Position of the Moon

START

the Sun for a month      the Sun for a day

Position of the Sun by Spreadsheet
for a year


download

Select the table 'input': sun position

Input (red frames):

1) hour UT, min

2) year

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

Don't modify any other cell.


Sun year position
                spreadsheetexcel download
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
                geocentricdistance
Select orbit to see data and a diagram of the ecliptic orbit. orbit


Example: 1991, 12:00 UT at 50N, 10E:

Sun position year elevation
          altitude azimuth Excel spreadsheet download


***




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))))
***

Sun position year
        elevation altitude azimuth Excel spreadsheet download


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 (0,012 0,004).



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

equation of time

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


The analemma, 50N, 10E at 11:30 UT

analemma sun

***



drclination geocentric
        distance
Declination of the sun:
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).

*

spring equinox

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
***

*

distance sun earth


Comparing the results of my spreadsheet with the values of MICA
the mean absolute error is (60 40) km in 1991.

***





orbit
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:

equinox

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:

angular ecliptic velocity

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





Download my speadsheet:

sun_year.xlsx    (Excel, Windows, Mac)

sun_year.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