OPTIMAL EARTH ESCAPE TRAJECTORY USING CONTINUATION METHOD AND COSTATE ESTIMATOR

Abstract

Multi-revolution, energy optimal trajectory for earth escape is addressed in this paper. The cost function is related to energy level’s fuel consumption of a lowthrust. The primary goal is to find initial costate values in applying indirect method. But seeking solution by the indirect method, especially for multirevolution orbit transfer problem, is quietly difficult due to the sensitivity caused by long duration and spiral type trajectory. A two-steps, continuation method based on polynomial interpolation approach is used to overcome the difficulties. At high Earth orbit with a short final time, the number of revolution is small, so this solution is used for the continuation method. The behavior of costate variable with respect to the initial radius is approximated. Then, for LEO case, the initial costates can be found with ease.