Accession Number : AD0621044

Title :   A CHEBYSHEV APPROXIMATION TO THE EARTH'S EXTERNAL GRAVIPOTENTIAL WITH INTERNALLY UNRESTRICTED MASS DISTRIBUTION,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Juncosa,M. L. ; Johns,R. K. C.

Report Date : SEP 1965

Pagination or Media Count : 34

Abstract : The global external gravitational potential is developed in a series of polynomials of direction cosines and inverse powers of the radius closely related to an expansion of the potential in spherical harmonics. The Chebyshev fitting criterion is used to obtain the coefficients in several sets of approximations. To various (up to nearly six) numbers of significant figures, these approximations agree with comparable customary expansions in zonal and tesseral harmonics whose coefficients are usually obtained with the less stringent least-squares criterion, but they contain fewer coefficients. Chebyshev linear fitting problems are equivalent to linear programming problems for which many routines already exist for use on electronic digital computers. The use of fewer coefficients and simpler functions in the expansion yields computational advantages. Because the internal mass distributions producing identical external potentials are not necessarily unique, no assumptions on the internal mass structure are made. (Author)

Descriptors :   (*GRAVITY, POTENTIAL THEORY), (*POLYNOMIALS, LINEAR PROGRAMMING), SERIES(MATHEMATICS), HARMONIC ANALYSIS, GEOPHYSICS, NUMERICAL ANALYSIS, NUMERICAL METHODS AND PROCEDURES

Distribution Statement : APPROVED FOR PUBLIC RELEASE