Optimum Impulsive Hohmann Coplanar Elliptic Transfer Using Energy Change Concept Part II

We present an elementary approach for the optimization of the elliptic coplanar coaxial Hohmann type transfer arising from the first principles. We assign the minimized increments of velocities at peri-apse and apo-apse by equating to zero the gradient of Δv1+ Δv2, then resolving a second degree algebraic equation in the variable x (the ratio of the velocities before and after the initial impulse). We consider the four feasible configurations, and we assign the most economic one. By setting e1 = 0, e2 = 0 for the terminal orbits, we confront the original circular Hohmann transfer case promptly.