Estimation of ballistic coefficients of space debris using the ratios between different objects

This paper proposes a new method to estimate the ballistic coefficient (BC) of low earth orbit space debris. The data sources are the historical two-line elements (TLEs). Since the secular variation of semi-major axes is mainly caused by the drag perturbation for space objects with perigee altitude below 600 km, the ballistic coefficients are estimated based on variation of the mean semi-major axes derived from the TLEs. However, the approximate parameters used in the calculation have error, especially when the upper atmosphere densities are difficult to obtain and always estimated by empirical model. The proportional errors of the approximate parameters are cancelled out in the form of ratios, greatly mitigating the effects of model error. This method has been also been validated for space objects with perigee altitude higher than 600 km. The relative errors of estimated BC values from the new method are significantly smaller than those from the direct estimation methods used in numerical experiments. The estimated BC values are used for the prediction of the semi-major axes, and good performance is obtained. This process is also a feasible method for prediction over a long period of time without an orbital propagator model.