Editing Supergalactic coordinate system (section)

== Definition ==
The supergalactic coordinate system is a [[spherical coordinate system]] in which the [[equator]] lies in the supergalactic plane.

By convention, supergalactic latitude is usually abbreviated SGB, and supergalactic longitude as SGL, by analogy to {{math|''b''}} and {{math|''l''}} conventionally used for [[galactic coordinates]]. [[File:GalEclipt.png|thumb|Supergalactic and Ecliptic plane]]
* The zero point (SGL = 0°, SGB = 0°)<ref>{{Cite web|last=Abarkahkašân|first=A.|date=n.d.|title=An Etymological Dictionary of Astronomy and Astrophysics|url=http://dictionary.obspm.fr/index.php?showAll=1&formSearchTextfield=supergalactic|archive-url=|archive-date=|access-date=|website=}}</ref> lies in the constellation [[Cassiopeia (constellation)|Cassiopeia]], coincides with (''l''<sub>x</sub> = 137.37°, ''b''<sub>x</sub> = 0°) and was chosen for convenience to lie along the line where the supergalactic plane intersects with the galactic plane. In J2000 [[Equatorial coordinate system|equatorial coordinates]], this is approximately  [[right ascension|RA]] = 2.82<sup>h</sup>, [[declination|Dec]] = +59.5°.
* The origin essentially coincides with the Earth, because the supergalactic plane is identified as a plane observed from Earth.
* The north supergalactic pole (SGB = 90°) lies in the constellation [[Hercules (constellation)|Hercules]] at galactic coordinates ({{math|''l''<sub>z</sub>}} = 47.37°, {{math|''b''<sub>z</sub>}} = +6.32°), or approximately RA = 18.9<sup>h</sup>, Dec = +15.7°.

The transformation from a triple of Cartesian supergalactic coordinates to a triple of galactic coordinates is
:<math>
  \begin{bmatrix} x \\ y \\ z\end{bmatrix}_\text{gal} =
  \begin{bmatrix}
    \cos l_x \cos b_x & \sin l_z \cos b_z \sin b_x - \sin b_z \sin l_x \cos b_x & \cos l_z \cos b_z \\
    \sin l_x \cos b_x & \sin b_z \cos l_x \cos b_x - \cos l_z \cos b_z \sin b_x & \sin l_z \cos b_z \\
             \sin b_x & \cos b_z \cos b_x \sin\left(l_x - l_z\right)                       & \sin b_z
 \end{bmatrix}
  \begin{bmatrix}x \\ y \\ z\end{bmatrix}_\text{superg}
</math>
[[File:Crossing-Galactic-Supergalactic-planes.png|thumb|Supergalactic and Galactic plane]]
The left column in this matrix is the image of the origin of the supergalactic system in the galactic system, the right column in this matrix is the image of the north pole of the supergalactic coordinates in the galactic system, and the middle column is the cross product (to complete the right-handed coordinate system).

The corresponding [[cartesian coordinate system]] allows points to be specified by coordinates (SGX, SGY, SGZ). In this system the supergalactic z-axis points towards the north supergalactic pole, the supergalactic x-axis points towards the zero point, and the supergalactic y-axis is perpendicular to both.