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
Projection, projections or projective may refer to:
Physics
* Projection (physics), the action/process of light, heat, or sound reflecting from a surface to another in a different direction
* The display of images by a projector
Optics, graphic ...
of Earth's
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 als ...
onto the
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, ...
(forming the
celestial equator), a primary direction towards the vernal
equinox, and a
right-handed convention.
[
]
The origin at the centre 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
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 als ...
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.
Primary direction
This description of the
orientation
Orientation may refer to:
Positioning in physical space
* Map orientation, the relationship between directions on a map and compass directions
* Orientation (housing), the position of a building with respect to the sun, a concept in building de ...
of the reference frame is somewhat simplified; the orientation is not quite fixed. A slow motion of Earth's axis,
precession, causes a slow, continuous turning of the coordinate system westward about the poles of the
ecliptic, completing one circuit in about 26,000 years. Superimposed on this is a smaller motion of the ecliptic, and a small oscillation of the Earth's axis,
nutation.
In order to fix the exact primary direction, these motions necessitate the specification of the
equinox of a particular date, known as an
epoch, when giving a position. The three most commonly used are:
; Mean equinox of a standard epoch (usually
J2000.0
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 ...
, but may include B1950.0, B1900.0, etc.): is a fixed standard direction, allowing positions established at various dates to be compared directly.
; Mean equinox of date: is the intersection of the ecliptic of "date" (that is, the ecliptic in its position at "date") with the ''mean'' equator (that is, the equator rotated by precession to its position at "date", but free from the small periodic oscillations of nutation). Commonly used in planetary
orbit calculation.
; True equinox of date: is the intersection of the ecliptic of "date" with the ''true'' equator (that is, the mean equator plus nutation). This is the actual intersection of the two planes at any particular moment, with all motions accounted for.
A position in the equatorial coordinate system is thus typically specified ''true equinox and equator of date'', ''mean equinox and equator of J2000.0'', or similar. Note that there is no "mean ecliptic", as the ecliptic is not subject to small periodic oscillations.
Spherical coordinates
Use in astronomy
A
star
A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
's spherical coordinates are often expressed as a pair,
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 paired w ...
and
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 ...
, without a
distance coordinate. The direction of sufficiently distant objects is the same for all observers, and it is convenient to specify this direction with the same coordinates for all. In contrast, in the
horizontal coordinate system
The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane to define two angles: altitude and azimuth.
Therefore, the horizontal coordinate system is sometimes called as th ...
, a star's position differs from observer to observer based on their positions on the Earth's surface, and is continuously changing with the Earth's rotation.
Telescopes equipped with
equatorial mount
An equatorial mount is a mount for instruments that compensates for Earth's rotation by having one rotational axis, the polar axis, parallel to the Earth's axis of rotation. This type of mount is used for astronomical telescopes and cameras. The ...
s and
setting circles employ the equatorial coordinate system to find objects. Setting circles in conjunction with a
star chart
A star chart is a celestial map of the night sky with astronomical objects laid out on a grid system. They are used to identify and locate constellations, stars, nebulae, galaxies, and planets. They have been used for human navigation since ...
or
ephemeris
In astronomy and celestial navigation, an ephemeris (pl. ephemerides; ) is a book with tables that gives the trajectory of naturally occurring astronomical objects as well as artificial satellites in the sky, i.e., the position (and possibly vel ...
allow the telescope to be easily pointed at known objects on the celestial sphere.
Declination
The declination symbol , (lower case "delta", abbreviated DEC) measures the angular distance of an object perpendicular to the celestial equator, positive to the north, negative to the south. For example, the north celestial pole has a declination of +90°. The origin for declination is the celestial equator, which is the projection of the Earth's equator onto the celestial sphere. Declination is analogous to terrestrial
latitude.
[
][
]
Right ascension
The right ascension symbol , (lower case "alpha", abbreviated RA) measures the angular distance of an object eastward along the
celestial equator from the vernal
equinox to the
hour circle passing through the object. The vernal equinox point is one of the two points where the
ecliptic intersects the celestial equator. Right ascension is usually measured in
sidereal hours, minutes and seconds instead of degrees, a result of the method of measuring right ascensions by
timing the passage of objects across the meridian as the
Earth rotates. There are = 15° in one hour of right ascension, and 24
h of right ascension around the entire
celestial equator.
When used together, right ascension and declination are usually abbreviated RA/Dec.
Hour angle
Alternatively to
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 paired w ...
,
hour angle (abbreviated HA or LHA, ''local hour angle''), a left-handed system, measures the angular distance of an object westward along the
celestial equator from the observer's
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
hour circle passing through the object. Unlike right ascension, hour angle is always increasing with the
rotation of Earth
Earth's rotation or Earth's spin is the rotation of planet Earth around its own axis, as well as changes in the orientation of the rotation axis in space. Earth rotates eastward, in prograde motion. As viewed from the northern polar star Pola ...
