Position of the Moon


the Sun for a day      the Sun for a year

Position of the Sun by Spreadsheet
for a month


Select the table 'input': 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 50N, 10E:

position sun
        elevation altitude azimuth spreadsheet download Excel


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

position Sun elevation
        altitude azimuth spreadsheet Excel download

position Sun elevation
        altitude azimuth spreadsheet Excel download

Azimuth is measured North(0) -> East(90) -> South(180) -> West(270) -> North (360).

1991 May, 00:00 UT mean abs. error
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:

equation of time


sun declination
In 1991, March, the summer solstice is computed: Mar 22.

winter solstice on Dec 22:


sun earth distance

perihelion is on Jan 3:

aphelion on Jul 7:




earth orbit

Download my speadsheet:

sun_month.xlsx (Excel, Windows, Mac)

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


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

HORIZONS Web-Interface (NASA, JPL)

2019, Aug 10