<p>This study investigates the bearing-only circumnavigation (BOC) problem involving the control of agent acceleration to encircle static and moving targets at a prescribed distance and tangential speed. The agent obtains navigation information by measuring its position and velocity. However, the agent only measures the bearing angle from the agent to the target to obtain information about the target, since the position of the target is unmeasurable. To estimate the unknown position of the target, we adopt Deghats vector estimator, the convergence of which relies on a persistent excitation condition. By modeling the dynamics of this problem as a fully actuated system (FAS), we apply a novel, flourishing FAS-approach-based control method to solve this acceleration-design BOC problem. For the static target case, we design an FAS-based controller and prove the stability of the closed-loop system. For the moving target case, we design a robust FAS-based controller and prove the boundedness property of the closed-loop system. Three simulations are conducted across noiseless static, noisy static, and moving target cases to verify the feasibility of the proposed control methods.</p>