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Wagner 1983
Wagner, C.A. (1983). Direct determination of gravitational harmonics from low-low GRAVSAT data. Journal of Geophysical Research 88: doi: 10.1029/JB080i013p10308. issn: 0148-0227.

An efficient method is developed to compute gravitational harmonics from low-low satellite-satellite range data measurements. The satellites are assumed to be nearly the same low eccentricity orbits. The residual range rate signal is modeled with frequencies derived from linear perturbation theory to an accuracy of about 99%. Significant nonlinear effects involving J2, not currently modeled, require both J2 and J3 to be known in the reference trajectories. Each harmonic (l,m) generates l+1 principal frequencies, but they are not unique. Yet it appears possible to design a low-altitude mission which keeps the pair at nearly constant separation and where the frequencies for all terms to (180,180) are separable after only about 4 weeks. A simple demonstration of the method is shown to recover (in two iterations) a complete (4.4) model (less J2 and J3) from 1 day of ''perfect'' measurements (every 7 min) generated by numerical integration. In this result, the effects of orbit determination are included in a crude wave, but no other gravitational effects (of higher degree or from luni-solar attraction) are present. Nevertheless, the method is easily extended to high degree with rapid new techniques (which are described) for calculating the required inclination functions of the orbits.

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Abstract

Journal
Journal of Geophysical Research
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American Geophysical Union
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