Abstract: Based on the Hill equation，the safety strategy of doubleimpulsive flyaround process is researched. Firstly, the model of doubleimpulsive flyaround is given and all the flyaround trajectories outside the global safety area are obtained by ergodic simulation. Then a curved surface can be plotted, which expresses the relations among flyaround time, the consumption of the fuel and the starting point. Furthermore, the curve which is critically safe can be obtained and fitted. Finally, the fitting error is analyzed and it is showed that the trajectory deviates slightly.

Key words: flyaround, safety, the consumption of the fuel, fitting