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Sébastien Rouillon

GREThA, université de Bordeaux

« A physico-economic model of orbital management »

We solve a stylized physico-economic model of orbital environment and space activity, in order to analyse the externality caused by the accumulation of space debris. In line with Gordon (1954) and Schaeffer (1957), we focus on the long term equilibrium of the orbit, induced by a constant rate of launching forever. We show that if, in the long run, the risk of satellite destruction by collision is increasing and convex with the launch rate and becomes arbitrarily large for finite values of the latter, then the curve representing the long term expected number of functioning satellites, as a function of the launch rate, has a reversed-U shape. Classically, we then define and compare typical ways of managing the orbital environment (maximum carrying capacity, open-access, social optimum). The maximum carrying capacity is defined as the maximum expected number of satellites that the orbit can sustain in the long run. The physico-economic equilibrium launch rate, that would presumably emerge under conditions of open-access to the orbit, is defined as the rate of launching such that the space sector makes no profit. Finally, the socially optimal rate of launching is the one that maximizes the present value profit of the space sector per launching campaign.