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Changes in the orientation of the Moon as seen from Earth, expressed in terms of the
longitude and latitude of the observed center (also known as the
The Moon basically keeps the same face (the "nearside") pointed towards the Earth. However, its exact orientation is constantly changing at the level of a few degrees.
By convention, the surface feature at the
average center point
of this apparent disk is taken as the point of zero longitude and latitude. At any moment, features up to about 12° from this point can occupy the apparent center. The
refer to the longitude and latitude of the feature currently seen at the Moon's apparent center.
The major part of the Moon's
libration in latitude
is due to the inclination of the Moon's spin axis relative to the plane of of its orbit. This amounts to a variation of about ±6½° in the latitude of the observed center point (Roncoli, 2005, puts the maximum at 6.87°).
The major part of the Moon's
libration in longitude
is due to its spinning like a top at constant velocity (relative to the stars), yet travelling in an elliptical orbit (which causes our angle of viewing it to change at a varying speed). The result is that the apparent center point varies by around ±8° in longitude (Roncoli, 2005, puts the maximum at 8.16°).
In addition to these basic rocking motions, an observer's exact location on Earth will can change his perspective. An observer in the Earth's far north sees more of the Moon's northern parts; while one observing the Moon at moonrise sees more of the leading limb. This affect alters the coordinates of the apparent center by up to about ±1°. These true
, as actually seen by the observer, are called the
(as opposed to the
-- which are computed for an imaginary observer at the Earth's center, and, although frequently tabulated in Almanacs, seldom apply to any real observer).
Any variation beyond that which can be attributed to an idealized spinning top (such as would be observed if the Moon's spin rate about its axis were not perfectly constant) is categorized as a
The Moon's librations tend to make the observed center point wander around the "official" center in a quasi-circular or elliptical pattern. It would be rare, indeed, for the point of zero longitude and latitude (the "
") to actually be observed in the center, and even then, it would be seen so only for a single observer.
The librations in longitude and latitude are frequently abbreviated by the letters "l" and "b" although this convention is by no means universal. "L" and "B" were probably originally abbreviations for the German words "
" (longitude) and "
" (latitude). On diagrams, and in mathematical discussions they are sometimes replaced by the Greek letters
, although again, this is not a universal conention.
The magnitudes of the librations are traditionally stated as +/- numbers (rather than N-S/E-W). As indicated in the definition, these are the selenographic coordinates of the Moon's apparent center. In longitude ("l"), positive values are in the
direction. In latitude ("b"), they are in the
direction. Hence a "+" value for "l" means the
limb is tipped into view. A "+" value for "b" means the
limb is tipped into view. The convention that longitudes towards
are positive is a very old one, so no change in the way librations are stated or understood was required when the IAU
the meaning of "east" and "west" on the Moon.
See LPOD list in page
Ralph B. Roncoli. 2005.
Lunar Constants and Models Document
. JPL Technical Document D-32296.
Weimer, Th. 1979.
Cartography of the marginal zones of the moon
Moon and the Planets
, vol. 20, Apr. 1979, p. 157-162. In French.
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