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Kessler Syndrome: System Dynamics Model
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Kessler syndrome: System dynamics model Jakub Drmolaa, Tomas Hubikb,∗ a Division of Security and Strategic Studies, Department of Political Science at the Faculty of Social Sciences of Masaryk University, Jostova 10, 602 00, Brno, Czech Republic b Department of Theoretical Computer Science and Mathematical Logic, Faculty of Mathematics and Physics, Charles University, Malostranske namesti 25, 118 00, Prague, Czech Republic
A R T I C LE I N FO
A B S T R A C T
Keywords: System dynamics Kessler syndrome Satellites Orbital debris Anti-satellite weapons Debris evolutionary model
The present paper explores the Kessler Syndrome (the potentially catastrophic accumulation of debris in the Low-Earth Orbit) through System Dynamics methodology. It models satellites and three classes of debris, their fragmentation, interactions and gradual decay over 50 years. It presents five scenarios: a) a “business as usual” approach, which leads to exponential accumulation and growing rate of satellite losses, but no catastrophic chain reaction; b) a conflict with a large-scale deployment of Anti-Satellite Weapons, leading to an accelerated accumulation and losses, but still no chain reaction; c) EMP scenario modeling loss of control over satellites en mass; d) cessation of all LEO satellite launches, illustrating high inertia of the system, which continues to produce more debris; and e) scenario representing an attempt to mitigate the situation via direct removal of some portion of inactive satellites from the LEO. All scenarios take place in 2040. The paper demonstrates the gravity of the situation and the necessity for a sustainable long-term solution, as orbital debris poses a threat to our future space operation even without triggering a catastrophic chain reaction.
1. Introduction
2. Related work and goals
There are over 29,000 man-made objects greater than 10 cm in size in the orbit. These objects include defunct satellites, pieces of spacecraft, mission related debris and other pieces of space junk. The number of these objects is continuously growing due to the continuing launch activity and spontaneous space collisions and breakups [1,2]. Atmospheric drag force alone is not sufficient to stop this trend. Methods and techniques on how to stop this growth are becoming a more and more relevant topic when talking about space programs and precise tracking of these objects is critical for any space mission to avoid potentially catastrophic collision. As the number of objects in the orbit increases, the likelihood of collisions increases as well. A typical space object experiences several close flybys (i.e. within few kilometers) per day. Each close encounter is a potential collision and every collision creates more debris making the probability of future collisions even higher. It has been conjectured, that when the number of objects in the orbit is sufficiently high, a selfsustaining collisional cascading process can be formed, the so-called Kessler Syndrome, named after D. J. Kessler [3,4].
Given the importance and potential impact of the problem, several models have been built to simulate and predict the future development of space debris. These models can be generally divided into two groups – engineering models and evolutionary models. Engineering models are models trying to describe and characterize the orbital debris environment. These models are then used to assess risk related to specific missions such as spacecraft launches, ISS and others. An example of the engineering model can be ORDEM 3.0 [5]. Purpose of the evolutionary models is to predict the future of the debris environment - its evolution. They provide understanding about the behavior of the space debris and these models are invaluable tools for testing and validating various mitigation practices and scenarios. An example of a model from this category can be NASA's ThreeDimensional Orbital Debris Evolutionary Model - so called LEGEND model [6]. Model presented in this paper also fits into this category and is based on currently estimated and already modeled aggregate values for debris populations and their development divided into four groups – inactive satellites, large debris (larger than 10 cm), medium debris
∗
Corresponding author. E-mail addresses: [email protected] (J. Drmola), [email protected]ff.cuni.cz (T. Hubik).
https://doi.org/10.1016/j.spacepol.2018.03.003 Received 23 October 2017; Received in revised form 7 March 2018; Accepted 13 March 2018 0265-9646/ © 2018 Published by Elsevier Ltd.
Please cite this article as: Drmola, J., Space Policy (2018), https://doi.org/10.1016/j.spacepol.2018.03.003
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After the initial model was built, a series of iterative simulations was performed in order to tune the parameters and revise the structure until the behavior of the model matches observed data (so called reference mode). Once the model is able to replicate baseline behavior sufficiently accurately, it is possible to use it as a basis for modifications and experimentation to simulate various scenarios, test various policies and observe how these changes affect modeled behavior. In other words, the system dynamics model is used to test whether the Kessler syndrome will occur under different model setups and scenarios. One might notice that this approach is somewhat similar to Petri nets mathematical modeling language. The main difference between Petri nets and System Dynamics is that Petri nets are based on statetransition approach with discrete time - so called discrete-event simulation. System Dynamics on the other hand is based on aggregated workflows and transitions modeled continuously through sets of differential and integral equations. Generally discrete-event simulations are more analytic and focused on individual entities and events. System dynamics approach is rather holistic with emphasis on dynamic complexity - it concentrates on homogenized entities and overall behavior of system [12].
