Revisiting Universal Variables for Robust, Analytical Orbit Propagation Under the Vinti Potential

Abstract

To meet the growing complexity and demands of modern spacecraft missions, analytical solutions to initial value problems see continued use, typically supporting global searches of large trajectory design spaces. These efforts often employ universal two-body orbit propagators for their recognized speed and robustness, but many applications, like active space debris removal, would benefit from a comparable propagator with greater accuracy. Vinti propagators, which consider planetary oblateness, may serve this purpose, but existing Vinti solutions possess computational difficulties in certain orbital regimes. To mitigate these deficiencies, the present study develops and validates an analytical, third-order universal Vinti propagator free of computational difficulties by leveraging standard, oblate spheroidal (OS) universal variables and OS equinoctial orbital elements. Accuracy of the third-order approximation is assessed for multiple examples across an array of orbital regimes. Computational runtime is also evaluated, and performance is directly compared to the benchmark Vinti6 algorithm. On average, the Vinti propagator implemented in this work is only slower than a typical universal Kepler propagator by a factor of 4.0 and slower than Vinti6 by a factor of 1.8, but with greater robustness than the benchmark. The new form of the equations of motion also has favorable implications for the associated boundary value problem.