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In astronomy, the altitude in the horizontal coordinate system and the zenith angle are complementary angles, with the horizon perpendicular to the zenith. The astronomical meridian is also determined by the zenith, and is defined as a circle on the celestial sphere that passes through the zenith, nadir, and the celestial poles .
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, [1] the alt/az system, or the alt-azimuth system, among
In Euclidean geometry, the right triangle altitude theorem or geometric mean theorem is a relation between the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse. It states that the geometric mean of those two segments equals the altitude.
It is the complement to the solar altitude or solar elevation, which is the altitude angle or elevation angle between the sun’s rays and a horizontal plane. [1] [2] At solar noon, the zenith angle is at a minimum and is equal to latitude minus solar declination angle. This is the basis by which ancient mariners navigated the oceans. [3]
The solar azimuth angle is the azimuth (horizontal angle with respect to north) of the Sun's position. [1] [2] [3] This horizontal coordinate defines the Sun's relative direction along the local horizon, whereas the solar zenith angle (or its complementary angle solar elevation) defines the Sun's apparent altitude.
The elevation is the signed angle from the x-y reference plane to the radial line segment OP, where positive angles are designated as upward, towards the zenith reference. Elevation is 90 degrees (= π / 2 radians) minus inclination. Thus, if the inclination is 60 degrees (= π / 3 radians), then the elevation is 30 degrees ...
The cosine of the hour angle (cos(h)) is used to calculate the solar zenith angle. At solar noon, h = 0.000 so cos(h) = 1, and before and after solar noon the cos(± h) term = the same value for morning (negative hour angle) or afternoon (positive hour angle), so that the Sun is at the same altitude in the sky at 11:00AM and 1:00PM solar time. [5]
[3]: ii It can be measured using a radar altimeter (or "absolute altimeter"). [3] Also referred to as "radar height" or feet/metres above ground level (AGL). True altitude is the actual elevation above mean sea level. [3]: ii It is indicated altitude corrected for non-standard temperature and pressure.