Improved semi-major axis iterated method for Lambert's problem

Lambert's problem, as the basis of designing the transfer orbit is reviewed. According to the Lagrange equations, the available range of the transfer time is proposed, then, the improved method for the Lambert's problem and the calculation method of part of the orbital elements basing on the thought of the semi-major axis iterated are obtained. Furthermore, the Newton iteration method is used in solving the semi-major axis, which has improved the computational efficiency. Then, through analyzing the results calculated by the classic Battin-Vaughan's solution and the improved semi-major axis iterated method, the new method is proved efficient and accurate. Finally, the formulas of elliptic orbit, hyperbolic orbit and the parabolic orbit derived from the orbital elements are given.