Determining satellite close approaches
Abstract
This paper presents a numerical method to evaluate close approaches of two satellites. The algorithm is based on a space curve modeling technique originally developed by Overhauser, presented here as an independent derivation. The method to determine minimum spacing between two space objects is based on creating a relative distance waveform, delta(t), versus time. The waveform is produced from either uniform or arbitrarily 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 computation of acceleration terms of the two objects of interest. For this study, a close approach truth table is constructed using a 0.1 second sequential step along the orbits, then differencing the two position vectors. The close approach entrance and exit times for an ellipsoidal quadric surface are then located using a piecewise linear interpolator, and serve as a benchmark for comparison. The simulation results show this algorithm produces encounter times almost identical to those in the truth table, with a 99.84 percent reduction in computer runtime. The results, created from real orbital data, include solution sets for three operational uses of close-approach logic. For this study, satellite orbital motion is modeled using first-order secular perturbations caused by mass anomalies.
- Publication:
-
Journal of the Astronautical Sciences
- Pub Date:
- June 1993
- Bibcode:
- 1993JAnSc..41..217A
- Keywords:
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- Curve Fitting;
- Satellite Communication;
- Satellite Orbits;
- Spacecraft Trajectories;
- Distance;
- Orbital Mechanics;
- Space Logistics;
- Space Communications, Spacecraft Communications, Command and Tracking