Graphic semi-major axis iteration algorithm for lambert problem

A new algorithm based on iteration of the semi-major axis and graphic analysis, which is called Graphic Semi-major Axis Iteration Algorithm (GSAIM), is presented for Lambert problem. The key concept of the proposed algorithm is using numerical iterative or graphic analysis to obtain the intersection of the curves of the given transfer time and the Lambert equation, so that the required semi-major axis of transfer orbit can be solved. Moreover, a transfer orbit model is built based on the new algorithm. The applicability, accuracy and efficiency of the algorithm are compared with existing algorithms, such as Batin-Vaughan algorithm and the bisection method. Finally, simulation results show that GSAIM can obtain the semi-major axis quickly and intuitively with high accuracy.