This paper develops an indirect optimization framework for planetocentric circular-to-circular solar-sail transfers using Pontryagin’s Maximum Principle. The formulation is general and applicable to any planet, with numerical results presented for Earth-centered transfers. The op
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This paper develops an indirect optimization framework for planetocentric circular-to-circular solar-sail transfers using Pontryagin’s Maximum Principle. The formulation is general and applicable to any planet, with numerical results presented for Earth-centered transfers. The optimal control problem is reduced to a two-point boundary value problem solved via single-shooting. Assuming an ideal sail, planar motion, and point-mass gravity (neglecting eclipses and third-body effects), the study yields three main findings. First, transfer performance, measured as final-radius gain for a given transfer duration, strongly depends on the “start-phase” (timing of departure relative to the Sun’s apparent motion). Optimal performance occurs when the Sun-line is parallel to the projection of the orbital angular momentum onto the ecliptic at transfer midpoint, whereas worst performance arises when it is perpendicular. This phasing effect dominates high-inclination transfers and becomes negligible at $\boldsymbol{0^\circ}$ inclination due to constant illumination. Second, dimensional analysis collapses the parameter space into three independent dimensionless groups. Numerical exploration reveals robust power-law scaling of transfer performance with these groups, enabling accurate extrapolation of results across sail designs and initial altitudes from a single benchmark optimization. Third, detailed investigation of the single-shooting solver shows wide convergence basins and smooth solution dependence on orbital parameters, sail characteristics, and transfer duration. Convergence is notably easier for longer transfers and higher ecliptic inclinations, whereas low-inclination, short-duration cases remain the most challenging. The proposed indirect optimization method is therefore demonstrated to be robust, efficient, and suitable for systematic performance mapping of planetocentric solar-sail orbit raising.