The odd zonal harmonics in the Earth's gravitational potential

Abstract

The odd zonal harmonics in the Earth's gravitational potential are determined by analysing the changes in the eccentricities of six satellites having orbital inclinations spaced 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 3 = −2.56, 10 6 J 5 = −0.15, 10 6 J 7 = −0.44, 10 6 J 9 = 0.12. The resulting potential is compared with that obtained by other authors. Three and five-coefficient solutions are also presented.