Home Search GeoAstro Applets Astronomy Chaos Game Java Miscel- laneous Physics Quiz Who is Who ?

Sun & Moon Polar Applet

 Select latitude (northern positive, southern negative), and longitude (eastern negative, western positive) from the menus. You may use the keys "y", "m", "d", "h", "n" to increase the year, month, date, hour, or minute, or Shift key and "y", "m", "d", "h", "n" to decrease the year, month, date, hour, or minute.

Berlin, 2003, April 16 at 20:26 CEST

Applet: Sun and Moon azimuth at Horizon
showing a diagram for one year

Watch the points (azimuth angles) of rise and set of the Sun and the Moon on the horizon as the are changing from day to day:

 Berlin, 2003 Jan 21 Berlin, 2003 Apr 21

Watch animation

The azimuth angle Az0 for rise and set can be computed from the declination (delta) and the geographical latitude (beta) by:

cos (Azo) = sin delta / cos beta

At Berlin (beta=52.51°) we get for the:

rising Sun

 declination Azimuth Az0 23.44° summer solstice 49.2° -23.44° winter solstice 130.8° 0° equinox 90°

rising Moon
(orbit inclination to ecliptic 5.145°)

 declination Azimuth Az0 +23.44° + 5.145° = = 28.585° 38.2° +23.44° - 5.145° = 18.295° 58.95° -23.44° + 5.145° = -18.295° 121.05° -23.44° - 5.145° = -28.585° 141.8° 0° + 5.145° = 5.145° 81.5° 0° - 5.145° = - 5.145° 98.5°

Moonrise and moonset may occur at any point of the horizon except in the grey sector:

Whereas the range of the azimuth angle of rise and set is constant for the sun, it varies for the moon:

Berlin, 1985 - 2017,
Major and minor northern and southern moonrise azimuth

In this diagram we find a period of about 18.5 years, the time for a turn of the line of nodes which rotates in the opposite direction to the Moon's movement ("regression of the nodes").

2006 is a major lunar standstill season.

Angular difference between major and minor moonrise azimuth

The directions of solar and lunar standstill are found at the Stonehenge observatory
Latitude beta = 51.18 N, Obliquity delta=24.0° (3000 BC).

green: moon azimuth for declination -5.145° and +5.145°
blue: moon azimuth for declination 24.0°-5.145° and 24.0°+5.145°,
-24.0°-5.145° and -24.0°+5.145°,
red: moon azimuth for declination 24.0° and -24.0°, Sun at solstices.

The applet is using the simple azimuth formula cos(Azo) = sin(delta)/cos(beta)
describing a "mathematical" sunrise (center of the Sun on the horizon, no atmospheric refraction).
Using the common definition of sunrise (elevation -0.83°), the azimuth angle of the rising Sun
is about 1.3° smaller at summer solstice.

"Grundriss von Stonehenge. Von aussen nach innen: Graben, Wall, Aubrey-Löcher,
Stationssteine 91-94, Y- und Z-Löcher, Sarsenkreis, Hufeisen, einige Blausteinpfeiler
und, verstreut, Pfostenlöcher."

Quelle: Rudolf Drößler: Astronomie in Stein. Archäologen und Astronomen enträtseln alte Bauwerke und Kultstätten. Lizenzausgabe Panorama Verlag, Wiesbaden, o.J., ISBN 3-926642-25-4. Seite 71, Bild 33.
Die Wiedergabe erfolgt mit freundlicher Genehmigung des Verfassers.

Obliquity of the ecliptic:

rising Sun

 declination Azimuth Az0 24.0° summer solstice 49.5° -23.44° winter solstice 130.5

rising Moon
(orbit inclination to ecliptic 5.145°)

 declination Azimuth Az0 +24.0° + 5.1° = 29.1° 39.1° Maj. Northern +24.0° - 5.1° = 18.9° 58.9° Min. Northern -24.0° + 5.1° = -18.9° 121.1° Min. Southern -23.44° - 5.145° = -28.585° 140.8° Maj. Southern

My "SunMoon Polar Applet" is calculating the sunrise/sunset (as usual in astronomy) at an altitude of -0.83°, and the moonrise/moonset at an altitude of +0.13°. The data computed by the applet were exported the the Java console and sorted by a spreadsheet program.

The observer is located at the centre of his "celestial sphere" with zenith Z above his head and the horizon N-E-S-W. The Sun, Moon or any other celestial body can be identified by the two coordinates altitude (elevation) h and azimuth az (horizontal coordinates). Altitude is the angular distance above the horizon (0 < h < 90°), and azimuth the angular distance, measured along the horizon, eastwards from the north point N in nautics (0 < alpha <360°), or westwards from the south point S (in astronomy).