the azimuth system** **is a** useful tool for locating the position and direction of an object** or place of interest in relation to a reference point. This coordinate system is based on the measurement of the azimuth angle to describe the direction of the object or point of interest in the horizontal plane, in relation to a given reference point. It is used in different areas, such as topography, navigation, astronomy, geodesy and cartography. In summary, the azimuth system is an effective technique to locate and determine the direction of objects or points of interest, which makes it a valuable tool for different applications.

## Concept and definition of azimuthal

the azimuth system **is a coordinate system,** It is developed to describe the direction and position of an object or point of interest, with respect to a reference point. By measuring a horizontal angle between the reference direction and the object or point of interest, with respect to a horizontal plane and an observation point.

In this system, the measurement angle is taken along a horizontal circle, which passes through the observation point and the object or point of interest, and is measured in degrees, from 0° to 360°. The address of **reference may vary according to context** in which the azimuth system is used, such as magnetic north, true north, south, east, or west.

the azimuth system **It is widely applied in different areas**, such as maritime navigation, topography, cartography, geology, scale in astronomy, engineering and architecture, among others. In each of these disciplines, the system is adapted and used in a specific way, according to their needs and objectives.

## What does the word azimuthal mean?

The word ‘azimuthal’ refers to something** related to the coordinate system** azimuthal. In this context, the term is used to describe the measurement and representation of the direction and position of an object or point of interest, relative to a reference point, by measuring a horizontal angle between the reference direction and the object or point of interest.

The word ‘azimutal’ its etymology comes from the French term ‘azimut’, which in turn derives from the Arabic ‘as-sumūt’, which in Spanish means ‘the paths’ or ‘the directions’. In this sense, ‘azimuthal’ makes **reference to measurement and representation of direction** as of the position of an object or point in different directions or paths, with respect to a reference point.

### What is the azimuthal projection?

The azimuthal projection is a technique used in cartography and astronomy to **represent the terrestrial or celestial surface in a two-dimensional plane**from an observation point and a reference direction.

To achieve this, the points of the surface are projected onto a plane tangent to the observation point and perpendicular to the reference direction.**usually the north or south pole.** In this way, the meridians become straight lines that converge at the opposite pole, and the parallels become concentric circles.

**There are different types of azimuthal projections**, depending on the reference direction and observation point used, such as equidistant, orthographic, and stereographic. In the projection, the zenith is the highest point, located in the center. The azimuthal projection is used to represent the sphere of the terrestrial or celestial surface from the perspective of an observation point, in situations such as air navigation, astronomical observation or flight route planning.

### What is the azimuthal quantum number?

The azimuthal quantum number, also known as orbital angular momentum or ℓ quantum number, is one of the four quantum numbers used in the **description of the quantum state of an electron in an atom**.

The azimuthal quantum number **refers to the shape or geometry of the orbital** in which the electron is located, and is related to the orbital angular momentum of the electron. Allowable values for the azimuthal quantum number are nonnegative integers, from 0 to n-1, where n is the principal quantum number.

Each value of **azimuthal quantum number defines a sublevel** of energy within a given energy level, and is represented by a lowercase letter indicating the shape of the corresponding orbital. Thus, ℓ = 0 corresponds to the s sublevel, ℓ = 1 to the p sublevel, ℓ = 2 to the d sublevel, ℓ = 3 to the f sublevel, and so on.

The azimuthal quantum number **is important in the description of the properties** and the behavior of atoms and their electrons. It is also fundamental in quantum chemistry and atomic physics.

### What is the azimuth angle?

azimuth angle **is the angle measured in the horizontal plane** between a reference direction and a given direction in an azimuthal coordinate system.

In an azimuth coordinate system, the azimuth angle** is measured along a horizontal circle **passing through the point of observation and the object or point of interest. This is measured in degrees, from 0° to 360°. The reference direction can vary depending on the context in which the azimuth system is used, such as magnetic north, true north, south, east, or west.

