Position of the Moon

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the Sun for a day      the Sun for a year

Position of the Sun by Spreadsheet
for a month

 Select the table 'input': Input (red frames): 1) hour UT, min 2) date: month, year 3) geogr. latitude und longitude     (eastern longitude positive) Don't modify any other cell. The table calc performs the calculations, using a lot of auxiliary variables. It should be neglected. Select elev az to see data and diagrams of elevation and azimuth. Select E o T for data and diagrams of the Equation of Time. Select declin  dist to see data and diagrams of the declination and distance. Select orbit to see data and a diagram of the ecliptic orbit. Example: 1991, May13:00 UT at 50°N, 10°E: ***  The value "elev" is not taking into account the atmospheric refraction.

Comparing the results "elev" (airless) of the spreadsheet with (4 decimal places) of HORIZONS Web-Interface
(NASA JPL) the mean absolute error is only (0,0058 ± 0,0011)°.

The refraction is calculated ("elev refr.") by
1.02/(60*tan(K*(elev+10.3/(elev+5.11))))  Azimuth is measured North(0°) -> East(90°) -> South(180°) -> West(270°) -> North (360°). 1991 May, 00:00 UT mean abs. error reference azimuth az (0.036 ± 0.018)° MICA right ascension RA (0.0051 ± 0.0012)° HORIZONS Web-Interface declination delta (0.0025 ± 0.0005)° HORIZONS Web-Interface ecliptic longitude L (0.0044 ± 0.0016)° HORIZONS Web-Interface

***  The equation of time can by computed (neglecting nutation in longitude) by
E = L0 - 0.0057183° - RA
EoT = 4*E in minutes

Example: 1991, May at 00:00 UT: ***   In 1991, March, the summer solstice is computed: Mar 22. winter solstice on Dec 22: * perihelion is on Jan 3: aphelion on Jul 7: ***     