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The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane. This conveniently divides the sky into the upper hemisphere that you can see, and the lower hemisphere that you cannot (because the Earth is in the way). The pole of the upper hemisphere is called the zenith. The pole of the lower hemisphere is called the nadir. The horizontal coordinates are: The horizontal coordinate system is sometimes also called the az/el* or Alt/Az coordinate system.
General observations The horizontal coordinate system is fixed to the Earth, not the stars. Therefore, the altitude and azimuth of an object changes with time, as the object appears to drift across the sky. In addition, because the horizontal system is defined by your local horizon, the same object viewed from different locations on Earth at the same time will have different values of altitude and azimuth. Horizontal coordinates are very useful for determining the rise and set times of an object in the sky. When an object's altitude is 0°, it is on the horizon, if at that moment its altitude is increasing, it is rising, if its altitude is decreasing it is setting. However all objects on the celestial sphere are subject to the diurnal motion, which is always from east to west, so the inherent cumbersome determination whether altitude is increasing or decreasing can be easily found by considering the azimuth of the object instead: Note that the above considerations are strictly speaking true for the geometric horizon only: the horizon as it would appear for an observer on sealevel on a perfect smooth Earth without atmosphere. In practice the apparent horizon, which you see, has a negative altitude, which absolute value gets larger when you come higher, due to the curvature of the Earth. In addition the atmospheric refraction adds another 0.5° to that value. Transformation of coordinates It is possible to pass from the equatorial coordinate system to the horizontal coordinate system and back, once the observer's geographic latitude is known (+90° on the northpole, 0° on the equator, -90° on the southpole). We will use for the azimuth, for the altitude. We will use for the declination, for the hour angle. equatorial to horizontal One may be tempted to 'simplify' the last two equations by dividing out the leaving one expression in only. But the tangent cannot distinguish between, let say an azimuth of 45° and 225°, while these two values are very different, they are opposite directions, NE and SW respectively. Only do this when the situation is such that one knows in advance in which quadrant the wanted azimuth has to be. If the calculation is done with an electronic pocket calculator, it is best not to use the functions arcsin and arccos when possible, because of their limited 180° only range, and also because of the low accuracy the former gets around ±90° and the latter around 0° and 180°. Most scientific calculators have a rectangular to polar (R->P) and polar to rectangular (P->R) function, which avoids that problem and gives us an extra sanity check as well. The algorithm then becomes as follows. horizontal to equatorial Same considerations as for the first set also holds for this set of formulas. The position of the Sun There are several ways to compute the apparent position of the Sun in horizontal coordinates. Complete and accurate algorithms to obtain precise values can be found in Jean Meeus's book Astronomical Algorithms. Instead a simple approximate algorithm is the following: Given: You have to compute: where is the number of days spent since January 1. | ||||||||
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