(between 1 and 10 cm) and small debris (smaller than 1 cm). This categorization is consistent with the one used by NASA, ESA, and other space agencies [7,8]. Naturally, every model trying to predict the future of the orbital debris faces a major limitation – uncertainty. With the power of today's sensors and supercomputers, we can rather reliably track many significant objects in the orbit, thus predicting collisions, but still not all of them. What is even more uncertain is what happens when the collision occurs. How many pieces of debris will be generated? What will be their velocity? And in which direction will the resulting fragments spread afterwards? These factors are very hard to predict and, in general, can be assessed only on aggregate level [9,10]. The aim of the model presented in this paper is not to duplicate or validate already existing models nor provide more accurate results than they do. It is arguably (and intentionally) less accurate than many aforementioned models, because it operates on a more aggregate level to better serve its purpose which is quite different. Main benefit of this specific model is that it is very easy to modify, computationally relatively undemanding, accessible to non-physicists and non-mathematicians, and therefore able to facilitate rapid and accessible evaluation of various scenarios. It can serve as a solid platform for possible policy analysis and discussions regarding space debris and its associated risks, impacts and mitigation strategies. In other words, we are building on the assumption that the above cited models are broadly correct and seek to present a simplified model, which can be easily used to explore an expanded spectrum of various possibilities. With this in mind, the paper includes several illustrative scenarios that demonstrate flexibility of the model and its wide applicability.
4. Model Primary component of the model are its feedback loops. Of primary concern (regarding the Kessler Syndrome) are the reinforcing feedback loops, meaning that the more debris there is in the space, the more collisions will occur, thus creating even more debris, which can be depicted by a heavily simplified Causal Loop Diagram focused around collisions and their effect on modeled populations These reinforcing feedback loops are noted with ‘R’ in the diagram (see Fig. 1). Arrows with plus and minus signs show the direction of causality: ‘plus’ sign means that increase (or decrease) of the variable at the start of the arrow would cause increase (or decrease) of the variable at the end of the arrow, and, conversely, the ‘minus’ sign implies that increase of first variable causes decrease of the second one (and vice versa). For example, faster orbital decay would cause the population of medium debris to decrease, which in turn causes the number of collisions to go down. The second diagram is more complex and depicts the fragmenting
3. Methodology The whole problem is highly non-linear. Resulting debris from the collisions is interacting with the rest of the system creating feedback loops. It is not possible to accurately capture this process using linear models interpolating historical behavior. To tackle the problem in an accessible manner, System Dynamics methodology was selected [11]. It is a methodology and mathematical modeling technique to describe, understand and analyze complex problems and issues and to design and discuss possible policies. The whole system is described using coupled, first-order, non-linear differential and integral equations. These equations just describe a system that is built from stocks, flows, variables, constants and connections with optional delays between those elements. Levels of stocks in the system represent a state of the system. By system we mean a set of independent elements that interact with each other, generating a behavior of the system in time. The model is usually presented not in a form of mathematical equations but in form of diagrams to be easier to read and more expressive. These diagrams are called causal loop diagrams and stock and flow diagrams. Causal loop diagram is a map of the system which consists of all entities (variables and constants) and arrows representing that one entity influences another entity. Causal loop diagram represents a structure of the system. Stock and flow diagram is more qualitative and visualizes not only system's structure, but also behavior. To do so, it is using four types of entities – stocks, flows, constants and variables. The model building process starts with definition of system boundaries and identification of system stocks (such as numbers of satellites), flows (satellites launches, orbital decay etc.), constants and variables (for example probabilities of collisions) within these boundaries. After identification of all the major elements, their mutual interactions and interferences are defined and feedback loops are created.
Fig. 1. Simplified causal loop diagram.
