The project's goal is a better understanding of the physics of the interactions between the solar wind and solar system objects by high resolution computer simulations. The main tool to accomplish this is an open source hybrid plasma solver that we have developed. The modeling is done in close interaction with the analysis of observational data (ions, electrons and neutral atoms) from our instruments. The focus is on the solar wind interaction of the Moon, Mars, comets and the Jovian moons. The simulations can provide insight into questions such as atmospheric erosion and surface weathering, apart from the fundamental physics of the interactions.