The past decade has seen a continuous increase of Earth observation missions, since they are regarded as an important tool to address global problems such as climate change or disaster mitigation. A commercial trend exists now towards higher resolution imagery, which drives the use of agile satellites. Nevertheless, a disadvantage of agile satellites is the increased complexity to compute the optimal imaging schedule. In fact, the problem can be interpreted as a time-dependent selective travelling salesman problem for which the travel between the cities is also a constrained optimal control problem. Considering the simplifying assumptions in literature, this MSc thesis presents a novel method which approximates the optimal control problem between the targets using an artificial neural network. This approach provides a significant improvement over any previous research resulting in an increase in scheduling performance of around 10%. Considering the high cost of agile Earth observation satellites, this advancement can offer important profit increases for satellite operators. Additionally, a new exact scheduling algorithm was developed based on dynamic programming logic. The algorithm is shown to be able to plan up to one hundred targets for a given restricted number of visible targets at each epoch, while previous research was only able to solve problem sizes of up to twelve targets. Furthermore, the new exact scheduling algorithm is also shown to have unmatched performance for cases of up to twelve targets, such that this should not be considered a difficult problem anymore.