Military Applications of High-Altitude Satellite Orbits in a Multi-Body Dynamical Environment Using Numerical Methods and Dynamical Systems Theory
Technical Report,01 Aug 2014,24 Mar 2016
AIR FORCE INSTITUTE OF TECHNOLOGY WRIGHT-PATTERSON AFB OH WRIGHT-PATTERSON AFB United States
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The circular restricted three-body problem CR3BP is a simplified dynamical model for a satellite under the gravitational influence of both the Earth and the Moon, maintaining closer fidelity to the gravitational environment experienced by a high-altitude Earth-orbiting spacecraft than modeling in the Earth-satellite two-body problem. Resonant orbit arcs are used to determine an initial guess to input into an algorithm that computes a trajectory solution with specific design requirements and constraints. A test case uses this method to compute a lunar fly-by transfer solution requiring less than two-body transfer methods and offers an unusual pathway that adds an unpredictability element to the design. Multiple-shooting and pseudo-arc length continuation methods are used to target trajectories and compute periodic orbits in the CR3BP to within a satisfactory tolerance. Invariant manifolds from an unstable periodic orbit around a liberation point in the Earth-Moon system are used as unpredictable transfer pathways when traveling from one Earth orbit to another, utilizing a map-based design process. Periapsis Poincare maps are also constructed to characterize the observed behaviors of orbits in the Earth-Moon system for a specified time, demonstrating utility for both designing trajectories with desired end characteristics and predicting an unknown spacecrafts future behavior.
- Unmanned Spacecraft
- Theoretical Mathematics
- Celestial Mechanics