Abstract: Based on the analytical solutions of TH equations and its state transition matrix form, the openloop control method of spacecraft impulsive relative hovering was studied, which is promising for practical engineering use. The true anomaly intervals of the hovering impulse were optimized by the nonlinear mathematical programming. Based on the calculation of collision probability, the method of safety analysis and risk management was proposed. The numerical simulations show that the introduced relative hovering method can be used for circular and elliptical reference orbits hovering. Furthermore,the local optimal solution can be obtained by applying the true anomaly intervals optimization method. The maximum collision probability and the minimum relative distance nearly appear at the same time. And, the smaller the relative distance is, the larger the collision probability.

Key words: spacecraft, impulsive hovering, collision probability, trajectory safety