Effect of resonance‐oblateness coupling on a satellite orbit

Second‐order effects of the coupling between geopotential resonance and oblateness on a satellite orbit are calculated. These effects arise from the interaction of resonance with the secular changes of the orbit's node, perigee, and mean anomaly. They have the same period and phase as first‐order resonance perturbations. But their amplitudes are proportional to the square of the period and dominate the first‐order effects as the orbit becomes commensurate. A striking example of this coupling is seen in the 18‐day resonance variation of the node of the orbit of the first earth resources technology satellite. Analysis of this 1 arc sec (31 m) variation yields a strong fourteenth‐order constraint to the geopotential field for odd degree terms. This constraint (lumped coefficient) is poorly predicted by most current models.