, if the object's distance is unknown or trivial.
Spherical coordinates
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the ''radial distance'' of that point from a fixed origin, its ''polar angle'' mea ...
, projected on the
celestial sphere, are analogous to the
geographic coordinate system
The geographic coordinate system (GCS) is a spherical or ellipsoidal coordinate system for measuring and communicating positions directly on the Earth as latitude and longitude. It is the simplest, oldest and most widely used of the vari ...
used on the surface of
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surf ...
. These differ in their choice of
fundamental plane, which divides the celestial sphere into two equal
hemispheres along a
great circle
In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point.
Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geometry ...
.
Rectangular coordinates, in appropriate
units, have the same fundamental () plane and
primary (-axis) direction, such as a
rotation axis. Each coordinate system is named after its choice of fundamental plane.
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
Hemisphere refers to:
* A half of a sphere
As half of the Earth
* A hemisphere of Earth
** Northern Hemisphere
** Southern Hemisphere
** Eastern Hemisphere
** Western Hemisphere
** Land and water hemispheres
* A half of the (geocentric) celestia ...
and defines the baseline for the latitudinal coordinates, similar to the
equator
The equator is a circle of latitude, about in circumference, that divides Earth into the Northern and Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the North and South poles. The term can al ...
in the
geographic coordinate system
The geographic coordinate system (GCS) is a spherical or ellipsoidal coordinate system for measuring and communicating positions directly on the Earth as latitude and longitude. It is the simplest, oldest and most widely used of the vari ...
. 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.
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
March equinox
The March equinox or northward equinox is the equinox on the Earth when the subsolar point appears to leave the Southern Hemisphere and cross the celestial equator, heading northward as seen from Earth. The March equinox is known as the vern ...
. 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
The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...
, 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
In astronomy, an epoch or reference epoch is a moment in time used as a reference point for some time-varying astronomical quantity. It is useful for the celestial coordinates or orbital elements of a celestial body, as they are subject to pertu ...
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
Nutation () is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behaviour of a mechanism. In an appropriate reference fra ...
, 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.
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
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems using a Kepler orbit. There are many different ways to mathematically describe the same ...
.
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.
[
, chap. 12
] See the
notes before using these equations.
Notation
*Horizontal coordinates
** ,
azimuth
An azimuth (; from ar, اَلسُّمُوت, as-sumūt, the directions) is an angular measurement in a spherical coordinate system. More specifically, it is the horizontal angle from a cardinal direction, most commonly north.
Mathematicall ...
** ,
altitude
Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...
*Equatorial coordinates
** ,
right ascension
Right ascension (abbreviated RA; symbol ) 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 in question above the earth.
When pai ...
** ,
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 t ...
** ,
hour angle
*Ecliptic coordinates
** ,
ecliptic longitude
The ecliptic coordinate system is a celestial coordinate system commonly used for representing the apparent positions, orbits, and pole orientations of Solar System objects. Because most planets (except Mercury) and many small Solar System b ...
** ,
ecliptic latitude
*Galactic coordinates
** ,
galactic longitude
** ,
galactic latitude
*Miscellaneous
** ,
observer's longitude
** ,
observer's latitude
** ,
obliquity of the ecliptic (about 23.4°)
** ,
local sidereal time
Sidereal time (as a unit also sidereal day or sidereal rotation period) (sidereal ) is a timekeeper, timekeeping system that astronomers use to locate astronomical object, celestial objects. Using sidereal time, it is possible to easily poin ...
** ,
Greenwich sidereal time
Hour angle ↔ right ascension
:
Equatorial ↔ ecliptic
The classical equations, derived from
spherical trigonometry
Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are grea ...
, 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.
[
, sec. 2A] The rotation matrix equivalent is given beneath each case. This division is ambiguous because tan has a period of 180° () whereas cos and sin have periods of 360° (2).
:
Equatorial ↔ horizontal
Note that azimuth () is measured from the south point, turning positive to the west.
Zenith distance, the angular distance along the
great circle
In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point.
Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geometry ...
from the
zenith
The zenith (, ) is an imaginary point directly "above" a particular location, on the celestial sphere. "Above" means in the vertical direction ( plumb line) opposite to the gravity direction at that location ( nadir). The zenith is the "high ...
to a celestial object, is simply the
complementary angle of the altitude: .
:
In solving the equation for , in order to avoid the ambiguity of the
arctangent
In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains). S ...
, use of the
two-argument arctangent, denoted , is recommended. The two-argument arctangent computes the arctangent of , 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 , it can be rendered positive by simply adding 360°.
