Applet: The Earth and the Sun seen from the Moon

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Kepler's Dream: Lunar Astronomy

Applet: The Earth and the Sun seen from the Moon

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

Left:

Topocentric view of the Moon,
geographic coordinates from the text fields "Lat.", "Long.".

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.

Select "Moon Orbit" from the View menu

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 and view options.

Selenographic coordinates of the observer on the Moon,
northern latitude positive, eastern negative,
eastern longitude positive, western negative.

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.

The (optical) in latitude and longitude.

Some observations in Levania:

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)

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°.

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.

At trans-earth locations (privolva) nights (black bars) are always longer than days (red bars).
The mean difference is about 1.2 hours.

Full Moon, seen from the Earth,

New Earth, seen from the Moon.

Full Moon, seen from the Earth,

New Earth, seen from the Moon.

New Earth, seen from 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).

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

On the Earth there is an eclipse of 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.

The duration of a lunar day (14.764 days) is half a synodic month (29.5306 days).

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

Lunar noon at 30 N, 30 E:
2011, Nov 8 at 5:32
The subsolar point (red) is exactly south of the location(white).

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."

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:

Starry Night CSAP 7 was used to check the altitude, azimuth, elongation, and illumination 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:

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

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, bibliothèque 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.

© 2011-2023 J. Giesen

Last update: 2023, Oct 06

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
	Left: Topocentric view of the Moon, geographic coordinates from the text fields "Lat.", "Long.".
	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.
	Select "Moon Orbit" from the View menu

	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 and view options.
	Selenographic coordinates of the observer on the Moon, northern latitude positive, eastern negative, eastern longitude positive, western negative.
	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.
	The (optical) in latitude and longitude.
Some observations in Levania:
	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)
	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°.
	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.
	At trans-earth locations (privolva) nights (black bars) are always longer than days (red bars). The mean difference is about 1.2 hours.
	Full Moon, seen from the Earth, New Earth, seen from the Moon.
	Full Moon, seen from the Earth, New Earth, seen from the Moon.
	New Earth, seen from 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).
	An eclipse of the Sun begins: e.g. 2010, Dec 10, about 12 UT On the Earth there is an eclipse of 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.	The duration of a lunar day (14.764 days) is half a synodic month (29.5306 days).
	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
	Lunar noon at 30 N, 30 E: 2011, Nov 8 at 5:32 The subsolar point (red) is exactly south of the location(white).
	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."
	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: Starry Night CSAP 7 was used to check the altitude, azimuth, elongation, and illumination 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: Comparing Starry Night CSAP 7, Stellarium 0.15.1 and my Somnium Applet: The results of my applet are closer to Stellarium than to SN 7.