Relative attitude stability analysis of double satellite formation for gravity field exploration in space debris environment

Spacecraft operating in low orbit are at risk of being hit by space debris. In the debris environment, the impact of debris is likely to cause the double satellite formation to exit science mode or even lead to the divergence of the control system, thus affecting the scientific exploration mission. In this paper, the attitude stability of the double satellite formation for gravity field in the near circular and polar orbit in the space debris environment is studied. Firstly, based on Lyapunov control and LQR, two sets of control models of stochastic collision for two satellites aligned with each other were proposed, and the actuators were modelled and assigned. Secondly, models of collision probability and momentum are developed. The distribution law of space debris is obtained according to the international common debris software. Meanwhile, probability density function of two independent collisions is gained. Finally, through Monte Carlo simulation and statistics, the changes of relative attitude and thrust torque are simulated when the satellite obtains the angular momentum for a short period of time due to being impacted by space debris. During the 10-year mission period, the number of times that the space debris impact makes the satellite attitude out of the science mode and the number of times that the control system diverges are obtained, which provides a reference for the normal manner of the double satellite formation for gravity field exploration.