Orbital body embeddings: Solitary, intercept, collision, and post-impact debris cloud behavior

Understanding and modeling orbital motion is critical for engineering applications. Orbital motion in the two-body problem while well-defined is critical in desiring solutions for orbital debris removal. This thesis focuses on the motion of particles in atmospheric and gravitational orbits and works to provide an understanding of the motion in these fields. The work here focuses on orbital mechanics in low-Earth orbit to provide an understanding of the current orbital debris environment. Estimating the conjunctions of trackable debris for satellites in low Earth orbit. Specifically focused on orbital companion satellites to protect a primary satellite in comparison with statistical engineering models such as ORDEM. In addition to defining the relative motion between two satellites in orbit, for estimation, and non-cooperative rendezvous control, which is essential for debris removal. Finally, the orbital mechanics and relationships are defined to generate theoretical debris clouds from hypervelocity impacts (HVI) in LEO. In addition to providing the tools to estimate where these collisions may occur for any relative velocity, (barv_r). Further, we provide a framework that rotates the HVI debris cloud motion to the Hill frame for the identified collision. Allowing for the rotated HVI data to be the initial conditions for a simulation using the relative equations of motion between two satellites. Thereby, simulating the debris cloud propagation using orbital mechanics and determining the change in orbit, and the resulting risk to satellites in the region human habitable region. This study specifically investigates the effect of debris cloud generation for ISS-like orbits from 400-500km and found in most cases 89% of the resulting cloud de-orbit within 1000s. Integrating the numerical ANSYS tool and classical orbital mechanics, with the relative motion, provides a setup to model short-term orbit cloud propagation and de-orbit simulation.