The main on-board algorithms of the Apollo landers were P63 ignition, P63-64 guidance, P66 horizontal guidance and P66 vertical guidance, throttle and attitude control algorithms. Among them, the P63 ignition and P63-64 guidance algorithms are of a critical importance to the proper understanding and execution of the targeting algorithms. Similar to the BP-targeting algorithm, the ignition algorithm involves the explicit computations of the transformation matrices and the central angle between the lander’s position vector and the LS vector. These computations in turn lead to a modification of the original algorithm, and add the corrected matrix of transformation between the platform and guidance systems to the list of the output parameters. However, the list of the main procedures of the on-board guidance algorithm remain unchanged. In this section, the modified version of the ignition algorithm with its inputs and outputs, and a brief description of the guidance algorithm in the context of the previous sections are presented.