Impact of Stochastic Atmospheric Density on Satellite Orbit Stability

The orbit stability of a satellite is a crucial aspect in its design and maintenance. Without an analysis of orbital trajectories, satellites, much like any small celestial objects, are prone to orbital decay, collision with other orbiting objects, or even variations in trajectory, leading to the impossibility of performing their tasks. Starting from an equation of angular momentum variation applied to a satellite in a circular orbit around Earth, the system of second-order ordinary differential equations of motion for the satellite can be determined. By introducing this term into the satellite’s stochastic dynamic system, results much closer to reality are obtained. This paper analyses the accuracy and stability of five finite difference schemes in solving SDEs, applying them to a second-order stochastic differential equation. The uniformity of the stabilisation behaviour in the stochastic trajectories of the stochastic dynamical system is discussed, and the noise impact on the results is analysed by comparing cases with variations in the noise coefficient. The graphical results of the SDEs presented in this paper highlight the symmetry of the stochastic trajectories around the solution of the deterministic system.