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Kepler's Dream: Lunar Astronomy

Applet: The Earth and the Sun seen from the Moon

Kepler somnium Levania
http://www.um.zagan.pl/kepler/kwz.htm
Johannes Kepler's (1571-1630) work "Somnium, sive Astronomia Lunaris" (A Dream, or Lunar Astronomy) is a fantastic tale of a journey to the Moon, which is called Levania by its inhabitants. The short work was published posthumously in 1634 by Kepler's son Ludovico.

Embedded in the narrative frames Kepler describes in details how astronomical observations might appear if they were conducted on the Moon.

The Moon is in synchronous rotation, keeping nearly the same face turned toward Earth at all times. One hemisphere of Levania (Moon) is always facing the Earth and one facing away, separated by the Divisor. Its inhabitants call the former hemisphere Subvolva (Under-Earth), and the latter Privolva (deprived-of-Earth). Our marvellous blue planet will never be seen from Privolva (Volva=Earth).

Daemon ex Levania
topocentric
                  Moon view
Left:

Topocentric view of the Moon,
geographic coordinates from the text fields "Lat.", "Long.".
earth view
                  sun view from the moon
Right:

The Earth (blue) and the Sun (red) as seen from a specified location on the Moon.

The apparent diameter of the Earth (2°) is approximately four times the Sun's diameter (32').

The apparent diameters are magnified by a factor of 3.3,
zoom may be disabled by a "Details" menu item.
Orbit of the
                  Moon

Select "Moon Orbit" from the View menu

keys 
You may use the keys d, m, h, or n to increase the date, month, hour, or minute,
or Shift key and d, m, h, or n to decrease the date, month, hour, or minute !
Click the applet first !

details
Details and view options.
selenograhic location
Selenographic coordinates of the observer on the Moon,
northern latitude positive, eastern negative,
eastern longitude positive, western negative.
Latitude
                  Longitude


Geographic coordinates of the location on the Earth,
enter decimal values:
northern latitude positive, eastern negative,
and press return key,
eastern longitude positive, western negative,
and press return key.
moon optical libration latitude
                  longitude

The (optical)  in latitude and longitude.
Some observations in Levania:
earth view
                  from Moon
The blue curve is the path of the Earth for the month selected, looking like an ellipse, but not closed.
The red line is the axis of the Earth.
0°N, 0°E is marked by a white dot.

Kepler is neglecting libration of the Moon:

"The moon always turns the same spots toward the earth.Therefore the line connecting the centers of the earth and the moon always pierces the moon's surface in the same spot...". (Rosen)


Kepler
                  Somnium Dream
libration
                  latitude libration longitude
The maximum libration in latitude is given by the sum of the inclination of the Moon's rotation axis to the ecliptic (1° 32), and the inclination of the Moon's orbit to the ecliptic (5° 09'):  1° 32 + 5° 09' = 6° 41. The maximum libration in longitude may be up to 8°.
Therefore the ellipse lies within an recangle of about 16° x 14°.
day and
                  night sub earth subvolva
At sub-earth locations (subvolva) days (red bars) are always longer than the duration of nights (black bars).
The mean difference is about 1.2 hours.

day and
                  night privolva
At  trans-earth locations (privolva) nights (black bars) are always longer than days (red bars).
The mean difference is about 1.2 hours.
phases of the
                  earth New Earth Full Earth

Full Moon, seen from the Earth,

New Earth, seen from the Moon.
Phases of the
                  Earth New Earth Full Earth
Full Moon, seen from the Earth,

New Earth, seen from the Moon.
new earth
                  phase


New Earth, seen from the Moon.
duration day
                  and night on the moon
For a Sub-Earth location (subvolva, small blue circle):
(2) sunrise
(3) noon
(4) sunset
(1) midnight
 The day-arc (2-3-4) is longer than the night-arc (4-1-2).

For a Trans-Earth location (privolva, small white circle):
(2) sunset
(3) midnight
(4) sunrise
(1) noon
 The night-arc (2-3-4) is longer  the day-arc (4-1-2).

eclipse
An eclipse of the Sun begins:
e.g. 2010, Dec 10, about 12 UT




On the Earth there is an eclipse of the Moon.
sunrise on the
                  moon  sunrise on the moon
Location on the Moon: 30° N, 30° E
Sunrise on 2011, Oct 31, at 21:06 UT
The divisor between day and night is crossing the location.
Select "Data Sunrise/Sunset" from the "Details",
please be patient waiting for the calculation.


error sunrise sunset

sunrise sunset on the moon

The duration of a lunar day (14.764 days) is half a synodic month (29.5306 days).
duration of
                  sunlight daylight on the moon

duration
                  of sunlight daylight on the moon

duration
                  of sunlight daylight on the moon
Within mean latitudes of the Moon there is always nearly equinox: the difference of daylight (sunlight) is small, increasing towards the pole.



