Computing NORAD Mean Orbital Elements From A State Vector.

Abstract : NORAD maintains and disseminates mean orbital elements on Earth-orbiting satellites in the form of Two-Line Element Sets (TLE). Five mathematical propagator models were developed for NORAD's use to predict the position and velocity using TLEs. This study investigated two approaches, Newton's method and direct iteration, to inverting this process by iterating to obtain NORAD-compatible mean orbital elements from a position and velocity state vector and the drag term. The Newton's iteration method was developed but not tested. The less computationally intensive direct iteration method was developed, coded in FORTRAN, and tested. The initial guess and subsequent corrections in the iterative process used the osculating elements computed from the state. The results showed the computation of the osculating elements to be unstable for low-Earth orbits with low eccentricity and moderate inclination, never converging to a solution for those cases. The scope of this research was limited to using two of the five propagators: Simplified General Perturbation Version 4 (SGP4) for low Earth orbits and SDP4 for deep space orbits.