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Moon Libration Applet



You may use the keys m, w, d, h, n to increase the month, week, day, hour, or minute,

or shift key and m, w, d, h, n to decrease the month, week, day, hour, or minute.

To activate the applet press the button "Apply input" first !

latitude longitude
input

Enter decimal degree values for Latitude (southern negative) into the text field of the applet,
enter decimal degree values for Longitude (western negative) into the text field of the applet,
then press the button "Apply input"

Latitude 51.51, Longitude 13.41 is Berlin/Germany.
Latitude 40.76, Longitude -73.97 is New York.

The applet is computing and visualizing the geocentric optical libration of the Moon.
The red dot is located at 0 longitude and 0 latitude (selenographic).


There are three types of libration:
  • Libration in latitude is a consequence of the Moon's axis of rotation being slightly inclined to the normal to the plane of its orbit around Earth. Its origin is analogous to the way in which the seasons arise from Earth's revolution about the Sun.
  • Libration in longitude is a consequence of the Moon's orbit around Earth being somewhat eccentric, so that the Moon's rotation sometimes leads and sometimes lags its orbital position.
  • Diurnal libration. This is a consequence of Earth's rotation, which carries an observer first to one side and then to the other side of the straight line joining Earth's center to the Moon's center, allowing the observer to look first around one side of the Moon and then around the other.
These librations permit a terrestrial observer to see slightly differing halves of the Moon's surface at different times. This means that a total of 59% of the Moon's surface can be observed from Earth.

(From Wikipedia, the free encyclopedia)


parallactic angle of the moon

The parallactic angle (position angle) q of a celestial body (X) is the angle of the body's hour circle (XP) and its vertical circle (XZ), or between the declination circle (the path of the body) and the local horizon.



Apparent view of the Moon

Animation of lunar libration

moon libration
                        latitude

Libration in latitude 2007.

The maximum value is:
 1.54 (tilt of the Moon's equator to the ecliptic)
+ 5.15 (tilt of the Moon's orbital plane in respect to the ecliptic)
=6.69



moon libration longitude

Libration in longitude 2007.

The libration in longitude creates an east-west displacement of +/- 8.0.

lobration latitude and longitude  The "total" libration is computed by SQRT(L*L+B*B).



The curves below are showing the motion of the 'zero-point' of the lunar globe around its mean position, due to the librations in longitude and in latitude (Select "Lib. Path Month" from the Details menu).
The curves repeat after a period of almost exactly 6 years, when the major axis has performed one complete revolution with respect to the line of nodes (cf. Meeus).


January 2006
  

February 2006

March 2006

When the major axis of the lunar orbit is perpendicular the line of nodes of this orbit, the curve is the most open (cf. Meeus).

April 2006

May 2006

June 2006

July 2006

August 2006

September 2006

When the major axis of the lunar orbit coincides with the line of nodes of this orbit, the curve reduces to a straight line
(cf. Meeus).

October 2006

November 2006

December 2006


optical libration
                            Moon

The 0ptical libration of the Moon from 2006, Jan 1 to 2009, Jan 1.



Select "Lib. Path Year" from the Details menu:


libration
0ptical libration of the Moon 2006


libration
0ptical libration of the Moon 2007


libration
0ptical libration of the Moon 2008


libration
0ptical libration of the Moon 2009


Select "Data Lib." from the Details menu:

data libration moon

Scroll down to see extreme librations in longitude.
The mean periode of the libration in longitude is the anomalistic month, 27.5545 days, the time between perigee passages. The result computed by the MoonLibration applet (2006-2024) is 27.526 days.


extrme libration


libration longitude

Diagram of minimum libration in longitude, 2006-2010.

libration latitude

The mean periode of the libration in latitude is the draconic month, 27.212 days, the time between node passages. The result computed by the MoonLibration applet (2006-2024) is 27.215 days.

Please visit:

Web Links

Animation: Lunar libration with phase

Apparent Disk of Solar System Object (NASA)

Inconstant Moon (J. Walker)

Libration of the Moon

Geocentric Ephemeris for the Moon

Moon Ephemeris

Ephemeris for physical observation of the solar system bodies

Moon Locator (JavaScript calculator)

Parallactic Angle

Books
Jean Meeus: Mathematical Astronomy Morsels,
Willmann-Bell, Richmond, Virginia, 2nd Printing 2000,
ISBN 0-943396-51-4
Chapter 6: The librations of the Moon.

Jean Meeus: Astronomical Algorithms,
Willmann-Bell, Richmond, Virginia, 1rst English Edition 1991,
ISBN 0-943396-35-2
Chapter 51: Ephemeris for Physical Observations of the Moon.

2006-2013 J. Giesen

Last modified: 2013, Dec 09