. Hour angle may be considered a means of measuring the time since upper
culmination
In observational astronomy, culmination is the passage of a celestial object (such as the Sun, the Moon, a planet, a star, constellation or a deep-sky object) across the observer's local meridian. These events were also known as meridian transits ...
, the moment when an object contacts the meridian overhead.
A culminating star on the observer's meridian is said to have a zero hour angle (0
h). One
sidereal hour (approximately 0.9973
solar hours) later, Earth's rotation will carry the star to the west of the meridian, and its hour angle will be 1
h. When calculating
topocentric phenomena, right ascension may be converted into hour angle as an intermediate step.
Rectangular coordinates
Geocentric equatorial coordinates
There are a number of
rectangular variants of equatorial coordinates. All have:
* The
origin at the centre of the
Earth.
* The fundamental
plane
Plane(s) most often refers to:
* Aero- or airplane, a powered, fixed-wing aircraft
* Plane (geometry), a flat, 2-dimensional surface
Plane or planes may also refer to:
Biology
* Plane (tree) or ''Platanus'', wetland native plant
* Planes (gen ...
in the plane of the Earth's equator.
* The primary direction (the axis) toward the vernal
equinox, that is, the place where the
Sun crosses the
celestial equator in a northward direction in its annual apparent circuit around the
ecliptic.
* A
right-handed convention, specifying a axis 90° to the east in the fundamental plane and a axis along the north polar axis.
The reference frames do not rotate with the Earth (in contrast to
Earth-centred, Earth-fixed frames), remaining always directed toward the
equinox, and drifting over time with the motions of
precession and
nutation.
* In
astronomy:
** The
position of the Sun is often specified in the geocentric equatorial rectangular coordinates , , and a fourth distance coordinate, , in units of the
astronomical unit.
** The positions of the
planets
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 young ...
and other
Solar System bodies are often specified in the geocentric equatorial rectangular coordinates , , and a fourth distance coordinate, (equal to ), in units of the
astronomical unit.These rectangular coordinates are related to the corresponding spherical coordinates by
* In
astrodynamics:
** The positions of artificial Earth
satellites are specified in ''geocentric equatorial'' coordinates, also known as ''geocentric equatorial inertial (GEI)'', ''
Earth-centred inertial (ECI)'', and ''conventional inertial system (CIS)'', all of which are equivalent in definition to the astronomical geocentric equatorial rectangular frames, above. In the geocentric equatorial frame, the , and axes are often designated , and , respectively, or the frame's
basis is specified by the
unit vectors , and .
** The ''Geocentric Celestial Reference Frame (GCRF)'' is the geocentric equivalent of the
International Celestial Reference Frame (ICRF). Its primary direction is the
equinox of
J2000.0
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 ...
, and does not move with
precession and
nutation, but it is otherwise equivalent to the above systems.
Heliocentric equatorial coordinates
In
astronomy, there is also a heliocentric
rectangular variant of equatorial coordinates, designated , , , which has:
*The
origin at the centre of the
Sun.
*The fundamental
plane
Plane(s) most often refers to:
* Aero- or airplane, a powered, fixed-wing aircraft
* Plane (geometry), a flat, 2-dimensional surface
Plane or planes may also refer to:
Biology
* Plane (tree) or ''Platanus'', wetland native plant
* Planes (gen ...
in the plane of the Earth's equator.
*The primary direction (the axis) toward the vernal
equinox.
*A
right-handed convention, specifying a axis 90° to the east in the fundamental plane and a axis along
Earth's north polar axis.
This frame is in every way equivalent to the , , frame, above, except that the origin is removed to the centre of the
Sun. It is commonly used in planetary orbit calculation. The three astronomical rectangular coordinate systems are related by
[''Explanatory Supplement'' (1961), pp. 20, 27]
See also
*
Celestial coordinate system
*
Planetary coordinate system
A planetary coordinate system is a generalization of the geographic coordinate system and the geocentric coordinate system for planets other than Earth.
Similar coordinate systems are defined for other solid celestial bodies, such as in the ''selen ...
*
Polar distance
*
Spherical astronomy
Spherical astronomy, or positional astronomy, is a branch of observational astronomy used to locate astronomical objects on the celestial sphere, as seen at a particular date, time, and location on Earth. It relies on the mathematical methods of ...
*
Star position
Star position is the apparent angular position of any given star in the sky, which seems fixed stars, fixed onto an celestial sphere, arbitrary sphere centered on Earth. The location is defined by a pair of celestial coordinate system, angular c ...
References
External links
MEASURING THE SKY A Quick Guide to the Celestial SphereJames B. Kaler, University of Illinois
University of Nebraska-Lincoln
University of Nebraska-Lincoln
{{Portal bar, Astronomy, Stars, Spaceflight, Outer space, Solar System
Astronomical coordinate systems