The computation of error transfer matrix is critical in precision transfer trajectory design and mid-course correction for lunar or Mars missions. This paper discusses an analytical solution and a numerical solution in detail, and shows that using the numerical method is advantageous since it has great flexibility and allows the use of high precision dynamic model in the design process so that the end error in realistic simulations can be made negligible. This paper also redefines the end condition requirements and a two-step procedure for precision transfer trajectory design is proposed.
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