A N INITIAL costates estimation method to solve optimal transfer orbit design problems is presented here. The target orbits are spiral trajectories with low-thrust input. Fuel optimal trajectory design problems have been previously investigated for a number of orbit transfer applications and interplanetary missions [1– 7].Among representative techniques is an indirect approach based on the variational principle, throughwhich the optimal control problems can be converted into a two-point boundary value problem. Transfer orbit design problems can be solved by finding the unknown initial costate variables, but the indirect method suffers from some critical drawbacks, such as a small radius of convergence. The estimation of initial costates for spiral trajectory design is particularly difficult due to a long transfer time and the multirevolution nature of such trajectories. Several advanced indirect methodologies, including functional approximation, continuation, homotopy, and the step-by-step approach, have been adopted to compute initial unknown costates [1,2,8,9]. In [1], properties of the initial costates were exploited to estimate the initial costates. In that work, the terminal specific energy with respect to the Earth and the initial radius of the circular orbit were fixed. The initial costates of the radial distance and tangent velocity can be approximated using exponential functions versus time; however, the initial costate behaviors of radial velocitywere not fully analyzed in [1]. Furthermore, if the initial radius, terminal specific energy, and central planet are changed, additional steps, such as determining a new curve fitting, may be necessary to design optimal trajectories with a longer transfer time. In this study, a new initial guess structure for costates is proposed to construct optimal spiral trajectories using the arbitrary initial radius, transfer time, terminal target energy, and central planet. The proposed initial guess structure requires neither functional approximation nor extrapolation. The structure is developed according to initial costate properties, and it can accommodate specific energy targeting problems.