Position of the Moon

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the Sun for a month      the Sun for a day

Position of the Sun by Spreadsheet
for a year

 Select the table 'input': Input (red frames): 1) hour UT, min 2) 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, 12:00 UT at 50°N, 10°E:

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The value "elev" is not taking into account the atmospheric refraction.

Comparing the results "elev" (airless) of my spreadsheet with the 4 decimal places of HORIZONS Web-Interface
(NASA JPL) the mean absolute error is (0,0036 ± 0,0017)°.

The refraction is calculated ("elev refr.") by
1.02/(60*tan(K*(elev+10.3/(elev+5.11))))
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Azimuth is measured North(0°) -> East(90°) -> South(180°) -> West(270°) -> North (360°).

Comparing the results "az" of the azimuth of my spreadsheet with the 4 decimal places of HORIZONS Web-Interface
(NASA JPL) the mean absolute error is (0,012 ± 0,004)°.

Elevation of the Sun: 1991 at 50°N, 10°E

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

The mean absolute error in 2019 compared with the Nautical Almanach
is (1.5 ± 0.5) s.

The analemma, 50°N, 10°E at 11:30 UT

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Declination of the sun:

Comparing the results "delta" (declination) of my spreadsheet with the 5 decimal values of HORIZONS Web-Interface
(NASA JPL) the mean absolute error is (0,0023 ± 0,0018)°.

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Computing the UT of spring equinox (declination=0),
the result for 1991 is: Mar 20 at 26h 56,
which is Mar 21 at 2:56
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Comparing the results of my spreadsheet with the values of MICA
the mean absolute error is (60 ± 40) km in 1991.

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Comparing the results "L" (ecliptic longitude) of my spreadsheet with the 7 decimal values of HORIZONS Web-Interface
(NASA JPL) the mean absolute error is (0,004 ± 0,002)°.
In 1900 the mean absolute error is (0,001 ± 0,001)°.
In 2100
the mean absolute error is (0,006 ± 0,003)°.

The spring equinox in 1991 Mar 21:

Comparing the hours of spring equinox in 1990 to 2010 with MICA,
the mean absolutr error is (9 ± 6) minutes.

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Ecliptic angular velocity of the Sun:

minimum 1991 on July 5 (aphelion Jan 03)
maximum 1991 on Jan 5 (perihelion Jul 06)