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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 maximum visible zenith angle occurs when the ray is tangent to Earth's surface; from triangle OCG in the figure at right, = + where is the observer's height above the surface and is the angular dip of the horizon. It is related to the horizon zenith angle by: = +
The pole of the upper hemisphere is called the zenith. The pole of the lower hemisphere is called the nadir. [5] The following are two independent horizontal angular coordinates: Altitude (alt.), sometimes referred to as elevation (el.) or apparent height, is the angle between the object and the observer's local horizon. For visible objects, it ...
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 ...
Its declination reaches a maximum equal to the angle of Earth's axial tilt (23.44° or 23°26') [8] [9] on the June solstice, then decreases until reaching its minimum (−23.44° or -23°26') on the December solstice, when its value is the negative of the axial tilt.
In the above equation, ψ s and θ s are respectively the azimuth and zenith angle of the Sun, and ψ and θ are respectively the azimuth and zenith angle of the observed point. This equation breaks down at the zenith where the angular distance between the observed pointing and the zenith, θ s is 0. Here the orientation of polarization is ...
When an inferior planet is visible after sunset, it is near its greatest eastern elongation. When an inferior planet is visible before sunrise, it is near its greatest western elongation. The angle of the maximum elongation (east or west) for Mercury is between 18° and 28°, while that for Venus is between 45° and 47°.
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 .