The vision behind this work is the creation of an interactive and truly immersive photorealistic virtual Solar System. While many ingredients for such a software have been thoroughly described in the literature, a lot of research is still required to ultimately achieve this vision. Use cases for such a system include scientific data exploration, space mission planning, astronaut training, science communication, or entertainment. To pave the road towards that vision, this thesis focuses on one major missing component: The real-time simulation of realistic solar and lunar eclipses. While plenty of research has been performed in this field already, most publications are limited to render eclipses on the surface of Earth and our Moon. In this thesis we will generalize existing approaches not only to arbitrary 3D-positions between Earth and Moon but also to other celestial bodies and their moons. This requires a novel parametrization of the 3D shadow volume behind a celestial occluder, as well as a generalized approach for simulating light scattering in planetary atmospheres. All contributions are implemented and evaluated in the context of the existing open source software CosmoScout VR.