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Dynamic radiators are thermal control systems that are able to vary emitting surface area or surface properties in order to control the amount of heat rejected. These systems are often used onboard spacecraft where large fluctuations in heat dissipation can exist. This work explores the performance of a dynamic spacecraft radiator design with annular geometry where the fin is concealed within a satellite architecture and then is deployed as additional heat rejection is required. The performance criteria analyzed are fin temperature profile, system turndown ratio, and fin efficiency. Furthermore, the effect of various thickness profiles, namely uniform, tapered, and a step-change in thickness, is analyzed. Two-dimensional heat transfer equations are developed to analyze the system heat transfer. Results are then validated with computer-aided design software that has capabilities for thermal analysis. It is found that turndown ratios of 3.3 are capable with the proposed system. Furthermore, it was found that fins with tapered thickness profile have the highest efficiency and turndown ratio. Uniform thickness fins have the largest difference between maximum and minimum fin temperature. Finally, it was found that fins with a single step-change in thickness differ in turndown ratio performance by less than 1% from those with tapered thickness fins.