Relative Motion Around an Arbitrary Ephemeris Reference Trajectory

Relative motion solutions are increasingly required in non-Keplerian models that lack analytic solutions. To address this gap, a relative motion model is proposed using an ephemeris reference trajectory defined by a Spacecraft, Planet, Instrument, C-matrix, and Events (SPICE) spacecraft and planet kernel (SPK) file. State transition matrices and tensors, incorporating ephemeris gravity along with spherical harmonics at the central body, enable linear and quadratic modeling. Model generation uses a dense integrator, yielding a continuous integrand. The reference trajectory and solutions to the variational equations are stored, enabling rapid propagation. The new model is validated against known Keplerian and perturbed solutions. The elements of the kernel-referenced flow partials are shown to retain no worse than eight digits of accuracy. Subsequently, a relative motion model for the Gateway reference kernel is computed, where the originating model is not exactly known. To demonstrate relative motion around an arbitrary reference, the model is used for nonlinear propagation of uncertainty around the Gateway orbit and the Cassini mission kernel. The kernel relative motion model is shown to provide accuracy improvement over non-kernel-referenced equivalent models. The Fortran source for computing kernel relative motion is published as part of this work, including Python and MATLAB interfaces.