Celestial coordinate system

In astronomy, a celestial coordinate system is a coordinate system for mapping positions in the sky. There are different celestial coordinate systems each using a coordinate grid projected on the celestial sphere, in analogy to the geographic coordinate system used on the surface of the Earth. The coordinate systems differ only in their choice of the fundamental plane, which divides the sky into two equal hemispheres along a great circle. For example, the fundamental plane of the geographic system is the Earth's equator. Each coordinate system is named for its choice of fundamental plane.

Coordinate systems

Equatorial coordinate system

Popular choices of pole and equator are the older B1950 and the modern J2000 systems, but a pole and equator "of date" can also be used, meaning one appropriate to the date under consideration, such as that at which a measurement of the position of a planet or spacecraft is made. There are also subdivisions into "mean of date" coordinates, which average out or ignore nutation, and "true of date," which include nutation.

Altitude

Altitude, also referred to as elevation, refers to the vertical angle measured from the geometric horizon (0°) towards the zenith (+90°). It can also take negative values for objects below the horizon, down to the nadir (-90°). Although some will use the term height instead of altitude, this is not recommended as height is usually understood to be a linear distance unit, to be expressed in meters (or any other length unit), and not an angular distance.

The term zenith distance is more often used in astronomy and is the complement of the altitude. That is: 0° in the zenith, 90° on the horizon, up to 180° at the nadir.

Converting coordinates

Equatorial to horizontal coordinates

Let δ be the declination and Failed to parse (Missing texvc executable; please see math/README to configure.): H

the hour angle.

Let φ be the observer's latitude.

Let Alt be the altitude and Az the azimuth.

Let θ be the zenith angle (or zenith distance, i.e. the 90° complement of Alt).

Then the equations of the transformation are:

Failed to parse (Missing texvc executable; please see math/README to configure.): \sin \mathrm{Alt} = \cos \theta = \sin \phi \cdot \sin \delta + \cos \phi \cdot \cos \delta \cdot \cos H

Failed to parse (Missing texvc executable; please see math/README to configure.): \cos \mathrm{Az} = \frac{\cos \phi \cdot \sin \delta - \sin \phi \cdot \cos \delta \cdot \cos H}{\cos \mathrm{Alt}}.

Use the inverse trigonometric functions to get the values of the coordinates.

NOTE: Inverse cosine is dual valued, i.e. 160° and 200° both have the same value of cosine. The above needs to be corrected. If H < 180 (or Pi radians) then Az = 360 - Az as derived from the above equation.

This article is based on Jason Harris' Astroinfo which comes along with KStars, a Desktop Planetarium for Linux/KDE. See http://edu.kde.org/kstars/index.phtml

    Inclination

  Longitude of the ascending node

    Eccentricity

   Argument of periapsis

    Semi-major axis

  Mean anomaly at epoch

      True anomaly

         Semi-minor axis

  Linear eccentricity

              Eccentric anomaly

         Mean longitude

          True longitude

              Orbital period

bs:Nebeski koordinatni sistem

de:Astronomische Koordinatensysteme el:Ουράνιες συντεταγμένες es:Coordenadas celestes fr:Système de coordonnées célestes hr:Nebeski koordinatni sustavi is:Himinhvolfshnitakerfi it:Coordinate celesti he:מערכת קואורדינטות שמימית hu:Csillagászati koordinátarendszer nl:Hemelcoördinaat ja:天球座標系 nn:Himmelkoordinat pl:Układ współrzędnych astronomicznych ro:Coordonate astronomice ru:Системы небесных координат sl:Nebesni koordinatni sistem vi:Hệ tọa độ thiên văn uk:Системи небесних координат