Method of Predicting the Deadline of Spacecraft Orbit “Life” Taking into Account Progressive Contamination in Near-Earth Space by Space Debris

This paper highlights the features of modeling the process of mechanical contamination of near-Earth space (NES), gives a brief description of existing models for predicting the mechanical contamination of NES, and analyzes the influence of uncertainty in the initial data on the accuracy of predictions of the mechanical contamination of NES by modern models. It has been proposed to predict the deadline of the “ecological life” of near-Earth orbit based on a description of increasing the density of mechanical contamination in NES with logistic dependences. The analytic function has been obtained and presented for the first time, allowing one to obtain the predicted value of the deadline of the near-Earth orbit in the form of an equation that includes the value of the maximum permissible contamination density given in the form of a fuzzy value. The solution of this fuzzy equation in the case of a triangular shape of the membership function of the maximum possible contamination density has been presented. The possibility of transforming the fuzzy prediction to a crisp interval form has been shown by finding the interval crisp alpha-level set closest to the considered fuzzy set (FS).