Azimuth in the context of Altitude (astronomy)

The four cardinal directions or cardinal points are the four main compass directions: north (N), east (E), south (S), and west (W). The corresponding azimuths (clockwise horizontal angle from north) are 0°, 90°, 180°, and 270°.

The four ordinal directions or intercardinal directions are northeast (NE), southeast (SE), southwest (SW), and northwest (NW).The corresponding azimuths are 45°, 135°, 225°, and 315°.

A sundial is a horological device that tells the time of day (referred to as civil time in modern usage) when direct sunlight shines by the apparent position of the Sun in the sky. In the narrowest sense of the word, it consists of a flat plate (the dial) and a gnomon, which casts a shadow onto the dial. As the Sun appears to move through the sky, the shadow aligns with different hour-lines, which are marked on the dial to indicate the time of day. The style is the time-telling edge of the gnomon, though a single point or nodus may be used. The gnomon casts a broad shadow; the shadow of the style shows the time. The gnomon may be a rod, wire, or elaborately decorated metal casting. The style must be parallel to the axis of the Earth's rotation for the sundial to be accurate throughout the year. The style's angle from horizontal is equal to the sundial's geographical latitude.

The term sundial can refer to any device that uses the Sun's altitude or azimuth (or both) to show the time. Sundials are valued as decorative objects, metaphors, and objects of intrigue and mathematical study.

A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It typically consists of a magnetized needle or another element, such as a compass card or compass rose, that pivots to align itself with magnetic north. Other methods may be used, including gyroscopes, magnetometers, and GPS receivers.

Compasses often show angles in degrees: north corresponds to 0°, and the angles increase clockwise, so east is 90°, south is 180°, and west is 270°. These numbers allow the compass to show azimuths or bearings which are commonly stated in degrees. If local variation between magnetic north and true north is known, then direction of magnetic north also gives direction of true north.

Radar is a system that uses radio waves to determine the distance (ranging), direction (azimuth and elevation angles), and radial velocity of objects relative to the site. It is a radiodetermination method used to detect and track aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations and terrain. The term RADAR was coined in 1940 by the United States Navy as an acronym for "radio detection and ranging". The term radar has since entered English and other languages as an anacronym, a common noun, losing all capitalization.

A radar system consists of a transmitter producing electromagnetic waves in the radio or microwave domain, a transmitting antenna, a receiving antenna (often the same antenna is used for transmitting and receiving) and a receiver and processor to determine properties of the objects. Radio waves (pulsed or continuous) from the transmitter reflect off the objects and return to the receiver, giving information about the objects' locations and speeds. This device was developed secretly for military use by several countries in the period before and during World War II. A key development was the cavity magnetron in the United Kingdom, which allowed the creation of relatively small systems with sub-meter resolution.

A compass rose or compass star, sometimes called a wind rose or rose of the winds, is a polar diagram displaying the orientation of the cardinal directions (north, east, south, and west) and their intermediate points. It is used on compasses (including magnetic ones), maps (such as compass rose networks), or monuments. It is particularly common in navigation systems, including nautical charts, non-directional beacons (NDB), VHF omnidirectional range (VOR) systems, satellite navigation devices ("GPS").

The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane to define two angles of a spherical coordinate system: altitude and azimuth.Therefore, the horizontal coordinate system is sometimes called the az/el system, the alt/az system, or the alt-azimuth system, among others. In an altazimuth mount of a telescope, the instrument's two axes follow altitude and azimuth.

In navigation, bearing or azimuth is the horizontal angle between the direction of an object and north or another object. The angle value can be specified in various angular units, such as degrees, mils, or grad. More specifically:

• Absolute bearing refers to the clockwise angle between the magnetic north (magnetic bearing) or true north (true bearing) and an object. For example, an object to due east would have an absolute bearing of 90 degrees. Thus, it is the same as azimuth.
• Relative bearing refers to the angle between the craft's forward direction (heading) and the location of another object. For example, an object relative bearing of 0 degrees would be immediately in front; an object relative bearing 180 degrees would be behind. Bearings can be measured in mils, points, or degrees. Thus, it is the same as an azimuth difference (modulo +/- 360 degrees).

In mathematics, the polar coordinate system specifies a given point in a plane by using a distance and an angle as its two coordinates. These are

• the point's distance from a reference point called the pole, and
• the point's direction from the pole relative to the direction of the polar axis, a ray drawn from the pole.

The distance from the pole is called the radial coordinate, radial distance or simply radius, and the angle is called the angular coordinate, polar angle, or azimuth. The pole is analogous to the origin in a Cartesian coordinate system.

The points of the compass are a set of horizontal, radially arrayed compass directions (or azimuths) used in navigation and cartography. A compass rose is primarily composed of four cardinal directions—north, east, south, and west—each separated by 90 degrees, and secondarily divided by four ordinal (intercardinal) directions—northeast, southeast, southwest, and northwest—each located halfway between two cardinal directions. Some disciplines such as meteorology and navigation further divide the compass with additional azimuths. Within European tradition, a fully defined compass has 32 "points" (and any finer subdivisions are described in fractions of points).

Compass points or compass directions are valuable in that they allow a user to refer to a specific azimuth in a colloquial fashion, without having to compute or remember degrees.

In navigation, a rhumb line (also rhumb (/rʌm/) or loxodrome) is an arc crossing all meridians of longitude at the same angle. It is a path of constant azimuth relative to true north, which can be steered by maintaining a course of fixed bearing. When drift is not a factor, accurate tracking of a rhumb line course is independent of speed.

In practical navigation, a distinction is made between this true rhumb line and a magnetic rhumb line, with the latter being a path of constant bearing relative to magnetic north. While a navigator could easily steer a magnetic rhumb line using a magnetic compass, this course would not be true because the magnetic declination—the angle between true and magnetic north—varies across the Earth's surface.

In quantum mechanics, the azimuthal quantum number ℓ is a quantum number for an atomic orbital that determines its orbital angular momentum and describes aspects of the angular shape of the orbital. The azimuthal quantum number is the second of a set of quantum numbers that describe the unique quantum state of an electron (the others being the principal quantum number n, the magnetic quantum number m_ℓ, and the spin quantum number m_s).

For a given value of the principal quantum number n (electron shell), the possible values of ℓ are the integers from 0 to n − 1. For instance, the n = 1 shell has only orbitals with ${\displaystyle \ell =0}$, and the n = 2 shell has only orbitals with ${\displaystyle \ell =0}$, and ${\displaystyle \ell =1}$.

The azimuthal equidistant projection is an azimuthal map projection. It has the useful properties that all points on the map are at proportionally correct distances from the center point, and that all points on the map are at the correct azimuth (direction) from the center point — that is, it is the exponential map on a sphere. A useful application for this type of projection is a polar projection which shows all meridians (lines of longitude) as straight, with distances from the pole represented correctly.

The flag of the United Nations contains an example of a polar azimuthal equidistant projection.