Азимут: Бағытты өлшеу бұрышы

Horizontal angle from north or other reference cardinal direction

An azimuth (/audio=en us azimuth. ogg/'/æ//z//ə//m//ə//θ/; from اَلسُّمُوت) is the angular measurement in a spherical coordinate system which represents the horizontal angle from a cardinal direction, most commonly north. Mathematically, the relative position vector from an observer (origin) to a point of interest is projected perpendicularly onto a reference plane (the horizontal plane); the angle between the projected vector and a reference vector on the reference plane is called the azimuth. When used as a celestial coordinate, the azimuth is the horizontal direction of a star or other astronomical object in the sky. The star is the point of interest, the reference plane is the local area (e. g. a circular area with a 5 km radius at sea level) around an observer on Earth's surface, and the reference vector points to true north. The azimuth is the angle between the north vector and the star's vector on the horizontal plane. Azimuth is usually measured in degrees (°), in the positive range 0° to 360° or in the signed range 180° to +180°. The concept is used in navigation, astronomy, engineering, mapping, mining, and ballistics.

The word azimuth is used in all European languages today. It originates from medieval Arabic السموت (al sumūt, pronounced as sumūt), meaning "the directions" (plural of Arabic السمت al samt = "the direction"). The Arabic word entered late medieval Latin in an astronomy context and in particular in the use of the Arabic version of the astrolabe astronomy instrument. Its first recorded use in English is in the 1390s in Geoffrey Chaucer's Treatise on the Astrolabe. The first known record in any Western language is in Spanish in the 1270s in an astronomy book that was largely derived from Arabic sources, the Libros del saber de astronomía commissioned by King Alfonso X of Castile.

In the horizontal coordinate system, used in celestial navigation, azimuth is one of the two coordinates. The other is altitude, sometimes called elevation above the horizon. It is also used for satellite dish installation (see also: sat finder). In modern astronomy azimuth is nearly always measured from the north.

In land navigation, azimuth is usually denoted alpha, α, and defined as a horizontal angle measured clockwise from a north base line or meridian. Azimuth has also been more generally defined as a horizontal angle measured clockwise from any fixed reference plane or easily established base direction line. Today, the reference plane for an azimuth is typically true north, measured as a 0° azimuth, though other angular units (grad, mil) can be used. Moving clockwise on a 360 degree circle, east has azimuth 90°, south 180°, and west 270°. There are exceptions: some navigation systems use south as the reference vector. Any direction can be the reference vector, as long as it is clearly defined. Quite commonly, azimuths or compass bearings are stated in a system in which either north or south can be the zero, and the angle may be measured clockwise or anticlockwise from the zero. For example, a bearing might be described as "(from) south, (turn) thirty degrees (toward the) east" (the words in brackets are usually omitted), abbreviated "S30°E", which is the bearing 30 degrees in the eastward direction from south, i. e. the bearing 150 degrees clockwise from north. The reference direction, stated first, is always north or south, and the turning direction, stated last, is east or west. The directions are chosen so that the angle, stated between them, is positive, between zero and 90 degrees. If the bearing happens to be exactly in the direction of one of the cardinal points, a different notation, e. g. "due east", is used instead.

+ From north, eastern side Direction Azimuth North 0° North northeast 22.5° Northeast 45° East northeast 67.5° East 90° East southeast 112.5° Southeast 135° South southeast 157.5°
+ From north, western side Direction Azimuth South 180° South southwest 202.5° Southwest 225° West southwest 247.5° West 270° West northwest 292.5° Northwest 315° North northwest 337.5°

There is a wide variety of azimuthal map projections. They all have the property that directions (the azimuths) from a central point are preserved. Some navigation systems use south as the reference plane. However, any direction can serve as the plane of reference, as long as it is clearly defined for everyone using that system.

If, instead of measuring from and along the horizon, the angles are measured from and along the celestial equator, the angles are called right ascension if referenced to the Vernal Equinox, or hour angle if referenced to the celestial meridian.

In mathematics, the azimuth angle of a point in cylindrical coordinates or spherical coordinates is the anticlockwise angle between the positive x axis and the projection of the vector onto the xy plane. A special case of an azimuth angle is the angle in polar coordinates of the component of the vector in the xy plane, although this angle is normally measured in radians rather than degrees and denoted by θ rather than φ.

For magnetic tape drives, azimuth refers to the angle between the tape head(s) and tape. In sound localization experiments and literature, the azimuth refers to the angle the sound source makes compared to the imaginary straight line that is drawn from within the head through the area between the eyes. An azimuth thruster in shipbuilding is a propeller that can be rotated horizontally.