his dissertation deals with the development of a method to predict the orbital lifetimes of uncontrolled free tethers and tether-trailing satellites originating in low-to-moderate altitude Earth orbits. The problem is solved by application of the "empirical method." Two mathematical models to simulate the orbital evolution of tethered systems are developed. In both models the system is discretized into a series of interconnected point masses, orbiting an oblate Earth and transiting an oblate, rotating, temporally and globally averaged atmosphere. For aerodynamic drag calculations, tether segments are modeled as right circular cylinders, and any end-body is modeled as a sphere. Drag coefficients vary as a function of shape and Knudsen number. In the "multibody model", connections between masses are elastic, and the system is free to assume any orientation. Newtonian equations of motion are numerically integrated. In the "orbital element propagation model", connections between masses are inelastic, and the system is constrained to remain aligned along the local vertical. Gauss' form of Lagrange's Planetary Equations, in terms of equinoctial elements, are used to propagate the orbital elements describing the orbit of the system's center of mass. The element propagation model is shown to provide, for initially unstretched systems aligned along the local vertical, accurate results, very quickly, as compared to those obtained using the multibody model. An algorithm to train feed-forward artificial neural networks, by minimizing the sum of the squares of percent errors, is derived and shown to be invaluable in training networks to represent widely-spread real-valued data. A hybrid training approach, using the derived algorithm in conjunction with the standard backpropagation training algorithm, is described and demonstrated. This approach often reduces network training time, and it is used to train three networks with lifetime data provided by the element propagation model: one to predict the orbital lifetimes of free tethers, one to predict lifetimes of upward-deployed subsatellites trailing a tether, and one to provide correction factors that account for the effects of initial orbit inclination and argument of latitude. The accuracies of network-predicted lifetimes, as compared to those obtained using the multibody model, are demonstrated in 90 cases with randomly chosen initial conditions and system physical dimensions. In all cases, the network's results are shown to be accurate to within
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