In recent years, various quantum computing devices have become available. At the present time, and in the near future these devices are not yet amendable for quantum algorithms which require quantum error correction. However, there are a few candidates for quantum algorithms which could be implemented on these near-term quantum computers and might outperform classical computers. A prominent example is the Quantum Approximate Optimization Algorithm which solves combinatorial optimization problems as they occur for example in satellite mission planning or optimal traffic management. We investigate this technology with respect to its applicability for aerospace research problems. Moreover, we develop strategies for mapping quantum algorithms onto near-term quantum computers while obeying severe hardware constraints (Quantum compiling).