Daylight duration:

30° N:  14.78 d +/- 0.17 d













Daylight duration:

60° N:  14.78 d +/- 0.45 d













Daylight :

85° N:  14.78 d +/- 2.9 d
noon on the
                  moon  noon on the moon
Lunar noon at 30 N, 30 E:
2011, Nov 8 at 5:32
The subsolar point (red) is exactly south of the location(white).
Noon
                  altitude of the sun on the moon
The altitude of the Sun (and the Earth) at lunar noon is depending on the selenographic latitude of the observer.

Kepler is writing:

"The inhabitants of this spot [i.e. the sub-earth point] have our earth, that is, their Volva, overhead. But in any place which is distant from this spot by a given number of degrees of a grat circle, Volva seems to deviate from the zenith by an equal number of degrees in the heavens."
sunrise
                  sunset on the moon
On the Moon, sunrise or sunset takes about 70 minutes (between upper/lower limb).
On the Earth, at 50° latitude,
sunrise or sunset takes only 4 minutes.
Accuracy of the applet

The
altitude and azimuth of the Earth as seen from different positions on the Moon (latitude B, longitude L) were compared with  Stellarium, using 7 dates (Jul/Aug 2015, at 20 UT). The mean error of the azimuth angle increases for high altitudes:

error earh position on the
                    moon


Starry Night CSAP 7 was used to check the altitude, azimuth, elongation, and illumination of the Earth as seen from the Moon:

Starry Night 7

Path of the earth as seen from the moon

Position of the Earth (2017, Jan 2, 20 UT) and path of the Earth as seen from the Moon (B=30°E, L=30°E), 2017 Jan


The altitude and azimuth of the Sun as seen from different positions on the Moon (latitude B, longitude L) were compared with  Stellarium, using 7 dates (Jul/Aug 2015, at 20 UT). The mean error of the azimuth angle increases for high altitudes:

error sun position



Comparing Starry Night CSAP 7, Stellarium 0.15.1 and my Somnium Applet:

Applet SN7

Applet Stellarium

Stellarium SN7

The results of my applet are closer to Stellarium than to SN 7.

More applet

Moon Motion (geocentric)

Moon Data

Moon Phase

Moon Phases for a Year

Sun & Moon Polar Applet

Azimuth of the Sun and the Moon at rise or set

Longitude of the Moon

Moon Light

Heliocentric and geocentric motion of the bright planets

More details:

Blue Moon

Full Moon distance

Lunar Perigee and Apogee Calculator


Cosmic voyages: authors and texts

Applet: Solar System Simulator (
Keith McClary)
watch the selenocentric motion of the Sun, the Earth, Venus, and Mars...

Web Links


Kepler's Somnium: Science Fiction and the Renaissance Scientist

Cosmic Voyages
Dictionary of the History of Ideas, Univ. of Virginia

Johannes Kepler: Somnium, seu Opus posthumum de astronomia lunari
(gallica, b
ibliothèque numérique de La Bibliothèque nationale de France)

Die Bewegung des Mondes, Anhang: Fragen zur Mondbewegung (PDF, U. Backhaus)

Der Mond, das unbekannte Objekt (U. Backhaus)
Dokumente, Powerpoint-Präsentationen, Programme für Windows

Lukian von Samosata: Die Wahre Geschichte (Projekt Gutenberg)
darin: 
eine Reise zum Mond

Lucian of Samosata:  
The True History, Book I

G. A. Bürger: Freiherr von Münchhausen:
Zehntes Seeabenteuer. Eine zweite Reise nach dem Monde.

R. E. Raspe: The Surprising Adventures of Baron Munchausen
Chapter XVIII: A second trip to the Moon

Current Moon View of the Earth from the Moon

Stellarium (free open source planetarium)

Books
Günther, Ludwig: Keplers Traum vom Mond, B.G. Teubner, Leipzig 1898.

Johannes Kepler: Der Traum, oder: Mond-Astronomie. Somnium sive astronomia lunaris, aus dem Lateinischen von Hans Baumgarten, herausgegeben und mit einem Leitfaden für Mondreisende von Beatrix Langner. Matthes & Seitz, Berlin 2011.

Edward Rosen: Kepler's Somnium: The Dream, or Posthumous Work on Lunar Astronomy, Translated with a Commentary, Dover Publications 2003.

Jaritz, Kurt: Utopischer Mond. Mondreisen aus drei Jahrtausenden.
Stiasny, Graz 1965.

Brunner, W.: Von Stern zu Stern. Eine Weltschau von verschiedenen Himmelskörpern aus, Rascher & Cie., Zürich 1923.

Kepler's Somnium: The Dream, or Posthumous Work on Lunar Astronomy.
Dover Publications 2003


Jean Meeus: Mathematical Astronomy Morsels, Willmann-Bell, p. 29-36.


© 2011-2017 J. Giesen

Last update: 2017,  Jan 18