## Altitude-Azimuth Coordinate System

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This section refers to coordinate systems designed to find objects in the night sky. Such coordinate systems must indicate the position of an object in the sky, but not its distance from Earth. Therefore, we can imagine that astronomical objects are all located on the walls of a celestial sphere, as the ancient Greeks imagined.

To define these coordinate systems, it is important to keep in mind that, due to the motion of Earth, objects in the sky are changing position constantly.

Altitude-Azimuth Coordinate System: based on the measurement relative to the horizon and the zenith. In this system, the coordinates of an object change with time and place, or depend of the time and place where the observer is. Altitude-Azimuth coordinates are local. They are very simple, but of limited use.

The coordinates are hz, and A.

h = altitude, angle measured from the horizon to the object along the great circle that passes through that object and the zenith.

z = zenith distance, angle measured from the zenith to the object.

z + h = 90º

A = azimuth, angle measured along the horizon eastward from north to the great circle.

Besides this great circle, another frequently used great circle is the meridian, which passes through the observer’s zenith and intersects the horizon at the north and south poles.

Representation of the altitude-azimuth coordinate system

These coordinates change within the same night due to the rotation of Earth, but also change between two equivalent times at two consecutive nights, due to the translation of Earth around the Sun. The solar time (the average interval of 24 hours between meridian crossings of the Sun) and the sidereal time (consecutive meridian crossings of a star) are different in about 4 minutes. In these 4 minutes, Earth rotates approximately 1º, which is the extra degree required to complete a solar day (361º). A full rotation with respect to the stars, however, always requires 360º, since they are so distant that do not move appreciably due to the translation of the Earth.

Also, due to the translation of the Earth around the Sun, we observe the Sun apparently move through the constellations along a path know as the ecliptic.

The last major influence on these coordinates is due to the seasons. The celestial equator (plane passing through Earth at its equator) is tilted approximately 23.5º with respect to the plane containing the translation of Earth. Thus the ecliptic has a sinusoidal shape (the Sun apparently moving up and down in the sky).

The Sun crosses the celestial equator twice during the year: during the autumnal equinox, and the vernal equinox. Also, the two “minima” of the sinusoidal motion of the Sun correspond to the summer solstice and the winter solstice.

The inclination of the Sun with respect to the celestial equator is the declination. It is measured in degrees, and the zero is set to the celestial equator, with positive (Sun above, i.e. summer in northern hemisphere) and negative values (Sun below, i.e. winter in northern hemisphere).