Determination of the Even Harmonics in the Earth's Gravitational Potential

Abstract

This paper describes a method for using the orbits of artificial Earth satellites to determine the first seven even zonal harmonics in the Earth's gravitational potential, that is, the coefficients J2, J4 … J14 of the expansion in terms of Legendre polynomials as given in equation (1). To apply the method, accurate orbital information is required for at least seven satellites with widely differing orbits. Although existing orbital information is inadequate for the full application of the method, the Earth's gravitational potential has been determined as accurately as possible from the orbits of seven satellites covering a wide range of latitude. The potential experienced by these satellites is found to be best represented by the following set of coefficients: 106J2 = 1082.86 ± 0.1; 106J4 = −1.03 ± 0.2; 106J6 = 0.72 ±0.2; 106J8 = 0.34 ± 0.2; 106J10 = −0.50 ± 0.2; 106J12 = 0.44 ± 0.2. The quoted errors are tentative estimates of the departures from the true physical values. If the potential is to be represented by fewer even harmonics, the best number is three, and the appropriate values are: 106J2 = 1082.92 ± 0.1; 106J4 = −1.30 ± 0.2; 106J6 = 0.85 ± 0.2. To give the complete potential, values of J3, J5, etc., must of course be added.