High-Fidelity Dynamics Modeling for Near-Earth and Cislunar Space Incorporating Non-Conservative Effects

This study investigates the patterns of propagated classical elements in LEO, MEO, and GEO orbits, compares the effectiveness of the SPG4 orbit propagator to a High-Fidelity Model for these orbits, and explores resonant orbits in xGEO orbit design. Orbital dynamics plays a critical role in understanding the motion of spacecraft under the influence of celestial bodies and perturbations. To explore these topics, a High-Fidelity Model was built in Python. This model is based on the two-body problem and incorporates perturbations found in the space environment, and applies them to the spacecraft being studied. The formulas for the perturbations are derived from Fundamentals of Astrodynamics by David Vallado. The inputs for this model are position and velocity vectors, and the output is a series of position and velocity vectors corresponding to sequential time steps. Exporting the propagated position and velocity vectors allowed a MATLAB script to calculate the classical orbital elements and compare the propagation results from the High-Fidelity Model to those from SPG4 (as described in Fundamentals of Astrodynamics). Due to the cyclical nature of Earth-centered orbits, a mean average of the classical orbital elements was taken to examine the trends over time. To compare the propagation of SPG4 and the High-Fidelity Model, the error between the two was calculated for position and velocity vectors at each time step. To explore xGEO orbits using the High-Fidelity Model, orbits were designed at different resonance frequencies to assess the stability of the resonance. From examining the classical elements in LEO, GEO, and MEO, the following trends were observed: In LEO, eccentricity decreases, inclination increases, and argument of perigee rises, while the semi-major axis, RAAN, and true anomaly remain constant; in MEO, eccentricity and inclination increase, RAAN and argument of perigee rise, and true anomaly remains constant; in GEO, eccentricity and semi-major axis increase, inclination decreases, and RAAN, argument of perigee, and true anomaly stay constant. The results of comparing SPG4 to the High-Fidelity Model showed that, for LEO, MEO, and GEO, the error in SPG4 grew exponentially over time, indicating that SPG4 is most effective for small time intervals. Using High-Fidelity Modeling, this study investigates the trends in propagated orbital elements, compares the accuracy of SPG4 versus High-Fidelity Modeling over time, and examines the design of xGEO orbits. The findings have implications for the design and execution of orbits in the Earth and Earth-Moon environment.