Editing Equatorial coordinate system (section)

==Generalization: heliocentric equatorial coordinates {{anchor|Heliocentric}}==
{{further|Heliocentric coordinate system}}

In astronomy, there is also a heliocentric [[Cartesian coordinate system|rectangular]] variant of equatorial coordinates, designated {{math|''x''}}, {{math|''y''}}, {{math|''z''}}, which has:

*The [[origin (mathematics)|origin]] at the centre of the [[Sun]].
*The fundamental [[Plane (geometry)|plane]] in the plane of the Earth's equator.
*The primary direction (the {{math|''x''}} axis) toward the March [[equinox]].
*A [[chirality|right-handed]] convention, specifying a {{math|''y''}} axis 90° to the east in the fundamental plane and a {{math|''z''}} axis along [[Earth]]'s north polar axis.

This frame is similar to the {{math|''ξ''}}, {{math|''η''}}, {{math|''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<ref>''Explanatory Supplement'' (1961), pp.&nbsp;20, 27</ref>
<math display="block">\begin{align}
    \xi &= x + X \\
   \eta &= y + Y \\
  \zeta &= z + Z
\end{align}</math>

{| class="wikitable floatright" style="text-align:center;"
|+ Summary of notation for astronomical equatorial coordinates<ref>''Explanatory Supplement'' (1961), sec. 1G</ref>
! rowspan="2" style="background:#89cff0;"                    | &nbsp;
! colspan="3" style="text-align:center; background:#89cff0;" | [[Spherical coordinates|Spherical]]
! colspan="2" style="text-align:center; background:#89cff0;" | [[Cartesian coordinate system|Rectangular]]
|-
! style="background:#89cff0;" | [[Right ascension]]
! style="background:#89cff0;" | [[Declination]]
! style="background:#89cff0;" | [[Distance]]
! style="background:#89cff0;" | General
! style="background:#89cff0;" | Special-purpose
|-
! style="background:#89cff0;" | Geocentric
| {{mvar|α}}
| {{mvar|δ}}
| {{mvar|Δ}}
| {{mvar|ξ}}, {{mvar|η}}, {{mvar|ζ}}
| {{mvar|X}}, {{mvar|Y}}, {{mvar|Z}} (Sun)
|- style="text-align:center;"
! style="background:#89cff0;" | Heliocentric
| &nbsp;
| &nbsp;
| &nbsp;
| colspan=2 | {{mvar|x}}, {{mvar|y}}, {{mvar|z}}
|}