DETERMINING SATELLITE CLOSE APPROACHES

This paper presents a numerical method to evaluate close approaches of two satellites. The algorithm is based on a space curve modeling tech nique originally developed by Overhauser, presented here as an indepen dent derivation. The method to determine minimum spacing between two s pace objects is based on creating a relative distance waveform, delta( t), versus time. The waveform is produced from either uniform or arbit rarily spaced data points, from which intervals of close approach are obtained by extracting the real roots of a localized cubic polynomial. This method is free of both transcendental equations and the computat ion of acceleration terms of the two objects of interest. For this stu dy a close approach truth table is constructed using a 0.1 second sequ ential step along the orbits, then differencing the two position vecto rs. The close approach entrance and exit times for an ellipsoidal quad ric surface are then located using a piecewise linear interpolator, an d serve as a benchmark for comparison. The simulation results show thi s algorithm produces encounter times almost identical to those in the truth table, with a 99.84% reduction in computer runtime. The results, created from real orbital data, include solution sets for three opera tional uses of close-approach logic. For this study, satellite orbital motion is modeled using first-order secular perturbations caused by m ass anomalies.