Position of the Moon

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the Sun for a month     the Sun for a year

Position of the Sun by Spreadsheet
for a day

 Select the table 'input': Input (red frames): 1) date, month, year 2) geogr. latitude und longitude (eastern longitude positive) Don't modify any other cells. 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, May 19 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 (0,0034 ± 0,0022)°.

The refraction is calculated ("elev refr.") by
1.02/(60*tan(K*(elev+10.3/(elev+5.11)))) ***  The hours of sunrise and sunset are computed by interpolation
(upper limb, airless elevation -50'):  The times agree with MICA and USNO within 1 minute. Azimuth is measured North(0°) -> East(90°) -> South(180°) -> West(270°) -> North (360°).

Comparing the azimuth results "az" of my spreadsheet with the 4 decimal values  of HORIZONS Web-Interface
(NASA JPL) the mean absolute error is (0,0077 ± 0,0024)°.

Diurnal motion of the Sun on May 19 at 50°N, 10°E: Diurnal motion of the Sun at 50°N, 10°E:  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 19:   On 1991, Dec 22, the UT hour of winter solstice is computed: USNO: 8:54

and on Jun 21, the UT hour of summer solstice: USNO: 21:19

* Perihelion on 1991, Jan 3 (0,983281 AU): USNO: 02:59

Aphelion on Jul 6: USNO: 15:26 *** Position of the Sun in the ecliptic plane (1991, May 19): ***  