A study of stochastic properties of the mid-altitude region of motion of global navigation system satellites

The study of the stochastic properties of the mid-altitude region of motion of global navigation system satellites at low and moderate area-to-mass ratios (0.001, 0.01, and 0.1 m2 /kg) is performed based on the numerical simulation results. The behavior of the integrated autocorrelation functions for the semi-major axis and Kholshevnikov metric is considered. The Kholshevnikov metric is specified in the three-dimensional factor space of the positional orbit elements. The initial orbits are assumed to be close to circular orbits with an eccentricity of 0.0001. The initial inclination is chosen according to the semi-major axis of the orbit: 64.8° near the GLONASS system, 55° near the GPS and BeiDou systems, and 56° near the Galileo system. The initial longitude of the ascending node is varied with a 90° step. The dependence of the integrated autocorrelation function on the initial semi-major axis of object's orbit is analyzed. The occurrence of stochastic evolution grows with an increase in the initial inclination and semi-major axis of the orbit due to luni-solar perturbations. The attributes of stochastic behavior are revealed even at small area-to-mass ratios corresponding to the satellites. It can be concluded that the estimates of the integrated autocorrelation function significantly depend on the initial orientation of the orbit plane with respect to the direction to the Sun. This should be considered when selecting orbits for the disposal of deactivated satellites of global navigation systems.