Orbital Propagation using Generalized Orbital Elements based on the Centrifugal Potential

Orbit propagation is typically formulated in inertial frames, yet the Earth and Moon rotate, making body-fixed frames inherently non-inertial. This thesis embeds the centrifugal potential into the Generalized Equinoctial Orbital Elements (GEqOE) of Baù et al. (2021), producing a Rotational GEqOE (RGEqOE) formulation validated against a LAGEOS reference orbit and benchmarked against classical GEqOE and Cowell propagation. A singularity in the formulation is identified for certain eccentricity–inclination combinations. The model is then extended to the Moon, whose rotational dynamics — characterized through an FFT analysis of its precession and nutation cycles — are considerably more variable than Earth's, requiring periodic rectification to preserve propagation accuracy. Results quantify the accuracy, efficiency, and rectification requirements of the proposed formulation for both bodies.