Future space exploration missions require new solutions in Guidance, Navigation and Control (GNC) for autonomous landing. The German Aerospace Centre, DLR, is developing the environment for autonomous GNC Landing experiments, EAGLE, acting as a demonstrator for vertical take-off and landing. The goal of this thesis is to develop a prototype real-time applicable guidance function based on convex optimal control theory for powered descent landing, which can be implemented and tested on the on-board computer of EAGLE. Applying loss less convexification, the powered descent landing fuel-optimal control problem is converted into a second order cone problem. A discretization and transcription method is designed in order to solve the resulting non-linear program by means of the embedded conic solver ECOS and the developed algorithm is verified by a comparison of simulation results for an example pinpoint landing on Mars.  In addition, a heuristic kinematic estimation for the fuel-optimal flight time is added, which defines a fixed flight time for the convex trajectory optimization problem. This enables to automatically generate trajectories optimized for the estimated flight time and given initial and final conditions. A processor-in-the-loop test proofs the potential to apply the developed guidance function on the onboard computer of EAGLE, while simulations with different sets of initial and final conditions reveal that the trajectories computed by the guidance function require more fuel than the actual fuel-optimal trajectory due to an inaccurate flight time estimation for several simulation sets. Therefore, the guidance function developed in this thesis provides a first step towards an optimal trajectory generation framework on-board of EAGLE.