Optimized Geographical Distribution of Robotic Observatory Networks for Space Surveillance and Tracking Using Goldberg Polyhedra and Voronoi Tessellations

The deployment of global robotic observatory networks requires a station distribution that ensures geometrical visibility coverage of space objects while minimizing the number of ground-based stations. This work proposes a geometrical framework combining visibility constraints, Goldberg polyhedra, and Voronoi tessellations to determine this distribution. The methodology relates orbital altitude and minimum observation elevation above the horizon to the angular separation required between observatories, estimating the number of stations from a spacing criterion. A GIS-based optimization procedure is then applied to maximize the placement of observatories over continental land masses through systematic rotation of the resulting configurations. The method is evaluated for orbital altitudes from 100 km to 2000 km and minimum observation elevations of 20° and 30°. Results show that the number of observatories estimated with a spacing criterion ranges from 6252 stations at 100 km to only 42 stations at 2000 km, with similar proportions of stations on land for the Goldberg and Voronoi configurations (between 29% and 50%, with differences below 2.4 percentage points). Case studies for Australia, Ukraine, and Ecuador show that reorienting the configuration to a specific territory increases the number of stations located inside it, with larger relative gains in the smaller territories. The proposed framework provides a practical tool for the design and planning of robotic observatory networks for Space Surveillance and Tracking applications.