The optimization of the orbital Hohmann transfer

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 a1a1, e1e1 and the semi-major axis a2a2 of the terminal orbit are uniquely given quantities. For optimization procedure, minimization is relevant to the independent parameter eTeT, 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 |ΔVA|+|ΔVB|=S|ΔVA|+|ΔVB|=S.We exposed in detail the multi-steps of the optimization procedure. We constructed the variation table of S(eT)S(eT) which proved that S(eT)S(eT) is a decreasing function of eTeT in the admissible interval [eTmin,eTmax][eTmin,eTmax]. Our analysis leads to the fact that e2=1e2=1 for eT=eTmaxeT=eTmax, i.e. the final orbit is a parabolic trajectory.