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Fig. 2. More detailed causal loop diagram.
solar activity (on 11-year cycle with its impact on decay times as it heats up the atmosphere and increases drag on orbiting objects) [13]. This decay is the eventual “sink” that over time removes debris from the model. This overall progression can also be visualized as a flowchart (Fig. 3) or as a simplified Stock and Flow Diagram (Fig. 4). Both diagrams show the “evolution” of satellites and the various routes they can take from being launched to either reentering the atmosphere intact or going through different stages of disintegration, thus eventually undergoing the reentry in the form of fragmented debris. Please note, that both of these diagrams, unlike the CLDs above, lack the feedback structure that cause the cycle of fragmentation in the first place. The probabilities and rates of collisions of objects from different groups were calculated using a coefficient converting the rate of collisions between objects from one group to the rate of collisions between objects from another group. The initial base rate was estimated using iterative simulations and comparison of the resulting runs with real data and outputs from other models. Detailed model built by a group of researchers from the Lawrence Livermore National Laboratory was used as a base for the calibration [see 9]. Since the major factor influencing collision probability is size, the probability increases with square of the diameter representing bigger area for possible impact. Speed would be another factor influencing the probability of impacts, but the speed depends on the distance from the Earth and is not influenced by debris size. It means that it will not vary between different debris groups and thus will not influence the collision probability conversion parameters in our model. One the most important limitations and simplifications of the model is the uncertainty of size, structure and composition of the satellites i.e. what debris the satellite will disintegrate into in case of a collision. Perhaps even more crucially, the rate of orbital decay changes significantly with the altitude and eccentricity of the trajectory. The lower the orbital altitude is or the more eccentric it is, the more drag the object experiences as it passes through the last vestiges of our atmosphere. Therefore, objects in the lower or more eccentric orbit will decay significantly faster. Thus, the actual lifetime of a piece of debris can easily vary from days to centuries. It also needs to be noted that while it may take many decades for a satellite to decay (especially from
collisions with more detail and accuracy (Fig. 2). Here it can be seen how these collisions generally destroy bigger objects and turn them into larger number of smaller ones. Interestingly, extra balancing loops (‘B’) can be seen here. These effectively act as breaks within the system, slowing down potential runaway feedback effects (but not necessarily eliminating them altogether). As was mentioned earlier, the debris populations are modeled on aggregate levels and within their respective size families are treated as homogenous (including the inactive satellites). Therefore we do not simulate their individual altitude, velocity, spin, angle of attack or composition, since doing so would increase complexity of the model immensely and would not allow for quick and easy generation of imagined scenarios and their outcomes. Instead, we assume averaged populations and then model their interactions to match previously mentioned (and computationally more intensive) models as closely as possible. It is also assumed that in order to fully fragment an object (i.e. not just render a satellite inoperable, but to fully disintegrate it) the collision must consist of objects of comparable size. In practice, this means that a modeled satellite can be fragmented only by another satellite or large piece of debris, a large object can be fragmented only by another large or medium object and a medium object can be fragmented by a medium or small object. Collision of an active satellite and medium object will disable the satellite, turning it into an inactive satellite that is not operating anymore and loses its ability to maneuver and actively avoid future collisions, which makes its future fragmentation more likely. The collision of small debris and a satellite usually does not cause any harm, as satellites are equipped with a shielding protecting them against these small fragments. Collisions of two active and fully operational satellites are not being modeled as their positions are known precisely, their trajectories plotted ahead of time, both can maneuver, and the evasion success rate is so high that such a collision has never occurred so far. Besides these spontaneous collisions, which act as debris “faucets”, the model also includes common satellite malfunctions (which are simulated as exogenous factors with parameters estimated based on realworld data) and an average orbital decay rate influenced by a variable
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Fig. 3. Flowchart of basic satellite and debris states and transitions.
