A simplified formulation of the satellite perturbed relative motion problem
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abstract
This paper presents a simplified procedure for propagating satellite relative motion for low-eccentricity orbits using Kaula's linear perturbation theory. The first-order theory is augmented with the second-order of J2 secular and short period corrections for the classical orbital elements. The inclination function is computed using a recursive approach and the eccentricity function is evaluated by Legendre-Gauss-Lobatto quadrature. The unit sphere approach is used to map the differential orbital elements into relative motion states. The accuracy of the closed-form relative motion propagation approach is evaluated by comparison against numerical integration results obtained from the GMAT software. Inclusion of the second-order secular and short period effects improves the long-term prediction accuracy of the proposed relative motion propagation model.
