Gravitational harmonics from shallow resonant orbits

Gravitational constraint (lumped coefficient) equations are derived from GEOS-2 data and a detailed analysis of the shallow resonance problem. The equations follow from elementary perturbation theory and show that all such lumped coefficients are harmonic in the argument of perigee. The best along-track constraints derived from them account for all but about 2% of the 13th-order resonant information in the tracking data. The equations are also in good agreement with recent comprehensive gravity models which use substantial amounts of GEOS-2 data.