The optimization of the orbital Hohmann transfer

摘要

There are four bi-impulsive distinct configurations for the generalized Hohmann orbit transfer. In this case the terminal orbits as well as the transfer orbit are elliptic and coplanar. The elements of the initial orbit a_1, e_1 and the semi-major axis a_2 of the terminal orbit are uniquely given quantities. For optimization procedure, minimization is relevant to the independent parameter e_T, the eccentricity of the transfer orbit. We are capable of the assignment of minimum rocket fuel expenditure by using ordinary calculus condition of minimization for |ΔV_A| + |ΔV_B| = S.rnWe exposed in detail the multi-steps of the optimization procedure. We constructed the variation table of S(e_T) which proved that S(e_T) is a decreasing function of e_T in the admissible interval [e_(T min), e_(T max)]. Our analysis leads to the fact that e_2 = 1 for e_T = e_(T max), i.e. the final orbit is a parabolic trajectory.