How to Calculate Azimuth: Step-by-Step Guide for Students
The azimuth is the angle between North and a celestial body, measured clockwise around the observer's horizon (sun, moon). It decides the celestial body's course. A celestial body facing North, for example, has an azimuth of 0º, one facing East 90º, one facing South 180º, and one facing West 270º.
In a spherical coordinate system, an azimuth is an angular measurement. The azimuth is the angle formed by the predicted vector and a reference vector on the reference plane. A reference plane is projected perpendicularly with the vector from a point of interest to an observer (origin).
The azimuth is the horizontal orientation of a star or other astronomical object in the sky when used as a celestial coordinate. The point of interest is the star, the reference plane is the local area around an observer on Earth's surface (For example, a circular area with a radius of 5 km at sea level), and the reference vector points north. On the horizontal axis, the azimuth is the angle formed by the north vector and the star's vector.
Azimuth is generally expressed as a number of degrees (°). Navigation, astronomy, engineering, mapping, mining, and ballistics all use the term.
Azimuth Astronomy
The sky is divided into two hemispheres by this celestial coordinate system: the upper hemisphere, where objects above the horizon can be seen, and the lower hemisphere, where objects below the horizon are obscured by the Earth. The celestial horizon is known as the great circle on the celestial sphere whose plane is normal to the local gravity vector, which separates the hemispheres. The horizon is characterized as the plane tangent to a still liquid surface, such as a pool of mercury, in practice. The pole of the upper hemisphere is the zenith. The nadir refers to the lower hemisphere's pole.
Azimuth and zenith vary from each other which is explained as: The solar azimuth is the angle of the sun's direction from the horizon measured clockwise north. The angle between the local zenith and the line of sight of the sun is known as the solar zenith.
Solar Azimuth
The solar azimuth angle is the angle formed by the Sun's location. The solar azimuth varies with sun azimuth. The solar zenith angle (or its complementary angle solar elevation) defines the Sun's apparent height, while the solar zenith angle (or its complementary angle solar elevation) defines the Sun's relative position along the local horizon. The solar azimuth is defined by many conventions, but it is most commonly defined as the angle between a line parallel to the equator and the shadow cast by a vertical rod on Earth. According to this convention, the angle is positive if the shadow is east of the south and negative if it is west of the south.
Despite popular belief, the most commonly accepted convention for analyzing solar irradiation, such as for solar energy applications, is clockwise from due north, with east at 90 degrees, south at 180 degrees, and west at 270 degrees. This is the convention used in the formulas discussed here, as well as the term used by NREL in their solar position calculators. Although Landsat images and other USGS products define azimuthal angles in relation to due north, counterclockwise angles are considered negative.
Azimuth and Altitude
Altitude is the angular distance between an object and the local horizon. It varies in angle from 0 degrees at the horizon to 90 degrees at the zenith, the highest point in the sky.
The angular distance of an object from the local North, measured along the horizon, is known as azimuth.
These angles define the orientation of any object in the sky in a special way. Alt-az mounts swivel in these two perpendicular axes on some telescopes; camera tripods and tank turrets are other examples of alt-az systems.
From a practical standpoint, an object's altitude azimuth is particularly important: any object with an altitude less than zero is below the horizon and therefore inaccessible. Furthermore, an object's altitude is connected to its air mass, which is a measurement of how much air the object's light must travel through to reach the observer. The greater the air mass, the more light is dispersed or absorbed by the atmosphere, making an object appear fainter.
However, two observers in separate parts of the world will not agree on an object's (alt, az) position. Furthermore, an entity in the sky tends to shift from East to West as the Earth rotates, so its (alt, az) location varies from moment to moment.
Converting from (RA, Dec) to (alt, az) or vice versa is possible. There are two things to be aware of:
The Observer's Position on the Planet
The Date and Time of Observation
Magnetic Azimuth
The angle between the vertical plane through the observed object and the vertical plane at which a freely suspended magnetic needle, unaffected by transients, is observed at the point of observation artificial magnetic disturbance, would come to rest, determined clockwise from magnetic north through 360 degrees.
Moon Azimuth
The cardinal direction of the Moon is defined by its azimuth which is referred to as moon azimuth. The azimuth is expressed in degrees, with 360 degrees in a complete circle and counting clockwise from north. The azimuth values for north, east, south, and west are 0 degrees, 90 degrees, 180 degrees, and 270 degrees, respectively.
FAQs on What Is Azimuth in Physics?
1. What is azimuth in physics, and can you provide an example?
In physics, azimuth is a horizontal angular measurement used to define the direction of an object from a reference point. It is measured clockwise from a fixed reference direction, which in physics coordinate systems is often the positive x-axis. For instance, in geography and navigation, if North is the 0° reference, an object due East has an azimuth of 90°, South is 180°, and West is 270°. It is sometimes called a bearing.
2. What is the common symbol for the azimuth angle in physics?
The most common symbol used to represent the azimuth angle in physics and mathematics is the Greek letter phi (φ). This symbol is a fundamental part of spherical and cylindrical coordinate systems, which are essential for describing positions and motion in three-dimensional space.
3. What is the importance of 'back azimuth' in practical applications like surveying?
Back azimuth is the directional angle from a second point looking back towards the original point. It is critical in surveying and navigation for verifying positions and closing a traverse (a path of connected points). The back azimuth is calculated by adding or subtracting 180° from the forward azimuth. For example, if the azimuth from point A to point B is 60°, the back azimuth from B to A is 60° + 180° = 240°.
4. How does the azimuth angle differ from the elevation angle?
Azimuth and elevation are two independent angles that together define an object's position, but they measure direction in different planes:
Azimuth (or Bearing): This is the horizontal angle measured along the horizon from a reference point (e.g., North or the x-axis). It answers the question, 'In which direction should I turn?'
Elevation (or Altitude): This is the vertical angle measured upwards from the horizon to the object. It answers the question, 'How high up should I look?'
To locate a satellite, you would first turn to the correct azimuth and then tilt your antenna up to the correct elevation.
5. How is the concept of azimuth applied in astronomy to locate celestial objects?
In astronomy, azimuth is a core component of the horizontal coordinate system, which helps observers locate objects in the sky from their specific location on Earth. An object’s position at any given moment is defined by two coordinates: its azimuth (the compass direction) and its altitude (the angle above the horizon). While this system is intuitive for pointing telescopes, the azimuth and altitude of a star constantly change due to the Earth's rotation.
6. How is the azimuth reference point different in physics compared to fields like navigation?
While the concept of a horizontal angle is the same, the crucial difference lies in the zero-degree reference direction:
In Physics Coordinate Systems (like spherical or cylindrical), the azimuth angle (φ) is typically measured from the positive x-axis counter-clockwise.
In Navigation, Surveying, and Geography, the azimuth is almost always measured clockwise from True North.
This distinction is vital for correctly interpreting directional data across different scientific and practical fields.
7. How is the azimuth angle mathematically related to Cartesian coordinates (x, y)?
The azimuth angle (φ) is the link for converting between Cartesian coordinates (x, y) and polar/cylindrical coordinates (ρ, φ). The mathematical relationship is based on right-angle trigonometry in the x-y plane. Given a point (x, y), its azimuth angle φ can be calculated using the arctangent function: φ = atan2(y, x). The `atan2` function is preferred over the simpler `tan⁻¹(y/x)` because it correctly determines the angle in all four quadrants, providing a full 360° range.
