Open AccessThe Even Zonal Harmonics of the Earth's Gravitational Potential
Author(s) -
KingHele D. G.,
Cook G. E.
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.tb03047.x
Subject(s) - gravitational potential , harmonics , spherical harmonics , representation (politics) , geodesy , standard deviation , gravitation , physics , orbital elements , notation , geophysics , geology , mathematics , classical mechanics , mathematical analysis , statistics , astrophysics , quantum mechanics , arithmetic , voltage , politics , political science , law
Summary The coefficients of the even zonal harmonics in the Earth's gravitational potential are evaluated by analysing the precessions of the orbital planes of seven satellites, having orbital inclinations distributed as uniformly as possible between 28° and 96°. The most satisfactory representation of the potential is found to be in terms of four coefficients, and their values are, in the usual notation, 10 6 J 2 = 1082.64 ± 0.02, 10 6 J 4 = ‐1.52 ± 0.03, 10 6 J 6 = 0.57 ± 0.07, 10 6 J 8 = 0.44 ± 0.11. The standard deviations quoted refer to a four‐coefficient representation of the potential. If more coefficients are used, the values will inevitably change, and more appropriate standard deviations would be 0.1 for the first three coefficients and 0.2 for the last. The potential experienced by the satellites we used can be more closely represented by six co‐efficients rather than four: values for these are given. The results are reviewed and possible future developments are outlined.