This paper presents a new Feedback-Accelerated Picard Iteration method for solving long-term orbit propagation problems and perturbed Lambert’s problems. This method is developed by combining the collocation method and the variational iteration method over large-time-steps. The resulting iterative formulae are explicitly derived so that they can be directly adopted to solve problems in orbital mechanics. Several typical orbit regimes incorporating high-order gravity and air drag force are used to demonstrate the application of the proposed method in orbit propagation.
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