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A system of longitude and latitude used for describing the location of lunar surface features in a way very comparable to the system of geodetic longitude and latitude used on Earth. As on Earth, latitude measures the distance north or south of an equator defined to be approximately 90° from the rotation axis, while longitude is measured east and west from an arbitrarily chosen central meridian. On Earth this prime meridian passes through a point in Greenwich, England. On the Moon, the origin of the coordinate system passes through
that is most nearly, on average, pointed towards the
center of the Earth
Unlike Earth, for determining longitudes and latitudes the Moon is regarded as a perfect sphere. This means that one can draw a radial line from the Moon's center through a given point, by drawing a line at the stated angles. On Earth, by contrast, latitudes are traditionally defined in terms of normals (lines perpendicular to the surface) to a flattened ellipsoid, requiring complicated mathematical corrections.
Another difference with earthly longitudes and latitudes, is that there are two systems in use on the Moon. The most commonly encountered one (the one described above) is technically called the
Mean Earth - Polar
(MEP) system. The alternative is the
(PA) system. In the latter axes related to the Moon's shape are used, but because the orientation of the Moon's shape is tidally locked to the Earth, the differences between the two are slight and assumed constant.
Although "east" and "west" are presently used in lunar mapping in the same way as they are on Earth, prior to 1961 their sense was reversed on the Moon. See
As on Earth, lunar longitudes are normally expressed as an angle in the range 0 to 180° east or west of the "Prime Meridian" (the point of
). Alternatively, they can be expressed in a 0 to 360° system, counting the direction towards
Also as on Earth, latitudes are measured from the equator, with +90° representing the Moon's
and -90° the
By international agreement, definitions regarding lunar coordinate systems are governed by the
IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements
Nearly all lunar maps are referenced to the MEP system, but the definitive source for the Moon's position and orientation in space at any instant (cited by the IAU) is the
JPL DE405 ephemeris
, which specifies the principal axes.
The WGCCRE defines the MEP system as being offset from JPL's PA system by three small rotations, which are sometimes identified as p1, p2 and tau. The most recent values recommended in Seidelmann (2007), and taken from Konopliv (2001) are: p1 = -79.0768 arc-sec, p2 = +0.1462 arc-sec, and tau = +63.8986 arc-sec. An independent article by Chapront
(1999) recommended p1 = -78.9316 arc-sec, p2 = +0.2902 arc-sec, and tau = +66.1898 arc-sec. Still other values have been recommended in the past.
In layman's terms, p1 can be thought of a counter-clockwise (CCW) twist about the East-West axis, viewed from the direction of Mare Crisium; p2 as a CCW twist about the Earth-Moon axis, as viewed from the Earth; and tau as a CCW twist about the North-South axis as viewed from over the Moon's north pole. The result of all of this is that the position of the
(commonly known as the
in longitude and latitude) is numerically different in the MEP versus the PA system. The libration in longitude in the MEP system is larger (more positive) by 0.018 degrees (this comes from tau); while the latitude in the MEP system is smaller (more negative) by 0.022 degrees (this comes from p1). The longitude of the
is similarly affected by tau, but its latitude can be higher or lower than in the PA system because when it is to the Moon's east or west it is raised or lowered by p2, while at the intermediate positions it is raised or lowered by p1. The total difference in numerical positions of the Sub-Earth point in the MEP versus the PA systems corresponds to an offset on the lunar surface of less than 1 kilometer. This is very small compared to the inherent imprecisions of 10 km or more in most mapping products.
It is not totally clear from the readily-available documentation if the "mean-Earth" direction is meant to be determined by an actual average over some particular period of time or is simply a somewhat arbitrarily chosen direction similar to that defined by the WGCCRE offsets from the Moon's PA directions.
Old editions of the
provided the following:
"The point of the surface of the Moon where it is intersected by the lunar radius that would be directed towards the centre of the Earth, were the Moon to be at the mean ascending node when the node coincided with either the mean perigee or the mean apogee, defines the mean centre of the apparent disk."
In addition to the ambiguities regarding the direction of the MEP axes, the center point of the system does not seem to be clearly defined. Slightly different results will be obtained if the direction to a surface feature is determined with reference to the Moon's center of mass as opposed to its so-called "center of figure".
The effort to determine the correct positions of lunar surface features in the MEP system is an on-going one, and always subject to changes in the definition of the rotation axis, the mean-Earth direction, and/or the center point of the selenographic system. The best guesses for the coordinates of specific identifiable features covering a substantial part of the lunar sphere, including not only their longitude and latitude but also there radial distance from the Moon's center, have been embodied in a succession of so-called
Unified Lunar Control Networks
. The most recent of these (the so-called
) is thought to include features misplaced by 1 km or more, far cruder than the accuracy with which geographic/geodetic positions on Earth are known (a fraction of a centimeter). The seleonographic longitude and latitude of the remaining surface features is normally determined by their offsets from nearby control points; or even more commonly, by reading off their positions on a map registered to the control points.
The most accurately known control points on the Moon are the
Lunar Laser Ranging Retroreflectors
(LRRR), whose positions have been determined by triangulation from Earth. It is not entirely clear if the
has been accurately tied to these or not. For example the coordinates or the LRRR's can be estimated by their offset from ULCN 2005 control points, or by their positions read from the older
map series. As a rule, the latter values tend to be closer to the known coordinates.
Selenographic coordinates are sometimes (presumably erroneously) said to be defined by giving the longitude and latitude of
. Since latitudes are referenced to the Moon's spin axis, one can no more "define" the latitude of
than one can "define" the latitude of the transit circle in Greenwich, England. More properly, by observing the excursions of
from the apparent center of the lunar disk over a long enough period of time one can estimate how far the mean-Earth point is offset from. Stating the varying coordinates assigned to
in successive ULCN's is mostly an indication of the errors in the latter; and as a single point, it is only a very rough indication.
Great Britain. 1961.
Explanatory supplement to the Astronomical ephemeris and the American ephemeris and nautical almanac
. London: H.M. Stationery Off.
J. Chapront, M. Chapront-Touze, and G. Francou. 1999.
Determination of the lunar orbital and rotational parameters and of the ecliptic reference system orientation from LLR measurements and IERS data
A. S. Konopliv
Recent Gravity Models as a Result of the Lunar Prospector Mission
P. Kenneth Seidelmann
Report of the IAU/IAG Working Group on cartographic coordinates and rotational elements: 2006
Celestial Mechanics and Dynamical Astronomy
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