Lambertian invariance and application to the problem of optimal fixed-time impulsive orbital transfer

To develop an efficient technique for the numerical solution of the Lambert problem, a new Lambertian invariant, the ratio of two invariable lengths, is proposed to replace the Gauss ratio of two areas as the main iterative variable in the time equation; iteration schemes are devised for fast convergence under various conditions. The problem of minimum fuel two impulse transfer between two coplanar circular orbits under fixed time of transfer is then analyzed and numerically solved by the technique developed. The use of multirevolution to improve the solution in the long duration case is outlined and numerically illustrated. The two cases wherein the two circular orbits are in the same direction of motion or in opposite direction are distinguished and compared. Finally, by extending the study from two impulse to three impulse transfer a global synthesis of the various possible types of fixed-time optima under different transfer conditions is briefly presented.