Part 2 of this monograph presents an extension and enhancement of the Apollo ground-based targeting and on-board guidance design by enabling explicit determination of the state and thrust vector control and on-board targeting capabilities. These capabilities are developed utilizing a new closed-form solution for the constant-thrust arc of the braking phase of the powered lunar-descent trajectory replacing the Apollo’s manual ground-based iterative approach. The main elements of the Apollo targeting theory and algorithms, including the key properties of the quartic phases on the descent trajectories, are retained. It is demonstrated that the implementation of the proposed thrust arc solution, unlike the Apollo algorithms, allows us to avoid repeated iterations on the lander’s state and target state vectors, and facilitates the on-board execution of targeting and re-targeting procedures at any time during the descent, thereby extending and enhancing the original Apollo targeting and guidance design. It is shown that the shape of the BP constant-thrust arc is highly dependent on initial mass and propulsion system parameters.