Evaluation of 15th- and 30th-order geopotential harmonic coefficients from 26 resonant satellite orbits

Abstract

The Earth's gravitational potential is usually expressed as an infinite series of harmonics, and the values of harmonic coefficients of order 15 and 30 can be determined most accurately by analysis of satellite orbits which experience 15th-order resonance. The results from two recent resonance analyses, for 1965-09A and 1968-70A, have here been added to those previously available, to produce an improved evaluation of 44 coefficients of order 15 and degree 15–36, and 12 coefficients of order 30 and even-degree 30, 32, …, 40. Compared with previous results, the new evaluation shows a great improvement in the standard deviations of many of the 15th-order coefficients of even-degree, thanks largely to the contribution of 1965-09A at inclination 31.8°: for the coefficients of degree 24, 26, 28 and 30, the standard deviation has been reduced by a factor of 3.1 on average; and for degree 32, 34 and 36 by a factor of 1.4 on average. For the other coefficients—those of 30th-order, and odd-degree 15th-order—the changes are relatively small. In the new 15th-order solution, all the 30 coefficients of degree 15–29 have standard deviations ⩽ 2.0 × 10 −9, and the average standard deviation of these 30 values is equivalent to an error in geoid height of 0.7 cm. Comparison of our values with those in comprehensive geoid models, which usually have larger standard deviation, lead us to conclude that, for order 15 and 30, the nominal standard deviations of the comprehensive models are quite realistic.