:
Again, in solving the equation for , 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
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
A solar equinox is a moment in time when the Sun crosses the Earth's equator, which is to say, appears zenith, directly above the equator, rather than north or south of the equator. On the day of the equinox, the Sun appears to rise "due east" ...
, they must be
precessed
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In othe ...
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
radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before tha ...
s depends upon the particular calculating machine or program. Negative angles must be carefully handled; must be converted as .
* Angles in the hours (
h ), minutes (
m ), and seconds (
s ) of time measure must be converted to decimal
degrees or
radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before tha ...
s before calculations are performed. 1
h = 15°; 1
m = 15′; 1
s = 15″
* Angles greater than 360° (2) or less than 0° may need to be reduced to the range 0°−360° (0–2) depending upon the particular calculating machine or program.
* The cosine of a latitude (declination, ecliptic and Galactic latitude, and altitude) are never negative by definition, since the latitude varies between −90° and +90°.
*
Inverse trigonometric functions
In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains). S ...
arcsine, arccosine and arctangent are
quadrant-ambiguous, and results should be carefully evaluated. Use of the
second arctangent function (denoted in computing as or , which calculates the arctangent of 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
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opp ...
, followed by the
arcsin function, is recommended when calculating latitude/declination/altitude.
* Azimuth () is referred here to the south point of the
horizon, the common astronomical reckoning. An object on the
meridian
Meridian or a meridian line (from Latin ''meridies'' via Old French ''meridiane'', meaning “midday”) may refer to
Science
* Meridian (astronomy), imaginary circle in a plane perpendicular to the planes of the celestial equator and horizon
* ...
to the south of the observer has = = 0° with this usage. However, n
Astropy
Astropy is a collection of software packages written in the Python programming language and designed for use in astronomy.
The software is a single, free, core package for astronomical utilities due to the increasingly widespread usage of Python ...
's AltAz, in the
Large Binocular Telescope
The Large Binocular Telescope (LBT) is an optical telescope for astronomy located on Mount Graham, in the Pinaleno Mountains of southeastern Arizona, United States. It is a part of the Mount Graham International Observatory.
When using both ...
FITS file convention, in
XEphem, in the
IAU
The International Astronomical Union (IAU; french: link=yes, Union astronomique internationale, UAI) is a nongovernmental organisation with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreach ...
library
Standards of Fundamental Astronomy and Section B of the
Astronomical Almanac
''The Astronomical Almanac''The ''Astronomical Almanac'' for the Year 2015, (United States Naval Observatory/Nautical Almanac Office, 2014) . is an almanac published by the United States Naval Observatory (USNO) and His Majesty's Nautical Almana ...
for example, the azimuth is East of North. In
navigation
Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navigation, ...
and some other disciplines, azimuth is figured from the north.
* The equations for altitude () do not account for
atmospheric refraction
Atmospheric refraction is the deviation of light or other electromagnetic wave from a straight line as it passes through the atmosphere due to the variation in air density as a function of height. This refraction is due to the velocity of ligh ...
.
* 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
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surf ...
's surface. This effect is significant for the
Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width ...
, less so for the
planet
A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a ...
s, minute for
star
A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night, but their immense distances from Earth make ...
s or more distant objects.
* Observer's longitude () here is measured positively westward from the
prime meridian
A prime meridian is an arbitrary meridian (a line of longitude) in a geographic coordinate system at which longitude is defined to be 0°. Together, a prime meridian and its anti-meridian (the 180th meridian in a 360°-system) form a great ...
; this is contrary to current
IAU
The International Astronomical Union (IAU; french: link=yes, Union astronomique internationale, UAI) is a nongovernmental organisation with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreach ...
standards.
See also
*
Apparent longitude
Apparent longitude is celestial longitude corrected for aberration and nutation as opposed to ''mean longitude''.
Apparent longitude is used in the definition of equinox and solstice. At equinox, the apparent geocentric celestial longitude of th ...
*
*
*
*
*
*
*
Notes
References
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
The International Astronomical Union (IAU; french: link=yes, Union astronomique internationale, UAI) is a nongovernmental organisation with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreach ...
'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,
KDE Desktop Planetariumfor
Linux
Linux ( or ) is a family of open-source Unix-like operating systems based on the Linux kernel, an operating system kernel first released on September 17, 1991, by Linus Torvalds. Linux is typically packaged as a Linux distribution, which i ...
/
KDE.''
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