Abstract
In the foregoing chapter we have outlined several methods for the determination of absolute (three-dimensional) coordinates of individual points on the lunar surface, and pointed out that determinations of the radial coordinates (i.e., of the distance of any such point from the Moon’s center) confront us with some of the most difficult and exacting problems encountered anywhere in the domain of astrometry. The outcome of such studies, and the harmonic analysis of their results, has revealed that within the limits of ±3 km (i.e., ±0.2 per cent of the lunar radius) the Moon is essentially a sphere of mean radius of 1738 km; though deviations of the actual surface from this sphere appear to be quite complicated, and their physical significance is still largely obscure.
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Bibliographical Notes
The definition of the lunar coordinates as introduced in this Chapter goes back to Tobias Mayer (1750); who together with Schröter and Lohrmann can be regarded as fathers of scientific selenodesy. The choice of the crater Mösting A as the fundamental zero point of lunar coordinates is due to Bessel(1839).
The detection of vertical irregularities on the surface of our satellite belongs among the first telescopic discoveries of Galileo Galilei (1610), who was also the first to attempt estimates of the heights of lunar mountains from the distance at which they become sunlit beyond the terminator. Needless to stress, Galileo was in no position to perform actual measurements with his rudimentary perspicill; and the altitudes assigned by him to some (unidentified) peaks — rendering them rivals in height of our Mount Everest — represented gross overestimates of the actual situation, as was pointed out only a little later by Hevelius (1647).
The first investigator actually to measure the extent of the visibility of individual lunar peaks beyond the terminator was William Herschel (1780), using a micrometer at his 6-foot telescope magnifying 222 times. Although Herschel customarily exaggerated the precision of his micrometric measurements (listing them to 0”.001, while their actual errors must have been several hundred times as large), he was correct in a realization that the lunar peaks are, in general, much lower than was thought by Galileo or even Hevelius; the majority of them being “between ½ and 1½ miles in height”.
Herschel’s work was soon followed by Schröter (1791, 1802) and, in the 19th century, by Beer and Mädler (1837) and Schmidt (1878), who abandoned the Galilei-Herschel method of watching for a beyond-the-terminator appearance, and set out to determine the relative altitudes of the lunar mountains from the observed lengths of their shadows cast by the individual peaks on the surrounding landscape at the time of lunar sunrise or sunset. The geometrical basis of this method had been credited to Olbers (see, e.g., Graff, 1901); while Beer and Mädler together with Schmidt, have provided (from observations with their modest-size telescopes) the bulk of the data on lunar altitudes available until the inception of the USAF-Manchester lunar mapping work in 1959.
In more recent times, the Olbers technique, developed further by Graff (1901), MacDonald (1929, 1931, 1932, 1940) and Cross (1954, 1955) of Fielder (1958) was adapted to photographic cine-technique by McMath, Petrie and Sawyer (1937). This method has since been exhaustively elaborated by Kopal and his collaborators of the Manchester Lunar Programme (cf., e.g., Kopal et al., 1961 ;
Kopal, 1959c; 1960a, 1961b, c, 1962d, 1963e; Kopal and Rackham, 1962; Rackham, 1962; Sudbury, 1965; Jones, 1965) who have jointly brought its “state of art” to the level at which it is presented in this volume. One particular contribution of Manchester astronomers to this field has been their recognition and appropriate treatment of the penumbral phenomena on the Moon. The same is true of the method of reduction of the shadow observations made from abroad a spacecraft approaching the lunar surface, as presented in this section; of the use of “over-exposed” terminator photography, etc.
Of subsequent work in this field, cf., e.g., Pohn, Murray and Brown (1962), Pohn (1963), Arthur (1963), Hopmann (1963) etc. A programme for an automatic transformation of the celestial and lunar coordinates by means of an electronic computer has been published by Wildey (1964).
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© 1966 Springer Science+Business Media Dordrecht
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Kopal, Z. (1966). Relative Coordinates on the Moon and their Determination. In: An Introduction to the Study of the Moon. Astrophysics and Space Science Library. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-6320-2_14
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DOI: https://doi.org/10.1007/978-94-017-6320-2_14
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