Position of the Moon

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Position of the Sun by Spreadsheet
for a day

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Select the table 'input':
sun position

Input (red frames):

1) date, month, year

2) geogr. latitude und longitude (eastern longitude positive)

Don't modify any other cells.

input
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.
equation of time
Select declin  dist to see data and diagrams of the declination and distance.
declination distance
Select orbit to see data and a diagram of the ecliptic orbit. ecliptic orbit


Example: 1991, May 19 at 50N, 10E:

Sun position
        altitude elevation azimuth Excel download


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))))



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Sun position altitude
        elevation azimuth Excel download

The hours of sunrise and sunset are computed by interpolation
(upper limb, airless elevation -50'):

sunrise    sunset

The times agree with MICA and USNO within 1 minute.

Sun position altitude
        elevation azimuth Excel download

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 50N, 10E:

 


Diurnal motion of the Sun at 50N, 10E:


 
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equation of time

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:


equation of time



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declination distance

declination of the sun

On 1991, Dec 22, the UT hour of winter solstice is computed:
solstice
USNO: 8:54

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

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distance of the sun

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

Aphelion on Jul 6:
perihelion aphelion
USNO: 15:26




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ecliptic orbit

Position of the Sun in the ecliptic plane (1991, May 19):

ecliptic position

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Download my speadsheet:

sun_day.xlsx   (Excel, Windows, Mac)

sun_day.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

USNO Astronomical Applications Department, Sun or Moon Rise/Set Table for One Year

USNO, Apsides and Seasons

2020, Jan 23