KAM Torus Orbit Prediction from Two Line Element Sets.

摘要

A new method for orbit prediction, which is as accurate as numerical methods and as fast as analytical methods, in terms of computational time, is desirable. This paper presents Kolmogorov Arnol'd Moser (KAM) torus orbit prediction using Simplified General Perturbations 4 (SGP4) and Two-Line Element (TLE) data. First, a periodic orbit and its Floquet solution is calculated. After that, perturbations, which are on the order of 10 and number 56256; number 56320; 5 and smaller, are added to the periodic orbit plus Floquet solution. Then, the low eccentricity KAM torus is least squares fitted to the SGP4 and TLE data. The performance of the theory is presented in various ways. The new method is approximately five times more accurate for the best fits and three times more accurate for mean fits comparing to SGP4 and TLE. History of TLEs and KAM torus theory can be used to make accurate orbit predictions, which is conceptually similar to extrapolation. In addition, the new method may rival numerical methods and it can be used for collision avoidance calculations, and formation flight applications. However, high eccentricity, polar and critical inclination, air drag, and resonance problems should be addressed.