ANALYTIC SOLUTION FOR SATELLITE RELATIVE MOTION WITH ZONAL GRAVITY PERTURBATIONS
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A state transition matrix for satellite relative motion including the effects of the higher-degree zonal gravity harmonics is presented. This work extends the earlier development by Gim and Alfriend which considered only the first-order secular and periodic perturbations due to the second zonal harmonic. Deprit's Lietransform based canonical perturbation theory is used to compute secular, shortperiod, and long-period perturbations in the orbital elements. Secular effects up to order three and periodic perturbations up to order two due to the zonal harmonics J2 through J6 are incorporated into the solution. The methodology presented in this work can be extended to include the second-order secular as well as short-period perturbations for the zonal harmonics up to an arbitrary degree. The improvement in prediction accuracy of relative motion resulting from each of the multiple effects is ascertained by considering projected circular orbit satellite formations.
author list (cited authors)
Mahajan, B., Vadali, S. R., & Alfriend, K. T.