A new procedure for improving fuel- and time-optimal orbit transfersthrough burn additions isintroduced and analyzedintermsofphysicalcharacteristics;resultsofitsusearepresented.Theprocedureisbasedonapropertyof the switching function for the optimal control problem. Criteria are given that may be used to determine whether other optimal control problems exhibit this property. This property and other properties of fuel-optimal orbit transfers related to number of burns and burn placement are examined. The orbit transfer problem formulation is given for e nal mass maximization allowing for second-harmonic oblateness effects, atmospheric drag effects, and three-dimensional, noncoplanar, nonaligned ellipticterminal orbits. A set ofextremal solutions parameterized by transfer time, referred to as a family, are obtained using a combination of the new procedure, homotopy, and other numerical methods. Notably, this family exhibits multiplicity in solutions; that is, terminal orbits, transfer times, and numbersof burnsareidentically specie ed, buttheresulting transfer trajectories and costs aredifferent. Reasons are suggested why one transfer is favored over the other, using physical rationale. Effects of the drag and oblateness terms are discussed. = craft’ s drag coefe cient C i j = space of functions with i continuous derivatives and j elements eT = thrust direction vector (unit vector) ex, ey, ez = Cartesian components of the eccentricity vector; additional subscript i or f indicates initial or e nal point, respectively Fdrag = force exerted by drag on the spacecraft Fthrust = force exerted by the spacecraft’ s thruster on the spacecraft f[x(t), t] = that part of the differential equation for x(t) that does not vary with the control variables u(t) and v(t) G = function, dee ned for convenience, that encompasses both the original performance index and the terminal constraints g0 = gravitational acceleration at sea level on Earth g[x(t), v(t), t] = that part of the differential equation for x(t) that varies with the control variable v(t) and linearly with u(t) H = Hamiltonian for the optimization problem; also H[x(t f), T, eT(t f), ¸(t f)] or H[x(t), w(t), u(t), ¸(t), t] HT