The relative motion of two spacecraft orbiting the Earth in low orbits in nominally circular orbits is studied in the presence of the J2 perturbation. An iterative scheme is developed which ultimately leads to closure of the relative motion after one orbit. Although not truly periodic, a numerical example indicates that it is very nearly so. The method makes use of a state transition matrix for the relative motion that is developed in the presence of feedback control in order to render the iterative scheme convergent. The example shows that the calculated initial conditions are relatively insensitive to small errors.
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