Aas 15-663 Analytic Power Series Solutions for Two-body and J2–j6 Trajectories and State Transition Models

Recent work has shown that two-body motion can be analytically modeled using analytic continuation models, which utilize kinematic transformation scalar variables that can be differentiated to an arbitrary order using the well-known Leibniz product rule. This method allows for large integration step sizes while still maintaining high accuracy. With these arbitrary order time derivatives available, an analytical Taylor series based solution may be applied to propagate the position and velocity vectors for the nonlinear two-body problem. This foundational method has been extended to demonstrate a highly effective variable step-size control for the analytic continuation Taylor series model. The current work builds on these earlier results by extending the analytic power series approach to trajectory calculations for two-body and J2–J6 gravity perturbation terms.