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The path of the Sun over the celestial sphere through the course of the day for an observer at 56°N latitude. The Sun's path changes with its declination during the year. The intersections of the curves with the horizontal axis show azimuths in degrees from North where the Sun rises and sets.
Above 60° latitude, the Sun would be even closer to the horizon, only 6.56° away from it. Then civil twilight continues almost all night, only a little bit of nautical twilight around the local midnight. Above 66.56° latitude, there is no sunset at all, a phenomenon referred to as the midnight sun. Solstice day arcs as viewed from 70° latitude.
The definition of geodetic latitude (ϕ) and geocentric latitude (θ) The geocentric latitude is the angle between the equatorial plane and the radius from the centre to a point of interest. When the point is on the surface of the ellipsoid, the relation between the geocentric latitude (θ) and the geodetic latitude (ϕ) is:
For example, with an axial tilt is 23°, and at a latitude of 45°, then the summer's peak sun angle is 68° (giving sin(68°) = 93% insolation at the surface), while winter's least sun angle is 22° (giving sin(22°) = 37% insolation at the surface). Thus, the greater the axial tilt, the stronger the seasons' variations at a given latitude. [4]
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.
This plot was created using the simple sunrise equation, approximating the sun as a single point and does not take into account effects caused by the atmosphere or the diameter of the Sun. The sunrise equation or sunset equation can be used to derive the time of sunrise or sunset for any solar declination and latitude in terms of local solar ...
The cosine of a latitude (declination, ecliptic and Galactic latitude, and altitude) are never negative by definition, since the latitude varies between −90° and +90°. Inverse trigonometric functions arcsine, arccosine and arctangent are quadrant-ambiguous, and results should be carefully evaluated.
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]