Accession Number:

AD0422250

Title:

DEVELOPMENT OF THE LUNAR TOPOGRAPHY INTO SPHERICAL HARMONICS, I,

Descriptive Note:

Corporate Author:

MANCHESTER UNIV (ENGLAND)

Personal Author(s):

Report Date:

1963-06-01

Pagination or Media Count:

29.0

Abstract:

Numerical values of the coefficients J sub ij and J sub ij of the expansion of the lunar topography into spherical harmonics are given. Terms up to the 8th order were considered and, therefore, 81 zonal and tesseral harmonics were included in this expansion. The basic data employed in the method of determining J sub ij and J sub ij ji 1, 2, .... 8 is that of the two independent variables least-square fitting. The usually employed method for determining J sub ij and J sub ij with the aid of volume integrals over a sphere, analogous to the integrals of the Fourier expansions, is not applicable in this case, because sufficiently accurate data are available for less than one-half of the lunar surface. Only 71 of Schrutka-Rechtenstamm points are approximated by the expansion with an error less than the observational one. More than 25 of the remaining points exceed the corresponding observational errors by a few hundred metres. Finally the few points approximated with an accuracy bigger by 1 km or so, from the error of observation, correspond to very abrupt morphological anomalies of the lunar surface. The coefficients provide sufficient basis for the preparation of a contour map of the lunar surface. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE