Dimensional and scale analysis applied to the preliminary assessment of the environment criticality of large constellations in LEO

Several analytical expressions, based on reasonable simplifying assumptions, were developed for the assessment of the environment criticality of large constellations and huge numbers of small satellites in low Earth orbit. They can provide preliminary quantitative answers to difficult questions, with no need of complex models and computations. Moreover, a specific figure of merit was introduced for gauging the environment criticality of new large constellations: the collision rate percentage increase. Because several systems might be operated at the same time, an alert threshold of no more than 10% per single constellation seemed a wise suggestion. Finally, several quantitative examples and the associated results were presented and discussed.