Editing Equatorial coordinate system (section)

== Rectangular coordinates: geocentric equatorial coordinates ==
[[File:Ra and dec rectangular.png|thumb|300px|Geocentric equatorial coordinates. The [[Origin (mathematics)|origin]] is the centre of the [[Earth]]. The fundamental [[Plane (geometry)|plane]] is the plane of the Earth's equator. The primary direction (the {{math|''x''}} axis) is the March [[equinox]]. A [[right-handed]] convention specifies a {{math|''y''}} axis 90° to the east in the fundamental plane; the {{math|''z''}} axis is the north polar axis. The reference frame does not rotate with the Earth, rather, the Earth rotates around the {{math|''z''}} axis.]]

There are a number of [[Cartesian coordinate system|rectangular]] variants of equatorial coordinates. All have:
* The [[origin (mathematics)|origin]] at the centre of the [[Earth]].
* The fundamental [[Plane (geometry)|plane]] in the plane of the Earth's equator.
* The primary direction (the {{math|''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 {{math|''y''}} axis 90° to the east in the fundamental plane and a {{math|''z''}} axis along the north polar axis.

The reference frames do not rotate with the Earth (in contrast to [[ECEF|Earth-centred, Earth-fixed]] frames), remaining always directed toward the [[equinox]], and drifting over time with the motions of [[axial precession|precession]] and [[astronomical nutation|nutation]].
* In [[astronomy]]:<ref>''Explanatory Supplement'' (1961), pp. 24–26</ref>
** The [[position of the Sun]] is often specified in the geocentric equatorial rectangular coordinates {{math|''X''}}, {{math|''Y''}}, {{math|''Z''}} and a fourth distance coordinate, {{math|''R''}} {{math|1=(= {{radical|''X''{{isup|2}} + ''Y''{{isup|2}} + ''Z''{{isup|2}}}})}}, 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 {{math|''ξ''}}, {{math|''η''}}, {{math|''ζ''}} and a fourth distance coordinate, {{math|''Δ''}} (equal to {{math|{{radical|''ξ''{{isup|2}} + ''η''{{isup|2}} + ''ζ''{{isup|2}}}}}}), in units of the [[astronomical unit]].{{paragraph}}These rectangular coordinates are related to the corresponding spherical coordinates by <math display="block">\begin{align}
\frac{X}{R} = \frac{\xi}{\mathit{\Delta}} &= \cos \delta \cos \alpha \\
\frac{Y}{R} = \frac{\eta}{\mathit{\Delta}} &= \cos \delta \sin \alpha \\
\frac{Z}{R} = \frac{\zeta}{\mathit{\Delta}} &= \sin \delta
\end{align}</math>
* In [[astrodynamics]]:<ref>Vallado (2001), pp. 157, 158</ref>
** The positions of artificial Earth [[satellite]]s are specified in ''geocentric equatorial'' coordinates, also known as ''geocentric equatorial inertial (GEI)'', ''[[Earth-centered inertial|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 {{math|''x''}}, {{math|''y''}} and {{math|''z''}} axes are often designated {{math|''I''}}, {{math|''J''}} and {{math|''K''}}, respectively, or the frame's [[Basis (linear algebra)|basis]] is specified by the [[unit vector]]s {{math|''Î''}}, {{math|''Ĵ''}} and {{math|''K̂''}}.
** The ''Geocentric Celestial Reference Frame (GCRF)'' is the geocentric equivalent of the [[International Celestial Reference Frame]] (ICRF). Its primary direction is the [[equinox]] of [[Epoch (astronomy)|J2000.0]], and does not move with [[Axial precession|precession]] and [[astronomical nutation|nutation]], but it is otherwise equivalent to the above systems.