The azimuth angle has multiple applications in different areas, including:

- The topography.
- cartography.
- Maritime and air navigation.
- The astronomy.
- engineering.
- The architecture.

Each of these disciplines **applies the azimuth angle specifically** and tailored to your needs and goals. For example, in topography it is used to measure the direction of a level line or the position of a point on the ground. On the other hand, in astronomy it is used to determine the location of a star in the sky.

### What is an azimuthal control line?

In the field of air navigation, an azimuth control line is an imaginary line drawn on the ground or on a map, which follows a given course or direction, and which** is put into practice as a guide for the flight** of an aircraft.

The azimuth control line is used to maintain the correct direction of flight of an aircraft, and is represented on the navigation chart with a straight line, which indicates the direction that the aircraft should follow on its route. In some cases, the azimuth control line may be made up of a series of points that connect to each other, indicating the necessary course changes. **to maintain the correct direction of flight**.

Tracking an azimuth control line is especially important in low visibility conditions, such as fog or darkness, as it allows the pilot to maintain the correct heading and avoid unwanted deviations. In addition, the azimuth control line can also be used to establish flight paths. **more efficient and economic**by avoiding restricted areas or congested air traffic zones.

## Where is azimuthal projection used?

The azimuthal projection is used in different areas and disciplines, such as cartography, geography, navigation, astronomy and physics, among others.

In cartography and geography, the azimuthal projection is used to map the earth’s surface in a flat image, projecting points on the earth’s surface onto a central plane, which may be tangent to the globe or intersect it at some point. Azimuthal projections can be of different types,** according to the position of the center point of the projection **and the type of projection executed.

In navigation, the azimuth projection is applied to determine the position and direction of a ship or an aircraft at sea or in the air, taking advantage of an azimuthal coordinate system. This information can be obtained using navigation instruments such as** compass, sextant, radar or GPS**.

In astronomy, the azimuthal projection is used to represent the position of the stars in the sky, using an azimuthal coordinate system. This information is run to determine the **position of the stars in relation to the position of the observer,** and to perform calculations of trajectories and movements of the stars.

In physics, the azimuthal projection is used to describe the direction and position of subatomic particles, such as electrons, in an atom, applying the azimuthal quantum number. This information is critical to understanding the properties and **the behavior of atoms and their electrons**It is also fundamental in quantum chemistry and atomic physics.

## How is the azimuthal projection made?

The azimuthal projection is performed **through a cartographic projection process**, in which the points of the terrestrial surface are projected on a central plane, which can be tangent to the terrestrial globe or cut it at some point. The general steps for making an azimuthal projection are described below:

**A central point of the projection is chosen**: This central point can be any point on the earth’s surface, but the north pole or the south pole is generally chosen, since it is a polar projection.**An azimuthal coordinate system is established**: Starting from the center point, an azimuthal coordinate system is established, consisting of a reference circle and radial lines extending from the center to the edge of the map.**Points on the earth’s surface are projected**: From the geographic coordinates of the points on the earth’s surface, the points are projected onto the plane of the azimuthal projection, applying mathematical formulas.**The map is drawn**: Once the points are projected on the plane, the map is drawn using the projected information.

It is important to note that the azimuthal projection can have different variations and types, depending on the position of the center point of the projection and the type of projection performed, so the specific steps may vary on a case-by-case basis.

## Who created the azimuthal projection?

The azimuthal projection is one of the **oldest known map projections**and its origin dates back to ancient Babylon, around 2000 BC In ancient Babylon, an azimuthal projection was used to represent the sky in a flat image, taking advantage of the horizon point as the center of the projection.

However, in modern cartography, the azimuthal projection has been put into practice by many cartographers and mathematicians throughout history. One of the first to use the azimuthal projection in modern cartography was Gerardus Mercator, who used it to create a map of Europe in 1569. In the 18th century, the French mathematician Joseph-Nicolas Delisle developed a version of the azimuthal projection that is currently practice for the representation of the poles. Since then, the azimuthal projection has been **used and perfected by many cartographers and mathematicians **Worldwide.