## 1 Introduction
However, the environmental impact and sustainability of these facilities must be carefully considered to ensure a balance between technological advancement and ecological preservation. One of the primary environmental concerns associated with satellite-based ground stations is their energy consumption. GSs require a significant amount of power to operate, particularly for tasks such as signal amplification and data processing. This energy demand can contribute to greenhouse gas emissions, particularly if the electricity used is generated from fossil fuels. To mitigate this impact, many ground station operators are turning to renewable energy sources, such as solar panels and wind turbines, to power their facilities. By harnessing clean energy, these stations can reduce their carbon footprint and contribute to global efforts to combat climate change. The energy consumption of GSs is related to the actual energy request, being correlated to the amount of data to be processed, and that energy is generated on demand. In particular, the higher the processing on ground, the higher the ground station energy consumption, and the more energy has to be produced to satisfy this need. Furthermore, energy available on ground is typically given by mixed resources; thus, it could be only in part renewable, if not completely non-renewable. Even in case that GSs are provided with totally renewable energy, any saving on the use of this energy can be made available on the energy grid. Starting from these premises, this paper proposes and investigates processing and bandwidth resource allocation strategies, based on the optimization problem and a heuristic, aiming at minimizing the energy consumption on GS by deciding when and where data shall be processed (i.e., in orbit or on ground and, in the former case, on which satellite of the constellation) and, jointly, determining the route the information has to follow. In particular, the contributions stemming from this work are as follows:  
* We propose a new modeling of the dynamic topology related to the orbital environment, based on a time-evolving graph where each node represents a satellite dealing with a service either unprocessed or processed at a certain time, simplifying the formalization of the optimization problem. * We formalize and solve an optimization problem aiming at jointly allocating processing and bandwidth resources to minimize the energy consumption on GS (i.e., to maximize the amount of data processed on board satellites), by taking into account constraints on energy, bandwidth, storage and processing capacity; furthermore, the proposed strategy provides for the leveraging of task offloading, in such a way that if a satellite which acquired an image has not enough resources to process it, the image can be delivered to another satellite which will be then in charge to process it, by taking advantage of the satellite network obtained through ISLs. * We propose a heuristic mimicking the optimization problem, allowing for obtaining the desired allocation in a real orbital case study, where the complexity of the optimization problem's solution would not allow us to obtain results in reasonable time, and we validate it by comparing the obtained results to the ones related to the optimization problem's solution in a simplified, but still representative, scenario. * By leveraging the proposed heuristic, we compare the energy saving in ground station consumption, with respect to having all images processed on the ground, in case our strategy is applied or a benchmark strategy not providing the possibility of task offloading to other satellites is considered. The remainder of this paper is structured as follows.