Abstract:For lunar module with low lift to drag ratio, skip entry trajectory must be flown to extend downrange. According to the key element of skip entry trajectory online planning or predictive guidance is how to predict the downrange of the first entry phase rapidly and precisely, an analytical method was proposed. Firstly, closed-form approximate solution of the longitudinal equation of motion was obtained from using matched asymptotic expansion method. Secondly, the first entry trajectory was divided into three phases. In the first phase, altitude served as the independent variable of integration, downrange was obtained from using a composite trapezoidal-rule. In the second and third phases, quadratic polynomial was used for drag-energy profile fitting, and the polynomial coefficients were solved according to the result of the approximate solution, and downrange was obtained by integrating the reciprocal of drag versus energy function. Finally, the accuracy and computational efficiency of the proposed method were analyzed. Simulation results indicate that the characteristic of the proposed method with high accuracy and computational efficiency is very suitable for online planning and guidance.