trends, which are simply extended into the future. An average 1% growth rate of yearly launches of new satellites (starting at 89) is assumed, together with constant success rate in satellites' ability to actively avoid collisions with debris and other satellites, constant lifetime and failure rate. This basic model lacks any sudden events or major policy changes that would markedly influence the debris propagation. However, it serves both as a foundation for all the following scenarios and as a basis of comparison to see what the impact would be. Given high uncertainty regarding future state of the satellite industry (how many satellites will be launched per year, of what type and size, etc.), we elected to limit our simulations to 50 years. The model can certainly continue beyond this point, but the associated unknowns make the simulations progressively less useful. Running this model for its full 50 years (2016–2066) yields the expected result of perpetually growing amount of debris in the LEO. One can observe nearly 2-fold increase in the large debris (over 10 cm) and 3-fold increase in small debris (less than 1 cm) quantities (Fig. 5). The oscillations visible in the graph are caused by the aforementioned solar cycles which influence the rate of reentry for all simulated populations except the still active (i.e. powered) satellites. Also please note, that throughout the paper the graphs use quite different scales for debris populations due to the considerable variations between scenarios. Using any single scale for all graphs would render some of them unintelligible. We can see that this increase in numbers still does not result in realization of the Kessler Syndrome as most of the satellites being
the popular orbits between 500 km and 800 km), we cannot assume the same about debris. That is because while satellite orbits typically have very low eccentricity, collisions result in fragments with velocities and trajectories that vary and differ from the original intact satellite (i.e. are more eccentric and decay faster). This makes estimating rate of orbital decay of debris quite difficult, especially when combined with the ongoing laudable efforts by IADC to shorten the lifetime of satellites after they cease planned operations [14,15]. Therefore, both the orbital and structural parameters used here are (and must be) overall averages designed to represent a “general LEO satellite” and are based on previous fragmentations, of which there are but few. Furthermore, this is getting increasingly more difficult as satellites are getting progressively more diverse, especially with the ongoing boom of the miniaturized CubeSats [16]. This leads to a relatively wide and heterogeneous population of real satellites being represented by a single, homogenized stock of simulated satellites in the model. It is also uncertain and difficult to predict how exactly is this going to evolve in the far future, what proportion of launched satellites will be of which size and into which orbit they will be placed. Lacking precise information, we simply extrapolate current and expected trends.
5. Scenarios and simulation results 5.1. Business as usual and beyond The baseline scenario represents a continuation of the current
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Fig. 4. Simplified stock and flow diagram (see Appendix for complete SFD).
Fig. 5. Satellites and debris during “business as usual” run.
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Fig. 6. Graph of diminishing launch efficiency defined as < satellites launched/satellites lost to collisions > .
This negative development of increasingly risky and costly operation of satellites can also be highlighted and visualized in a graph by comparing the number of satellites launched to the number of satellites lost (to collisions as well as malfunctions) in each given year (Fig. 6). This ratio shows diminishing efficiency of the system, where number of losses per launch increases. After fully acknowledging limitations stemming from inherent uncertainties, we can also try to “make things expectedly worse” by doubling the growth rate of yearly launches (to what it perhaps might end up being due to the boom in satellites industry because of
launched remain intact for their full expected service life. However, it comes with a considerable increase in risk to satellites, which is manifested by their higher yearly losses, making satellites operations riskier and more expensive for governments and private companies alike. This increased amount of debris in LEO combined with the larger number of active satellites makes it approximately twice as likely that an active satellite will suffer a disabling hit or a total disintegration during its lifetime. It should be noted, that this risk might possibly be offset by future improvements in satellite reliability, debris tracking and navigation [17].
Fig. 7. Extended graph for run with doubled growth of yearly launch rate.
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Fig. 8. Satellites and debris during run with assumed conflict.
collapse of sorts around the year 2163. However, it does not look like a suddenly triggered chain reaction leading to widespread fragmentation of the entire LEO, but rather like a gradually reached point at which LEO is so full of debris and the rate of active satellite fragmentation is so high (almost one every day) that the launches cannot keep up anymore. This is consistent with the findings reported by LaFleur and Finkelman, who found the debris system to be unconditionally stable [18,19].
increasing privatization of space, growing demand for communication satellites, etc.) and also extending the simulation timeframe to 200 years (Fig. 7). It must be stressed, that the model was not designed with such long outlooks in mind and many of the assumptions will certainly not hold over the next 200 years (such as static launch rate growth, size and structure of the satellites, their lifetime, evasion rates, lack of mitigation and many others). But in the overwhelmingly unlikely case that these assumptions stay true, the simulated outcome seems to suggest a
Fig. 9. Satellites and debris during run with assumed conflict with relaunch.
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Fig. 10. Graph of diminishing launch efficiency - comparative graph of ASAT scenario variants.
method of destruction (a collision of a missile with a satellite) leads to extensive fragmentation and creation of large debris clouds. A prime example of this was the Chinese 2007 ASAT test which destroyed China's own decommissioned weather satellite FengYun-1C. This hypervelocity collision created around 3000 pieces of medium to large debris and tens of thousands of smaller pieces, most of which will remain in orbit for decades, thus considerably contributing to overall risk of future orbital collisions [20]. As much as occasional tests of ASATs are increasing the amount of debris in the LEO, a greater danger by far is the possibility of a large-
5.2. ASAT scenario Apart from the usual collisional risks that satellites face in the LEO, there has been growing concern regarding the development of antisatellite weapon systems (ASATs) by several world powers (namely China, Russian Federation and the US). These weapons are designed to intercept and destroy orbiting satellites and are, for the most part, descended from the anti-ballistic missile defense systems. While there are some alternative designs under development, the current generation mostly takes form of a boosted missile with a kinetic kill vehicle. This
Fig. 11. Satellite loss due to EMP.
