DEVELOPMENT OF THE LUNAR TOPOGRAPHY INTO SPHERICAL HARMONICS, I,

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 (j<i = 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)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1963
Accession Number
AD0422250

Entities

People

  • C. L. Goudas

Organizations

  • University of Manchester

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Coefficients
  • Errors
  • Functions (Mathematics)
  • Harmonics
  • Integrals
  • Lunar Topography
  • Mathematics
  • Observation
  • Spherical Harmonics
  • Topography

Readers

  • Analytical Mechanics
  • Approximation Theory.
  • Space Exploration and Orbital Mechanics.

Technology Areas

  • Space
  • Space - Orbital Debris