Analytical Solution of Two-Impulse Transfer Between Coplanar Elliptical Orbits

An optimization solution of the two-impulse coplanar transfer of a spacecraft in Earth's gravitational field has been obtained on the basis of Lawden's primer-vector theory development. This analytical solution minimizes the total velocity impulse based on the transfer semilatus rectum and on the transfer angle between fixed points of the initial and final orbits. The primer vector satisfies the necessary and sufficient conditions for minimum on the transfer semilatus rectum and on the transfer angle. The global minimum of the total velocity impulse was obtained. It is shown that setting one of Lawden's constants to zero in the primer-vector expression complies with the necessary optimality condition of the transfer angle. It follows that the direction of the optimal velocity impulses lies between the normal in-plane and cotangential directions.