Determining the Probability of Close Approach between Two Satellites
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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This thesis develops methods to calculate probability of close approach between two satellites. The investigation was restricted to satellite orbits and time intervals where the mean anomaly of both satellites can be treated as independent, uniformly distributed random variables. All orbital parameters, except for mean anomaly, were assumed to be constant over time which means that all the methods developed to calculate the probability of close approach will only be valid over very long time intervals where the ratio of the orbital periods of the two satellites can be approximated as an irrational number. Likewise, there can be no perturbations in the orbital parameters of both satellites. A general method was developed for calculating the probability of close approach between two satellites in elliptical orbits. Another method was developed for calculating the probability of close approach between two satellites in circular orbits. Both the elliptical orbit and the circular orbit methods of computing probability of close approach yielded results that compare favorably with estimates of probability of close approach derived from statistical simulations.
- Celestial Mechanics
- Spacecraft Trajectories and Reentry