Sun position spreadsheets


the Moon for a year      the Moon for a month

Position of the Moon by Spreadsheet
for a day


Select the table 'input': moon day

Input (red frames):

1) Date, Month, Year

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

Don't modify any other cell.

input spread sheet

moon position
The table 'calc' performs the calculations, using a lot of auxiliary variables. Don't edit any cell!

Select 'elev az illum' to see data and diagrams of elevation, azimut and illumination.
Select 'distance' for data of the geocentric distance.

Culmination and Transit

The culmination of a celestial body means that the body is at its greatest altitude, whereas the transit is the passage of its center through the meridian.

Only the fixed stars culminate really in the meridian. The Sun, Moon, and the planets culminate out of the meridian.
At mid-latitudes (50) the difference may be up to 18 seconds for the Sun, and more than 6 minutes for the Moon.

The Moon, 50N, 0E

JPL Horizons System

Transit before culmination: ∆T ≈ 5 min, az ≈ 1,77, ∆elev ≈ 0.013

My spradsheet is computing transit by linear interpolation, culmination by parabolic interpolation.


Solar Eclipse of 2022, Oct. 25

On Oct. 25 at 14 UT equal longitudes:
                    elcipse 2022

On Oct. 26 at 6:30 UT the Moon passes the descending node:

eclipse 2022
                    Oct 26solar

Rise of the Moon occurs 13 to 87 minutes later than on previous day, and set 12 to 82 minutes later.

Example: 2019, Jan 1 at 50N, 10E:

        moon position download

moon elevation altitude
        spreadsheet download

The value "elev1" is not taking into account the atmospheric refracion.

Comparing the results "elev1" (airless) of my spreadsheet with the 4 decimal values of MICA
the mean absolute error is only (0,007 0,005).

The refraction is calculated ("elev refr.") by

Rise and set (UT) of the Moon are computed by interpolation:

moon rise         moon set

The mean error is (0.650.55) minutes (MICA)

In 2022 (1st of month): (0.72 0.63) minutes (MICA)

In 2023 (1st of month): (0.58 0.58) minutes (USNO)


The illuminated fraction k of the moon is geocentric, computed (Meeus, Astronomical Algorithms, Ch. 46)

k = [1+cos(i)]/2

cos(i)= cos(Bmoon) cos(Lmoon-Lsun)

moon spreadsheet excel download
        altitude illumination

moon position azimuth
        elevation illuminated fraction 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 (0,009 0,005).

The Moon on Jan 01:

moon path diurnal motion sky


The Total Solar Eclipse of 2019 Jul 02 (NASA):
Greatest Eclipse: 19:22:58.5 UT
Lat = 1723.3'S, Long = 10900.0'W
Sun Altitude =  49.6
Sun Azimuth = 359.0

|Lsun-Lmoon|='small'  and |Bmoon|='small'

solar eclipse 2019

solar eclipse 2019

topocentric distance

At 50N 15E the mean abs. error for 1st of month in 2022 and 2023 (reference MICA) is
(3.4 2.6) km

Download speadsheet :

moon_day.xlsx   (Excel, Windows and Mac)

moon_day.ods   (LibreOffice, Windows and 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 1800-2051), US Naval Observatory 2011, no longer published

Table of Sunrise/Sunset, Moonrise/Moonset, or Twilight Times for an Entire Year
(USNO Astronomical Applications Department)

2022, Oct 23