Azimuth

Azimuth is a horizontal angle measured from a cardinal direction, typically north, within a local coordinate system centered on an observer. Mathematically, it is the angle on a horizontal plane between a reference vector (often true north) and the projection of a vector pointing from the observer to a target. In astronomy, azimuth describes the horizontal direction of a celestial object, measured from north on the observer's local horizontal plane. It is usually expressed in degrees, either from 0° to 360° or from -180° to +180°.

The word comes from medieval Arabic as-sumūt, meaning "the directions," and entered Latin through astronomical texts, notably those involving the astrolabe. Its first recorded English use is in Geoffrey Chaucer's A Treatise on the Astrolabe (1390s), with an earlier Spanish record in the 1270s in a book commissioned by King Alfonso X.

In astronomy, azimuth pairs with altitude in the horizontal coordinate system used for celestial navigation and satellite dish alignment. Modern astronomy nearly always measures azimuth from north. In navigation, azimuth is often denoted α and defined as a clockwise angle from a north baseline, though south or other references may be used. Bearings can be expressed in formats like "S30°E," meaning 30 degrees east of south (or 150° clockwise from north).

In geodesy, azimuth calculations account for Earth's shape. For a spherical Earth, the azimuth between two points can be approximated using trigonometric formulas. For a more accurate oblate spheroid model, two slightly different azimuths exist: normal-section azimuth and geodetic azimuth, though their difference is negligible over short distances.