Feedback-Accelerated Picard Iteration for Orbit Propagation and Lambert’s Problem

This paper presents a new feedback-accelerated Picard iteration method for solving long-term orbit-propagation problemsandperturbedLambert’s problems.Thismethod is developedby combining the collocationmethodand the variational iterationmethod over large time steps. The resulting iterative formulas are explicitly derived so that they canbedirectly adopted to solve problems in orbitalmechanics. Several typical orbit regimes incorporatinghigh-order gravity and air drag force are used to demonstrate the application of the proposed method in orbit propagation. Further, the feedback-accelerated Picard iteration method is used to solve perturbed orbit-transfer problems. The combination of it with a fish-scale-growing method successfully extends its convergence domain and provides a potential approach for solving long-duration two-point boundary-value problems in conservative systems. The numerical results show that the proposed method is highly precise and efficient.