An Interpolated Second-Order Relative Motion Model for Gateway

Understanding of relative motion dynamics is essential for many spaceflight objectives, from orbit determination to rendezvous. Although these dynamics are well understood in a Keplerian context, non-Keplerian regimes are increasingly relevant. To address relative motion in arbitrary dynamics, a Quadratic Interpolated State Transition (QIST) model is presented with test cases taken from the dominant dynamics governing the NASA Gateway. The QIST model uses interpolated state transition tensors to propagate arbitrary relative motion trajectories without numerical integration of the relative trajectory. Both Chebyshev and spline interpolants are used to parameterize the time-varying state transition tensors. The new relative motion model is applied to a Gateway reference trajectory adapted to the circular restricted three-body problem. Performance is benchmarked in terms of memory, accuracy, and speed of QIST for both interpolation methods and a model representing the current standard of practice. The spline version of QIST works directly in the time domain and requires 6.5 MB to achieve 14 digits of interpolant accuracy, while the Chebyshev version requires regularization but only consumes 130 kB of memory for the same result. At runtime, the QIST models demonstrate order of magnitude speed improvements over state of practice methods requiring numerical integration. Solutions propagated to first order with QIST agree with the standard of practice, while second order solutions show order of magnitude accuracy improvements throughout almost all of the Gateway orbit.