Geopotential harmonics of orders 15 and 30

Abstract

The Earth's gravitational potential is usually expressed as a double infinite series of spherical harmonics. In recent models^1–3, derived from photographic, radio and laser observations of satellites, gravimetry and satellite altimetry, the harmonics have been evaluated up to a degree and an order of 36 or more, so that there are 1,296 or more coefficients to be evaluated. The geoid surfaces derived from such models have errors of approximately 1 m, but much better accuracy is required to take advantage of satellite altimeter measurements accurate to 10 cm or better. So there is a continuing demand to improve the models. The accuracy of the individual coefficients is questionable, and difficult to estimate⁴. The most precise technique for determining coefficients of a particular order is by analysis of satellite orbits which experience resonance with the Earth's gravitational field. We have recently⁵ re-evaluated individual harmonic coefficients of orders 15 and 30 from analyses of 24 orbits having a wide range of inclinations to the Equator. These coefficients have standard deviations equivalent to an accuracy in geoid height of 1 cm, for degree up to 23, and are valuable as a standard against which the comprehensive gravity field models can be tested.