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This is the coordinate system normally used to calculate the position of the Sun in terms of solar zenith angle and solar azimuth angle, and the two parameters can be used to depict the Sun path. [3] This calculation is useful in astronomy, navigation, surveying, meteorology, climatology, solar energy, and sundial design.
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.
A 2021 publication [8] about solar geometry first calculates the x-, y-, and z-component of the solar vector, which is a unit vector with its tail fixed at the observer's location and its head kept pointing toward the Sun, and then uses the components to calculate the solar zenith angle and solar azimuth angle. The calculated solar vector at 1 ...
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 equation above neglects the influence of atmospheric refraction (which lifts the solar disc — i.e. makes the solar disc appear higher in the sky — by approximately 0.6° when it is on the horizon) and the non-zero angle subtended by the solar disc — i.e. the apparent diameter of the sun — (about 0.5°). The times of the rising and ...
The value of a solar beta angle for a satellite in Earth orbit can be found using the equation = [ + ()] where is the ecliptic true solar longitude, is the right ascension of ascending node (RAAN), is the orbit's inclination, and is the obliquity of the ecliptic (approximately 23.45 degrees for Earth at present).
To calculate the azimuth of the Sun or a star given its declination and hour angle at a specific location, modify the formula for a spherical Earth. Replace φ 2 with declination and longitude difference with hour angle, and change the sign (since the hour angle is positive westward instead of east). [citation needed]
For example, at 10:30 AM local apparent time the hour angle is −22.5° (15° per hour times 1.5 hours before noon). [4] 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 ...