Position of the Sun by speadsheet

Position of the Moon

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the Sun for a month the Sun for a day

The Analemma of the Moon

Position of the Sun by Spreadsheet
for a year

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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:

Sun position year elevation
altitude azimuth Excel spreadsheet download

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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 (0,0035 ± 0,0015)°
(computed by 2 days per month in 1991).

The refraction is calculated ("elevRefr.") by
1.02/(60*tan(K*(elev+10.3/(elev+5.11))))
***

Sun position year
elevation altitude azimuth Excel spreadsheet download

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 (0,011 ± 0,004)°
(computed by 2 days per month in 1991).

Elevation of the Sun: 1991 at 50°N, 10°E
Sun position year elevation
altitude azimuth Excel spreadsheet download

***

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

analemma sun

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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 ***

*

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)°.

ecliptic orbit

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.

*

Ecliptic angular velocity of the Sun:

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

Download my speadsheet:

sun_yearA.xlsx (Excel, Windows, Mac)

sun_yearA.ods (LibreOffice, recommended, Windows, Mac)

updated!

Web Links

Die Zeitgleichung: Eine einfache Formel zu Sonnenaufgang und Untergang

General Solar Position Calculations (PDF)

Solar Calculation Details

MICA (Multiliyear Interactive Computer Almanac), US Naval Observatory

2019, Jun 13