Analysis on Propagation Accuracy of Deep-Space TLE Objects Affected by Solar/Lunar Orbit Calculation

Abstract

Two Line Element set (TLE) is a widely used catalog data of space objects, consequently its propagation accuracy and error characteristic became one of the concerned problems in space debris research. TLEs should be propagated with the compatible SGP4/SDP4 (Simplified General Perturbations 4/Simplified Deep Space 4) model. For a deep-space object, SGP4/SDP4 model includes $J_2,J_3$, $J_4$ zonal perturbations, solar/lunar third-body perturbation, and an extra treatment for 12 h/24 h orbit resonance problem. In regard to third-body perturbation, the SGP4/SDP4 model describes solar/lunar orbit, with a set of time-varying elements, as a simple two-body mean motion, of which there would be $2^{\circ }$–$3^{\circ }$ solar/lunar position error after a 10 d extrapolation. A modest accuracy solar/lunar orbit model has been chosen to provide a more precise position estimation at the TLE element epoch. Due to the difference between solar/lunar motion complexity, the lunar is directly modeled by its true anomaly function, while the solar is modeled by the two-body mean motion. The result that approximately $1^{\prime }$–$2^{\prime }$ for the solar position and ${15}^{\prime }$–${20}^{\prime }$ for the lunar position is achieved for a 10 d extrapolation. The laser ranging satellite Etalon 1 and Galileo 23 were taken as examples to show that the evolution of position accuracy of the TLEs could have an abnormal change during the propagation, while an “improved” TLE with solar/lunar orbit correction will have better performance.