Theequatorial coordinate system is acelestial coordinate system widely used to specify the positions ofcelestial objects. It may be implemented inspherical orrectangular coordinates, both defined by anorigin at the centre ofEarth, afundamental plane consisting of theprojection of Earth'sequator onto thecelestial sphere (forming thecelestial equator), a primary direction towards theMarchequinox, and aright-handed convention.[1][2]
The origin at the centre of Earth means the coordinates aregeocentric, that is, as seen from the centre of Earth as if it weretransparent.[3] The fundamental plane and the primary direction mean that the coordinate system, while aligned with Earth'sequator andpole, does not rotate with the Earth, but remains relatively fixed against the backgroundstars. A right-handed convention means that coordinates increase northward from and eastward around the fundamental plane.
This description of theorientation 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 theecliptic, 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.[4]
In order to fix the exact primary direction, these motions necessitate the specification of theequinox of a particular date, known as anepoch, when giving a position. The three most commonly used are:
A position in the equatorial coordinate system is thus typically specifiedtrue 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.[5]
Astar's spherical coordinates are often expressed as a pair,right ascension anddeclination, without adistance 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 thehorizontal coordinate system, 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 withequatorial mounts andsetting circles employ the equatorial coordinate system to find objects. Setting circles in conjunction with astar chart orephemeris allow the telescope to be easily pointed at known objects on the celestial sphere.
The declination symbolδ, (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 terrestriallatitude.[6][7][8]
The right ascension symbolα, (lower case "alpha", abbreviated RA) measures the angular distance of an object eastward along thecelestial equator from the Marchequinox to thehour circle passing through the object. The March equinox point is one of the two points where theecliptic intersects the celestial equator. Right ascension is usually measured insidereal hours, minutes and seconds instead of degrees, a result of the method of measuring right ascensions bytiming the passage of objects across the meridian as theEarth rotates. There are360°/24h = 15° in one hour of right ascension, and 24h of right ascension around the entirecelestial equator.[6][9][10]
When used together, right ascension and declination are usually abbreviated RA/Dec.
Alternatively toright ascension,hour angle (abbreviated HA or LHA,local hour angle), a left-handed system, measures the angular distance of an object westward along thecelestial equator from the observer'smeridian to thehour circle passing through the object. Unlike right ascension, hour angle is always increasing with therotation of Earth. Hour angle may be considered a means of measuring the time since upperculmination, 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 (0h). Onesidereal hour (approximately 0.9973solar hours) later, Earth's rotation will carry the star to the west of the meridian, and its hour angle will be 1h. When calculatingtopocentric phenomena, right ascension may be converted into hour angle as an intermediate step.[11][12][13]
There are a number ofrectangular variants of equatorial coordinates. All have:
The reference frames do not rotate with the Earth (in contrast toEarth-centred, Earth-fixed frames), remaining always directed toward theequinox, and drifting over time with the motions ofprecession andnutation.
In astronomy, there is also a heliocentricrectangular variant of equatorial coordinates, designatedx,y,z, which has:
This frame is similar to theξ,η,ζ frame above, except that the origin is removed to the centre of theSun. It is commonly used in planetary orbit calculation. The three astronomical rectangular coordinate systems are related by[16]
| Spherical | Rectangular | ||||
|---|---|---|---|---|---|
| Right ascension | Declination | Distance | General | Special-purpose | |
| Geocentric | α | δ | Δ | ξ,η,ζ | X,Y,Z (Sun) |
| Heliocentric | x,y,z | ||||
