A Correction on the Lambert Targeting Problem in the Perturbed Space Environment

This article introduces a novel correction algorithm designed to enhance the Lambert Targeting Problem (LTP) by addressing space perturbations. The proposed LTP Correction (LTPC) algorithm integrates the traditional LTP with the shooting method and Particle Swarm Optimization (PSO) to improve targeting accuracy. Following an initial solution using the LTP, the LTPC employs five sequential and iterative refinement stages to converge on a more precise result. The LTPC modifies the classical LTP to incorporate space perturbations, with Earth's oblateness being the primary perturbation considered. However, the algorithm is versatile and can be adapted to account for various types of space perturbations, broadening its applicability. The results demonstrate that the delta true anomaly, the difference between the desired arrival true anomaly and the actual arrival true anomaly, achieved by the LTPC is significantly smaller than that of the traditional LTP. This improvement highlights the LTPC's superior targeting accuracy. Notably, the LTPC achieves this enhanced precision without requiring a substantial increase in flight time or total velocity change compared to the classical LTP. This balance of accuracy and efficiency underscores the LTPC's effectiveness as a robust solution for space missions influenced by perturbations, paving the way for more reliable mission planning and execution.