# horizontal coordinate system

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## horizontal (or horizon) coordinate system

A coordinate system in which the fundamental reference circle is the observer's astronomical horizon and the zero point is the north point (see cardinal points). The coordinates are altitude and azimuth (see illustration).

The altitude (h) of a celestial body is its angular distance north (counted positive) or south (counted negative) of the horizon; it is measured along the vertical circle through the body and ranges from 0°, when the object rises or sets, to 90°, when the object is directly overhead at the zenith. The zenith distance (ζ) is the complement of the altitude (90° – h) and is frequently used instead of altitude in the horizontal system. The azimuth (A) of a body is its angular distance measured eastward along the horizon from the north point (or sometimes the south point) to the intersection of the object's vertical circle.

The horizontal system is simple but is strictly a local system. At any given moment a celestial body will have a unique altitude and azimuth for a particular observation point, the coordinates changing with observer's position. The coordinates of a star, etc., also change with time as the Earth rotates and the observer's zenith moves eastward among the stars.

Collins Dictionary of Astronomy © Market House Books Ltd, 2006
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Simplification can be achieved by applying an auxiliary local 3D Cartesian horizontal coordinate system. In that way, the complicated measurement model linked to the variable curvature of earth's ellipsoid surface in 3D used for the determination of object geographic placement using the polar method is avoided.
Such an auxiliary coordinate system may be a 3D Cartesian horizontal coordinate system with its origin at the position of the measurement instrument, Geodetic or 3D Cartesian geocentric equatorial coordinates of point should be known for relating observations to the geodetic coordinate system.
The positive direction of the x axis of the horizontal coordinate system points to the North Pole, y points to the east, z points to the zenith, i.e.
This geometric model of polar observations is suitable for the geodetic horizontal coordinate system (when the z axis coincides with normal direction to ellipsoid).
For the reduction of observation data from astronomical to geodetic horizontal coordinate system, the values of azimuth and zenith distance in a formula (1) should be corrected by corrections (2) and (3).
2 are given the reduced ITRF 2000 velocity components transformed into local horizontal coordinate system. denoted as [delta][v.sub.n], [delta][v.sub.e], [delta][v.sub.v].
The coordinate differences were transformed to the local horizontal coordinate system [delta]n, [delta]e, [delta]v (Leick, 1989).
The final [delta] X, [delta] Y, [delta] Z results were transformed to the local horizontal coordinate system [delta] n, [delta] e, [delta] v.

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