14th-order harmonics in the geopotential from analysis of satellite orbits at resonance

Abstract

The Earth's gravitational potential is usually expressed as a double series of tesseral harmonics of degree l and order m, and values of coefficients for l and m up to 36 or more are determined in recent models. The individual harmonic coefficients of a particular order m can most accurately be evaluated by analysing the perturbations on satellites which experience mth-order resonance (i.e. repeat their ground track after m revolutions). Here we use results from analyses of 15 satellite orbits at 14th-order resonance to evaluate 7 pairs of individual coefficients of 14th order and odd degree ( l = 15, 17,… 27), and 6 pairs of coefficients of even degree ( l = 14, 16,… 24). The five most accurate pairs of values, for l = 14, 15, 16, 17 and 19, have a mean standard deviation corresponding to an accuracy of 0.9 cm in geoid height. These values are used as a test of the accuracy of three recent comprehensive models of the geopotential : the agreement is generally satisfactory, the differences being consistent with the expected errors (about 3 × 10 −9) in the models. We also obtain values for the pair of coefficients of order 28 and degree 28, again with standard deviation equivalent to 0.9 cm in geoid height.