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Formula
The formula for calculating the solar elevation angle is extremely complex, and relies on a number of precise measurements. The exact latitude must be known, for example, and to make the formula as accurate as possible the degrees, minutes and seconds should all be known. Measurements like this can be obtained with an accurate GPS reading, but to determine the sun elevation angle, it is simpler to use a calculator. The National Oceanic and Atmospheric Administration provides such a calculator.
Uses
There are several uses for the information provided by the solar elevation angle formula. In extreme southern or northern regions, for instance, knowing the solar elevation angle can be used to determine how much daylight, if any, a region close to either of the poles will receive. The solar elevation angle is also useful to know for installing solar panels, and knowing if any land forms or buildings will interfere with the sun's rays reaching the solar panels.
The Solar System
The reason that a complex formula is necessary to determine where in the sky the sun will appear, relative to a particular position on the Earth, is that the solar system is a complex place. The Earth, for instance, does not travel around the sun in a perfectly elliptical pattern. Similarly, the tilt of the Earth, which is what determines seasons here on Earth, dramatically changes the angle of the sun. As our solar system moves amongst the rest of the galaxy, interactions with other heavenly bodies and other solar systems alter, in subtle ways, the motion of heavenly bodies in the Earth's solar system, and hence the position of the sun in the sky.
Solar Azimuth Angle
A measurement which is similar to the solar elevation angle is the solar azimuth angle. The solar azimuth angle is a measure of where in the sky the sun appears relative to the direction north or south. The angle is a measurement of the difference between the northern or southern point and the position of the sun, relative to the observer. Like the solar elevation angle, the solar azimuth angle is useful when you need to know what the exact position of the sun will be in the sky.