A Physico-Economic Model of Low Earth Orbit Management
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A Physico‑Economic Model of Low Earth Orbit Management Sébastien Rouillon1 Accepted: 3 October 2020 © Springer Nature B.V. 2020
Abstract We analyze the externality caused by the accumulation of space debris, focusing on the long-term equilibrium induced by a constant rate of satellite launches. We give conditions such that the long-term population of functioning satellites is an inverted-U shape function of the launch rate. We compare typical ways of managing the orbit. The maximum carrying capacity is the maximum population of satellites that the space sector can sustain in the long run. The physico-economic equilibrium occurs under open-access to the orbit. The optimal policy maximizes the present value profit of the space sector. Finally, we discuss the use of standard economic instruments (command-and-control, tax and market) to regulate space activity in order to achieve an optimal outcome. A numerical application based on a realistic calibration illustrates all results. Keywords Space economics · Orbital debris · Sustainability Mathematics Subject Classification L1 · L9 · Q2
1 Introduction Since the launch of Sputnik in 1957, the number of objects in orbit around the Earth, either operational satellites or space debris, has increased considerably (ESA 2019). Unfortunately, the population of space debris has now reached levels that are beginning to damage the space sector (Weinzierl 2018) and could even compromise its activity (Kessler and Cour-Palais 1978; Cordelli et al. 1993; Dolado-Perez et al. 2015). Space debris remains in orbit for long periods of time (i.e., decades or centuries, depending on altitudes) and poses a threat for existing operational satellites (i.e., risk of damage or breakup by way of collision). Moreover, the process propagates itself, with past collisions contributing to the accumulation of space debris.
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s1064 0-020-00515-z) contains supplementary material, which is available to authorized users. * Sébastien Rouillon sebastien.rouillon@u‑bordeaux.fr 1
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In previous decades, the rise of the “New Space” has ushered in an era in which commercial companies play a major role in space activity (Weinzierl 2018). Revenues currently exceed $300 billion yearly, with the bulk of it going to the satellite market (i.e., around $220 billion yearly). In this context, the threat of space debris was soon recognized as critical by the international community (UN 1999). In 2007, the United Nations General Assembly endorsed the Space Debris Mitigation Guidelines (UN 2010), recommending to limit the debris released by launch vehicles and spacecrafts, to avoid intentional destructions, and to minimize the risk of breakups, explosions and collisions. These measures are not legally binding under international law. Nevertheless, they have been formalized into a set of internatio
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