PREDICTION ACCURACIES OF DRAPER SEMI-ANALYTICAL SATELLITE THEORY IN LEO, MEO AND HEO REGIME FOR SPACE OBJECT CATALOGUE MAINTENANCE

Abstract

Currently, the number of catalogued space objects in LEO and MEO orbit is about 15000, out of which approximately 12000 are in low Earth orbits (LEO) and 2000 objects are in medium Earth orbits (MEO). These are tracked by the radar and optical sensors of the US Space Surveillance Network and orbit determination solutions are generated by least squares fit to these tracking data. These orbit determination solutions are distributed to the space users and the space operations community to support a variety of military and civilian space control requirements including: • Prevention of false alarms in missile warning systems • Manned space flight program safety • Unmanned flight safety • Support to commercial entities • Space-situation awareness data To control the growth of the current space object population, it is important to track and maintain a catalogue of these objects. To determine orbits of tracked objects and to propagate them in time, to correlate for not having duplicates in a catalogue, and to predict the close encounters of the satellites with tracked objects, it is important to have computationally efficient ephemeris propagators. For this purpose, the Draper Semi-analytical Satellite Theory (DSST) – which makes use of the generalized method for averaging, is examined for its best possible fit with numerically generated orbits and also for its computational loads. DSST is a mean element orbit propagator based upon the generalized method of averaging. DSST was developed by P. Cefola with his colleagues at the Draper Laboratory, Massachusetts and the Computer Sciences Corporation, Maryland. The mathematical development relies on recursive series to model conservative perturbations and numerical quadrature in modeling non-conservative effects. This semi-analytical propagator represents the state of the art in satellite theory with a wide variety of force modeling options configurable at run time. The flexibility allows the user to customize force modeling options from low accuracy to high accuracy options which are comparable to special perturbation (SP) theories. The investigation is conducted in three parts – first, to investigate the orbit generator options for optimized speed and accuracy combination for DSST standalone propagator. Trade-offs between speed and accuracy are made, so that the propagator is set with the requirements of the catalogue maintenance of space objects. Second, is to determine the fit accuracy using these options for selected orbital classes. Lastly, the DSST accuracy and computational speed characteristics are compared with those for the SGP4-SDP4 (Simplified General Perturbation Theory-4) models The orbit classes considered were based on the definitions made in the ephemeris theory accuracy study, such that to cover all orbital regimes and also to investigate the critical scenarios handled by analytical formulations, these cases are: • Low altitude circular orbits (semi-major axis (a) : 250 - 2000 km, eccentricity (e) <0.05) • Medium altitude circular orbits (a : 2000 - 36000 km, e <0.05) • Highly eccentric orbits (0.05 < e < 0.8) For a broad selection of orbits within these ranges, speed and accuracy of the selected semi-analytical theory is determined. Semi-analytically generated orbits are fitted with SP theory orbit for the arc lengths of few days. The details are elaborated in the paper.