Velocity corrections in generalized coplanar coaxial Hohmann and bi-elliptic impulsive transfer orbits

摘要

We shall investigate the problem of the differential corrections of the orbital elements a, e of the final elliptic orbit, in order that we might obtain the required very precise one. This will be achieved by the application of differential motor thrust impulses △v_A, △v_B at peri-apse A and apo-apse B, to induce correctional △a, △e increments. We apply differential thrusts at peri-apse and apo-apse of the generalized Hohmann and bi-elliptic transfer impulsive systems of orbits. Our purpose is to find the differential corrections in major axes and eccentricities of the two considered transfer systems. Thus we can obtain a very precise final elliptic orbit, throughout differential velocity increments perpendicular to the coaxial major axes and tangential to peri-apse and apo-apse of the elliptical terminal orbits. We find out the four relationships between △a_1, △a_T, △e_1, △e_T and △v_A, △v_B the velocity increments at the points A and B , for the four cases of the Hohmann type trajectories . We notice that △a_1 and △e_1 are related to △v_A whilst △a_T and △e_T are combined with , △v_B. This occurs for the four Hohmann configurations. Referring to the bi-elliptic type of impulsive transfer we have: △v_A = f(△a_1); △v_C = f(△v_A) = ψ(△a_1); △v_B = f(△v_A) = ψ(△a_1), △a_T = f(a_1, a_2, e_1, e_2) for all four feasible cases. △a_(T') = f(△v_a) = ψ(△a_1) for all four bi-elliptic cases. In addition for all feasible bi-elliptic cases we have Ae = /(Ava).