Thermal limits and optical-property uncertainty in constant-pitch solar-sail escape trajectories

Solar sails gain more acceleration near the Sun, but the same radiation heats the sail and limits how closely it can approach. This study examines how optical-property uncertainty changes the best feasible perihelion in a restricted, reproducible trajectory model. A flat, opaque sail begins at a prescribed parabolic perihelion, maintains a constant pitch angle, and is removed at the first outward crossing of 1 AU. The model includes specular and diffuse reflection, absorption, thermal recoil, and two-sided radiative equilibrium. Published coefficients for aluminized CP-1 film are used with an assumed total area-to-mass ratio of 100 square metres per kilogram and a 533.15 K temperature cap. Within this family, the nominal optimum occurs at 0.2834 AU and a pitch angle of 27.61 degrees, giving a post-removal hyperbolic excess speed of 29.25 kilometres per second. A radial sail operated at its own thermal boundary gives 24.15 kilometres per second. The nominal optimum reaches 545.08 K at the hottest corner of the specified optical-property range. Enforcing the temperature cap throughout that range moves the optimum to 0.2959 AU and reduces nominal excess speed by 2.77 percent. Analytical checks and numerical refinement confirm that integration error is much smaller than these changes. The results show why a nominal thermal boundary is insufficient when optical properties are uncertain. They describe an outbound benchmark, not a complete mission or a qualified sail design.