The Capacity of Low Earth Orbit Computed using Source-sink Modeling

Abstract

The increasing number of Anthropogenic Space Objects (ASOs) in Low Earth Orbit (LEO) poses a threat to the safety and sustainability of the space environment. Multiple companies are planning to launch large constellations of hundreds or thousands of satellites in the near future, increasing congestion in LEO and the risk of collisions and debris generation. This paper employs a new multi-shell multi-species evolutionary source-sink model, called MOCAT-3, to estimate LEO orbital capacity. In particular, a new definition of orbital capacity based on the stable equilibrium points of the system is provided. Moreover, an optimization approach is used to compute the maximum orbital capacity of the low region of LEO (200-900 km of altitude), considering the equilibrium solutions and the failure rate of satellites as a constraint. Hence, an estimate for the maximum number of satellites that it is possible to fit in LEO, considering the stability of the space environment, is obtained. As a result, considering 7% of failure rate, the maximum orbital capacity of LEO is estimated to be about 12.6 million satellites. Compatibility of future traffic launch, especially in terms of satellite constellations, is also analyzed and a strategy to accommodate for future traffic needs is proposed.

Effects of Orbit Raising and Deorbiting in Source-Sink Evolutionary Models

“…Collisions are modeled according to the kinetic theory of gases; this approach has already been used in previous works [8,10,13]. The collision interactions can be simplified by first summing all active satellites in a specific shell, where 𝑆 = 𝑆 ℎ + 𝑆 𝑟 + 𝑆 𝑑 .…”

“…Indeed, those effects can be taken into account by performing an atmospheric density adjustment to have a piecewise-continuous formulation with a mean solar activity [23]. Therefore, the height scale is considered a function of the exospheric temperature (i.e., the asymptotic value of the temperature reached at a higher altitude of the exosphere), which in turn depends on the F10.7 solar flux index [13,16]. Nevertheless, solar activity and geomagnetic storms cause frequent and significant changes over time in the atmospheric density.…”

“…Carlo models, has already been exploited to study and analyze different aspects of the space environment evolution as well as the orbital capacity. D'Ambrosio et al [13] used the MOCAT-3 to estimate the LEO orbital capacity, the definition of which is based on the stable equilibrium points of the source-sink model. Moreover, Miles et al [14] and D'Ambrosio et al [15,16] developed different versions of MOCAT by considering the effects of orbital slotting and the impacts of untracked debris, respectively.…”