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A lifting, thrusting vehicle operating at orbital speeds about a spherical planet is considered. The general problem posed is that of moving the vehicle from a given set of initial conditions to a given set of terminal conditions while minimizing the characteristic velocity of the maneuver. The maneuver is accomplished by a combination of thrust and aerodynamic force. The first problem solved is transfer from an initial circular orbit to a final non-coplanar circular orbit. Pure thrusting maneuvers are compared with combined thrust-aerodynamic maneuvers, with the optimal solutions given in closed form., See also Volume 3, AD/A-004 184.

Solution of the optimum cotangential transfer between two coplanar, noncoaxial, elliptical orbits is presented. The characteristic velocity is expressed explicitely in term of a single parameter. By optimizing this function with respect to the variable, a resultant equation which is a high order algebraic equation is obtained. Numerical solution can be calculated to the desired degree of accuracy. Exact analytical solutions are given for all special cases of the terminal conditions. Second order approximate solution which can be applied to a large range of missions (interplanetary transfer, transfer of a satellite from a parking orbit to a high energy elliptical orbit...) is derived and gives an excellent degree of accuracy (less than 1 ft/sec for the characteristic velocity and less than 30' for the position of transfer). (Author), Presented at the AIAA Aerospace Sciences Meeting (2nd) in New York City, 25-27 Jan 1965. See also AD-430 481.