Variation ranges of motion parameters for space debris in the geosynchronous ring

We propose a method that uses only one set of known orbital elements to directly determine the motion state and variation ranges of motion parameters, including the inclination, right ascension of the ascending node (RAAN), evolution period of the orbital plane, maximum libration amplitude of the semi-major axis, commensurable angle, libration period and drift period, for space debris in the geosynchronous ring. These variation ranges of motion parameters characterize the evolution of debris quantitatively and illustrate the three-dimensional (3D) variations. Employing the proposed method, we study the motion state and variation ranges of motion parameters for catalogued and uncontrolled space debris with existing two-line element (TLE) data in the geosynchronous ring, and present specific results. We also compare our results with actual observational results derived from long-term TLE historical data, and find that, in the vast majority of cases, our proposed method of determining the motion state and variation ranges of motion parameters via only one set of known orbital elements is effective. In addition, before the elaboration of the variation ranges of motion parameters stated above, we obtain the statistical distribution of space debris in the orbital plane and the daily motion from the TLE historical data. We then derive two mathematical formulae that explain the statistical distribution and daily motion on the basis of the essence of dynamics, which contributes to the characterization of the evolution of debris.