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.[3] 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.
This description of the
orientation 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.[4]
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, 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.[5]
Spherical coordinates
Use in astronomy
A
star's spherical coordinates are often expressed as a pair,
right ascension and
declination, 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, 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 mounts and
setting circles employ the equatorial coordinate system to find objects. Setting circles in conjunction with a
star chart or
ephemeris allow the telescope to be easily pointed at known objects on the celestial sphere.
The declination symbol δ, (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.[6][7][8]
The right ascension symbol α, (lower case "alpha", abbreviated RA) measures the angular distance of an object eastward along the
celestial equator from the March
equinox to the
hour circle passing through the object. The March 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 360°/24h = 15° in one hour of right ascension, and 24h of right ascension around the entire
celestial equator.[6][9][10]
When used together, right ascension and declination are usually abbreviated RA/Dec.
Alternatively to
right ascension,
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 to the
hour circle passing through the object. Unlike right ascension, hour angle is always increasing with the
rotation of Earth. Hour angle may be considered a means of measuring the time since upper
culmination, 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). 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 1h. When calculating
topocentric phenomena, right ascension may be converted into hour angle as an intermediate step.[11][12][13]
Rectangular coordinates
Geocentric equatorial coordinates
There are a number of
rectangular variants of equatorial coordinates. All have:
The fundamental
plane in the plane of the Earth's equator.
The primary direction (the x axis) toward the March
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 y axis 90° to the east in the fundamental plane and a z 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.
The
position of the Sun is often specified in the geocentric equatorial rectangular coordinates X, Y, Z and a fourth distance coordinate, R(= √X2 + Y2 + Z2), in units of the
astronomical unit.
The positions of the
planets and other
Solar System bodies are often specified in the geocentric equatorial rectangular coordinates ξ, η, ζ and a fourth distance coordinate, Δ (equal to √ξ2 + η2 + ζ2), in units of the
astronomical unit.These rectangular coordinates are related to the corresponding spherical coordinates by
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 x, y and z axes are often designated I, J and K, respectively, or the frame's
basis is specified by the
unit vectorsÎ, Ĵ and K̂.
The fundamental
plane in the plane of the Earth's equator.
The primary direction (the x axis) toward the March
equinox.
A
right-handed convention, specifying a y axis 90° to the east in the fundamental plane and a z axis along
Earth's north polar axis.
This frame is in every way equivalent to the ξ, η, ζ 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[17]
^
Vallado, David A. (2001). Fundamentals of Astrodynamics and Applications. Microcosm Press, El Segundo, CA. p. 157.
ISBN1-881883-12-4.
^
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. M2, "apparent place".
ISBN978-0-7077-4082-9.