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\documentclass[../Main.tex]{subfiles}
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\begin{document}
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In September of 2019, the European Space Agency (ESA) released a tweet explaining that they had performed an
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maneuver to avoid a collision with a SpaceX Starlink Satellite in Low Earth Orbit (LEO)\autocite{EsaTweet}.
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While later reports\autocite{ArsTechnicaStatement} described it as the result of miscommunications,
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ESA used the opportunity to highlight the difficulties arising from coordinating avoidance maneuvers and how
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such coordination will become more difficult as the size and number of
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single purpose, single operator satellite fleets (satellite constellations) increase in low earth orbit\autocite{EsaBlog}.
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% Background on issues of congestion and pollution
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% Kessler Syndrome
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In spite of the fact that there is a lot of maneuvering room in outer space,
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%\footnote{``Space is big. Really big. You just won’t believe how vastly hugely mind bogglingly big it is.
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%I mean, you may think it’s a long way down the road to the chemist,
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%but that’s just peanuts to space.''\cite{DouglasAdams}}
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the repeated interactions of periodic orbits make collisions probable.
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Consequently, objects in orbit are subject to both a congestion effect and a pollution effect.
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Congestion effects are primarily derived from avoiding collisions between artificial satellites.
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Pollution in orbit consists of debris, both natural and man-made, which increases
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the probability of an unforeseen collision.
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The defining feature of pollution in orbit is that it self-propagates as debris collides with itself
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and orbiting satellites to generate more debris.
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This dynamic underlies a key concern, originally explored by Kessler and Cour-Palais \autocite{Kessler1978}
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that with sufficient mass in orbit (through satellite launches), the debris generating process
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could undergo a runaway effect rendering various orbital regions unusable.
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This cascade of collisions is often known as Kessler syndrome and
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may take place over various timescales.
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% ---------------
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%Discuss how various definitions of kessler syndrome
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% have been proposed in the economics literature to match the models.
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%Not sure if the following contributes much given the previous paragraph.
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%Although Kessler and Cour-Palais determined that a runaway pollution effect could make a set of orbits
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%physically unusable, Adilov et al \autocite{adilov_alexander_cunningham_2018} %Kessler Syndrome
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%have shown that economic benefits provided by orbits will drop sufficiently to make the net marginal
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%benefit of new launches negative before the physical kessler syndrome occurs.
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% ---------------
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Orbits may be divided into three primary groups,
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Low Earth Orbit (LEO),
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Medium Earth Orbit (MEO), and High Earth Orbit (HEO) where Geostationary Earth Orbit (GEO)
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considered a particular classification of HEO.
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While the topic of LEO allocation has historically remained somewhat unexplored, the last 6 years has seen
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a variety of new empirical studies and theoretical models published.
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% ---------------
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%Allocative efficiency
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Macauley provided the first evidence of sub-optimal behavior in orbit
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by estimating the welfare loss due to the current method of assigning GEO slots to operators\autocite{Macauley_1998}.
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The potential losses due to anti-competitive behavior were highlighted by Adilov et al ,
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who have analyzed the opportunities for strategic
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``warehousing'' of non-functional satellites as a means of increasing competitive advantage by
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denying operating locations to competitors in GEO\autocite{Adilov2019}.
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The primary concern expressed in many of the published papers is whether or not orbits will be overused
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due to their common-pool nature, and which policies may prevent kessler syndrome.
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On this topic, Adilov, Alexander, and Cunningham examine pollution
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using a two-period salop model, incorporating the effects of launch debris on
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survival into the second period\autocite{adilov_alexander_cunningham_2015}.
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They find that the social planner generates debris and launches at lower rates
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than a free entry market.
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This same result was found by Rao and Rondina in
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the context of an infinite period dynamic model.
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%Potential Edit
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Their approach is defined by the assumption that there are
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numerous operators in a free entry environment who
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can each launch a single, identical constellation\autocite{RaoRondina2020}.
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Rao, Burgess, and Kaffine use this model to estimate that achieving socially optimal
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behavior through orbital use fees could increase the value generated by the
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space industry by a factor of four\autocite{Rao2020}.
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% ---------------
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%In addition to analyzing the allocative results, a significant area of interest is
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%what impact various policy interventions can have.
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%The policies and methods used to analyze their impact have been widely varied.
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% What policies have been evaluated?
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% - Muller et al analyze debris removal
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% - Grzelka and Wagner \autocite{GrzelkaWagner2019} explore methods of encouraging satellite quality (in terms of debris) and cleanup.
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% - Rao compares launch vs operation taxes
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% - Adilov et al ?????
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%Other papers to review:
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% Muller, Rozanova, Urdanoz (Economic Valuation of Debris Removal, IAC conference 2017)
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% Salter (Space Debris, Mercantus Working Paper 2015)
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%
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%
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% ---------------
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My %FP
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objective is to %explore the effects from organizing satellites into constellations on satellite launch decisions and operation.
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describe the dynamic decision-making process facing constellation operators,
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how their launch decisions diverge from the socially optimal,
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and the ways in which various policies encourage or discourage optimal decision making.
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%I %FP
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%do this by extending Rao and Rondina's dynamic satellite operators model\autocite{RaoRondina2020}
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%to account for non-symmetric constellation sizes and
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%incorporate the effects of both economies of scale as satellites in constellations complement each other and
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%collision avoidance efficiencies where satellites are less likely to collide with constellation members.
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%Explain what the article does.
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% The primary results of this paper are:
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% preliminary development of the dynamic model,
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% characterization of the general solutions to both the constellation operators' problems and
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% the fleet planner's problem,
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% and an analysis of survival rates within constellations and the entire fleet.
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%Contribution statement
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%Adds to raoRondina2020 and adilov2018 in extedning to more diverse situations.
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This work is mainly a theoretical expansion of two models:
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\begin{itemize}
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\item Rao and Rondina's model \autocite{RaoRondina2020} dynamic model.
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\item Adilov et al's \autocite{adilov_alexander_cunningham_2018} dynamic model.
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\end{itemize}
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In addition to the expansion, I contribute a general computational solver that allows
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us to examine complex scenarios similar to those encountered in actual policymaking.
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%Similarities
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% - Rao
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% - Law of debris:
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% - law of motion for stocks
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% - Adilov
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% - law of Debris
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% - constellations
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%Differences
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% - Rao
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% - constellation
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% - avoicance efficiencies
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% - Adilov
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% - Allows for non-firm participants
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% - avoidance efficiencies
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Below I describe the similarities and differences to these previous models to the current one.
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As far as similarities go, it directly inherits the general laws of motion for debris and constellation stocks,
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and follows the DSGE modelling approach chosen by Rao.
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It is distinguished from these most models by the way it accounts for the following factors:
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\begin{itemize}
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\item Heterogeneous agent types (represented by utility functions),
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including commercial, scientific, and military.
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\item Neither constellations are not assumed to be symmetric.
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\item Collision avoidance efficiencies, i.e. within-constellation collisions are highly unlikely.
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\item Heterogeneous risk between various satellite constellations.
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\end{itemize}
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The heterogeneity that I permit is the distinguishing feature of the model.
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\end{document}
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