"Quantum theory has been confirmed to extreme accuracy in a vast variety of experiments over the last century. While most of these experiments have been limited to a microscopic scale, several milestones in demonstrating quantum effects for more and more massive objects have been achieved, in particular by experiments on the interference of large molecules. In the last few years, a new approach to test quantum physics with significantly more massive objects has emerged where the electromagnetic field is used to achieve control over massive mechanical resonators, eventually into the quantum regime. In particular, quantum optomechanics deals with resonators that are coherently controlled via optical fields. Such systems allow for unprecedented levels of accuracy in the measurement of forces. Eventually, by preparing these massive resonators in non-classical states of motion, they may enable the investigation of quantum effects in a regime where gravitation becomes non-negligible. A limiting factor so far has been the coupling of the resonator to its environment. Using nanospheres levitated in optical trapping potentials, promises to overcome that limitation and will allow for high-precision measurements of gravitation as well as novel experiments on the frontier between quantum theory and the theory of relativity. Space provides an ideal environment for such experiments. Using a spacecraft like the one used in the LISA Pathfinder mission, it is possible to combine a micro-gravity environment, which allows for a much higher mass of the levitated spheres and reduces many sources of noise (e. g. seismic), with readily available optical space technology. This research proposal aims at designing possible experiments with levitated optomechanical resonators in space, testing the feasibility of these schemes in ground-based experiments, and investigating the prerequisites of fundamental optomechanical experiments in space."