Johnson, Kirk Wayne (2016-12). Approaches for Modeling Satellite Relative Motion. Doctoral Dissertation. Thesis uri icon

abstract

  • This dissertation explores new approaches for modeling perturbed and unperturbed satellite relative motion. It extends Hoots orbit theory, an analytical averaging-method perturbation solution to the Zonal Problem, to second order. In addition, this study develops a new hybrid numerical/analytical algorithm for converting initial conditions from osculating elements to mean elements, so that a single set of osculating initial conditions may be taken as simulation inputs. Also, this study develops a new version of the Gim-Alfriend State Transition Matrix (GA STM) for linearized perturbed relative motion, in terms of the variables from Hoots theory. These variables, the Hoots elements, are advantageous (although not unique) in that they have no singularities for orbit eccentricity or inclination and they require only one solution of Kepler's Equation at each time step, even when using the GA STM. The new models are compared by simulation with orbit theories and GA STMs using the so-called nonsingular elements (which are in fact singular for zero inclination) and the equinoctial elements. This study predicts and verifies the order of magnitude of modeling error due to various sources. This study also considers two special applications in satellite relative motion modeling. First, Projected Circular Orbit (PCO) formations, originally defined for unperturbed motion about a circular reference orbit, have important applications and are widely studied. This dissertation removes the singularity for zero inclination by implementing the PCO initial conditions in equinoctial elements, allowing PCO formations to be initialized about equatorial orbits. Furthermore, this study reveals how the choice of variables for writing the PCO initial conditions changes the geometric interpretation of the PCO phase angle parameter ?. Second, this study develops an alternative to the standard methods for mitigating along-track drift in perturbed satellite formations. The new method eliminates all along-track secular motion to first order by sacrificing one degree of freedom in the formation design.
  • This dissertation explores new approaches for modeling perturbed and unperturbed satellite relative motion. It extends Hoots orbit theory, an analytical averaging-method perturbation solution to the Zonal Problem, to second order. In addition, this study develops a new hybrid numerical/analytical algorithm for converting initial conditions from osculating elements to mean elements, so that a single set of osculating initial conditions may be taken as simulation inputs. Also, this study develops a new version of the Gim-Alfriend State Transition Matrix (GA STM) for linearized perturbed relative motion, in terms of the variables from Hoots theory. These variables, the Hoots elements, are advantageous (although not unique) in that they have no singularities for orbit eccentricity or inclination and they require only one solution of Kepler's Equation at each time step, even when using the GA STM. The new models are compared by simulation with orbit theories and GA STMs using the so-called nonsingular elements (which are in fact singular for zero inclination) and the equinoctial elements. This study predicts and verifies the order of magnitude of modeling error due to various sources.

    This study also considers two special applications in satellite relative motion modeling. First, Projected Circular Orbit (PCO) formations, originally defined for unperturbed motion about a circular reference orbit, have important applications and are widely studied. This dissertation removes the singularity for zero inclination by implementing the PCO initial conditions in equinoctial elements, allowing PCO formations to be initialized about equatorial orbits. Furthermore, this study reveals how the choice of variables for writing the PCO initial conditions changes the geometric interpretation of the PCO phase angle parameter ?. Second, this study develops an alternative to the standard methods for mitigating along-track drift in perturbed satellite formations. The new method eliminates all along-track secular motion to first order by sacrificing one degree of freedom in the formation design.

publication date

  • December 2016