The Even Zonal Harmonics of the Earth's Gravitational Potential

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, 106J2 = 1082.64 ±0.02, 106J4= −1.52 ± 0.03, 106J6 = 0.57 ±0.07, 106J8 = 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 coefficients rather than four: values for these are given. The results are reviewed and possible future developments are outlined.