Azimuth
Horizontal angle from north used in navigation and astronomy.
Azimuth is an angle measured horizontally from a reference direction, usually north, within a local coordinate system centered on an observer. In mathematical terms, it is the angle on a horizontal plane between a projected line from the observer to a point of interest and a reference vector on that same plane. In astronomy, this describes the horizontal direction of a celestial object, such as a star, relative to true north. Azimuth is typically expressed in degrees, either from 0° to 360° or from -180° to +180°, and is applied in fields like navigation, astronomy, engineering, mapping, geodesy, mining, and ballistics.
The word comes from medieval Arabic *as-sumūt*, meaning "the directions," which entered late medieval Latin through astronomical use of the astrolabe. Its first recorded English use is in Geoffrey Chaucer's *A Treatise on the Astrolabe* from the 1390s, while the earliest known Western record is in a 1270s Spanish astronomy book commissioned by King Alfonso X of Castile.
In astronomy, azimuth pairs with altitude (or elevation) in the horizontal coordinate system used for celestial navigation and satellite dish alignment. Modern astronomy nearly always measures azimuth from north.
In land navigation, azimuth is often denoted by the Greek letter α and defined as a clockwise horizontal angle from a north baseline or meridian. It can also be measured clockwise from any fixed reference plane. Today, true north is the typical reference, with east at 90°, south at 180°, and west at 270°, though some systems use south as the zero. Bearings may be expressed as, for example, "S30°E," meaning 30 degrees east of south, which corresponds to 150 degrees clockwise from north. When the bearing aligns exactly with a cardinal point, terms like "due east" are used.
In geodesy, calculating azimuth between two points on Earth involves approximations. For a spherical Earth, the azimuth α from a point at latitude φ₁ and longitude zero to a point at latitude φ₂ and longitude L (positive eastward) is given by tan α = sin L / (cos φ₁ tan φ₂ − sin φ₁ cos L). For a more accurate oblate spheroid model, two slightly different azimuths exist: normal-section azimuth, measured by a theodolite perpendicular to the surface, and geodetic azimuth, the angle between north and the shortest path on the spheroid. The difference is negligible for distances under 100 km.
- field
- Navigation, Astronomy, Geodesy, Engineering
- known_for
- Horizontal angle measurement from north in celestial and terrestrial coordinate systems
- etymology
- From medieval Arabic 'al-sumūt' meaning 'the directions'
Lore & Background
The azimuth is the horizontal angle measured from a reference direction, most commonly true north, in a local spherical coordinate system centered on an observer. It is defined mathematically by projecting the relative position vector from the observer to a point of interest onto a horizontal reference plane; the angle between this projected vector and a reference vector on that plane is the azimuth. In celestial contexts, the azimuth of a star or other astronomical object is its horizontal direction, with the reference plane being the local area around an observer on Earth’s surface and the reference vector pointing to true north. Azimuth is typically measured in degrees, either in a positive range from 0° to 360° or in a signed range from -180° to +180°. In navigation, azimuth is often denoted by the Greek letter alpha and defined as a horizontal angle measured clockwise from a north base line or meridian. While true north is the standard reference, some systems use south as the zero, and bearings may be expressed with notations such as “S30°E,” indicating 30 degrees eastward from south. The concept is fundamental in navigation, astronomy, engineering, mapping, geodesy, mining, and ballistics. In geodesy, azimuth can refer to either normal-section azimuth, measured by a theodolite perpendicular to the spheroid’s surface, or geodetic azimuth, the angle between north and the shortest path on the ellipsoid. The difference between these two is negligible for distances under 100 kilometers. In cartography, grid azimuth is calculated from the known coordinates of two points on a flat plane, with the axes swapped relative to a standard mathematical polar coordinate system to maintain clockwise measurement from north.
Reader's Guide
Azimuth is a key coordinate in the horizontal coordinate system used in celestial navigation, where it is paired with altitude. In modern astronomy, azimuth is nearly always measured from the north. In land navigation, azimuth is usually denoted by alpha (α) and defined as a horizontal angle measured clockwise from a north base line or meridian. Today, the reference plane for an azimuth is typically true north, measured as 0° azimuth, though other angular units such as grad or mil can be used. Some navigation systems use south as the reference vector. The concept is also used for satellite dish installation.
Did You Know?
- Azimuth is derived from medieval Arabic 'al-sumūt', meaning 'the directions'.
- Its first recorded use in English is in the 1390s in Geoffrey Chaucer's 'A Treatise on the Astrolabe'.
- In the horizontal coordinate system, azimuth is one of two coordinates, the other being altitude.
Frequently Asked Questions
What is Azimuth?
Azimuth is a horizontal angle measured from a cardinal direction—most often north—within a local or observer-centric spherical coordinate system. It provides a consistent way to express bearing in both celestial and terrestrial frameworks.
Where does the word 'Azimuth' come from?
The term traces back to the medieval Arabic phrase 'al-sumūt,' meaning 'the directions.' This etymology reflects the concept's original purpose of denoting directional orientation.
Which fields rely on Azimuth?
Azimuth is a core measurement in navigation, astronomy, geodesy, engineering, mining, and ballistics. Any discipline that needs to specify a horizontal bearing relative to north draws on this concept.
Why is Azimuth important in mapping and navigation?
It gives observers a shared, relative angular reference for expressing horizontal direction, making it essential for plotting courses, locating celestial objects, and aligning survey measurements. Without a common angular baseline like azimuth, coordinating positions across different coordinate systems would be far more difficult.
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