Within this thesis, methods for on-board trajectory optimization and optimal control regarding different tasks of an autonomous deep space exploration mission are investigated. These include cruise flight maneuvers towards a small celestial body, more specifically an asteroid, operations in its vicinity, and the performance of landing procedures. Therefore, dynamic models and respective optimal control problems are formulated. The former include where appropriate the gravitational influence of the Sun, of further planets, and of the asteroid, and the effects due to solar radiation pressure. Because of the high complexity and large a priori uncertainty about asteroids as well as the limited resources on a spacecraft, high precision methods of nonlinear optimization and optimal control are necessary. In this course, optimal control problems are transcribed into large sparse nonlinear optimization problems via direct transcription techniques. Conflicting mission aims, that is, short flight times and low energy consumption, are considered within the objective functions. Additionally, an on-board capable parametric sensitivity analysis is implemented, allowing for an approximation of deviations in optimal solutions in case of perturbations within model parameters. Thus, additional stability information is provided. Furthermore, the approximation of perturbed controls can be used for real-time control in time critical situations. The results strengthen the need for trajectory optimization and sensitivity analysis as a foundation for autonomous decision making and fault detection, isolation, and recovery (FDIR) techniques regarding flight maneuvers during deep space missions. However, the field of space science is just a sample application. By changing the dynamics and model properties, the developed algorithms can easily be adapted for terrestrial applications such as autonomous driving or deep sea navigation.