Open AccessOn the Determination of the Even Zonal Harmonics in the External Gravitational Potential of the Earth
Author(s) -
Cook A. H.
Publication year - 1965
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1965.tb03061.x
Subject(s) - harmonics , solid harmonics , spherical harmonics , geodesy , harmonic , harmonic analysis , gravitational potential , geopotential , physics , geology , geophysics , mathematics , gravitation , mathematical analysis , classical mechanics , acoustics , quantum mechanics , voltage
Summary A comparison is made between the data used and the results obtained in four recent studies of the determination of the even zonal harmonics in the external potential of the Earth from the secular motions of the orbits of artificial satellites. It appears that the sets of data used in the studies are inconsistent in the sense that the standard deviations of the observations do not represent the residuals with respect to sets of harmonics fitted to the data and in that sets of harmonics derived from one set of data do not represent other sets of data. It is argued that the reason for these discrepancies is that harmonic terms beyond those that it is sought to fit to the data are not negligible. It is found that reliable values of the harmonics of order 2,4 and 6 can be obtained from data on satellites with large semi‐major axes, that the data are inadequate to separate higher harmonics, but that the magnitudes of harmonics in the neighbourhood of the 14th are probably of the order of 0.2 × 10 6 . The coefficients of the three harmonics determined from the four satellites with the largest semi‐major axes are 10 6 × J 2 = 1082.65, s. d. 0.1 10 6 × J 4 = ‐1.61, s. d. 0.15 10 6 × J 6 = 0.73, s. d. 0.4.