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A numerical optimization study of a minimum-fuel LEO-to-MEO orbital trajectory trans- fer is solved using a bang-bang and singular optimal control (BBSOC) method with multi- domain Legendre-Gauss-Radau quadrature collocation. Modified equinoctial elements are used to avoid singularities that occur in orbital elements. The time, t, state components, (p, f,g,h,k,L,m), and control components, (ur,ut,un,T) are optimized in this one phase prob- lem where seven cases of the initial thrust acceleration values are considered. The structure of the thrust was not assumed, therefore the optimizer determined the number of switch points. The solutions were categorized as partial and multiple revolution optimal trajec- tories. The initial thrust accelerations considered for the partial revolution solutions are s0 = 􏰃1.0206 × 100, 5.1029 × 10−1, 1.0206 × 10−1, 5.1029 × 10−2 􏰄 AU. Furthermore, as the ini- tial thrust acceleration decreased, the final mass decreased while the total time thrusting increased. The initial thrust accelerations considered for the multiple revolution solutions are s0 = 􏰃1.0206 × 10−2, 5.1029 × 10−3, 1.0206 × 10−3 􏰄 AU. Furthermore, as the initial thrust acceleration decreased, the final mass increased while the total time thrusting increased. An in-depth study was completed for the cases of s0 = 􏰃1.0206 × 10−1, 1.0206 × 10−3 􏰄 AU, where the final mass was [0.6683, 0.5991] MU and the total time thrusting was [4.0305, 487.3276] TU.