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Fig. 12. Satellites and debris with no launches after year 2040.
5.3. EMP scenario
scale ASAT deployment during an armed conflict between two or more major, technologically advanced powers. Given the reliance of modern militaries on satellites for intelligence, communication and navigation, it is generally presumed that the initial phase of any such conflict would involve mutual destruction of each other's satellites in order to blind the enemy and hinder their offensive operations [21,22]. Such opening salvos could involve immediate destruction of dozens of satellites, thus creating massive clouds of debris threatening the remaining satellites and possibly leading to cascading disintegration across the entire orbit. This kind of hypothetical event is simulated in the second scenario, where an imaginary major military conflict erupts in the year 2040, during which roughly half of all military satellites is destroyed by intentional kinetic impacts using Anti-Satellite weapons. With military and dual-use satellites generally representing a little over one third of all satellites [23] (depending on criteria and the operating country), this results in some 200 satellites destroyed by ASATs in 2040 (Fig. 8). However, even this sudden event is not enough to trigger a chain reaction of satellites disintegrating in LEO, at least according to this model. Nevertheless, the number of collisions with active satellites ends up nearly twice as high at the end of the simulation (i.e. 25 years after the conflict and ASAT strikes) when compared to the previous run. This shows that the damage would be long-term and would negatively affect satellite operations (including commercial and scientific ones) for many years after any conflict involving ASATs. And again, much like in previous chapter, we can make bad situation even worse by imagining a more destructive initial volley of ASATs (double) and by adding some aftereffects. In this case, it is a rapid relaunch of even more satellites to replace the lost military capacity. Therefore, 400 satellites are shot down and then replaced by 800 new ones (Fig. 9). Of course, we have no way of knowing how such a conflict would really unfold. Maybe even more satellites would be targeted, or maybe the attack would be more gradual. Shown here are only some examples, but the model allows one to simulate whatever scenario one might imagine. Impact of these scenarios and the sudden decrease in operational safety of even civilian satellites can be made apparent by plotting their launch efficiency in a single graph (Fig. 10). Two more variants of this scenarios are added for further comparison and to fill in the continuum between the two described above. Gradual return to “standard” levels can be also observed.
The third custom scenario (Fig. 11) is modeling a high-altitude electro-magnetic pulse (EMP) going off, leading to a loss of control over satellites en mass. These kinds of blasts are mostly associated with nuclear weapons and, more specifically, with the high-altitude nuclear weapons tests which were conducted before they were banned by the Partial Test Ban Treaty [24] signed in 1963. Considering the perpetually growing dependence of our civilization on information and communication technology, the EMP (in the form of nuclear bomb or some other device) remains a potential threat. The exact effect that the EMP would have on LEO satellites would depend greatly on the weapon, shielding used and the location of its deployment. Contrary to popular belief, EMP of this type does not necessarily lead to an instantaneous shutdown of all electronic equipment in range, but rather creates a belt of lingering radiation, which damages the equipment as it passes through. Herein modeled EMP attack is based on the Starfish Prime nuclear weapon test, which was conducted by United States on July 9, 1962, 400 km above Pacific Ocean with an approximate yield equivalent to 1.4 megatons of TNT. It led to a gradual failure of roughly one third of all LEO satellites at the time [25]. This is notably less catastrophic (from the debris point of view) than using ASATs. Even though the total number of affected satellites is larger than in the ASAT scenario, the impact on the LEO environment is comparatively mild. This is because the disabled satellites remain intact and do no disintegrate into many thousands of pieces. At least until they collide with something, but even that is comparatively less likely, as tracking and evading hundreds of inactive satellites is simpler task than doing the same with potentially millions of small fragments. We could also compare multiple variants of this scenario (multiple EMPs, relaunches, etc.) but the effect of EMP on LEO debris populations is markedly less pronounced than what we observed in the ASAT scenario, thus making such comparisons (beyond already described difference between the effect of EMP versus that of ASAT volley) relatively unenlightening. 5.4. Cessation of launches Next, a hypothetical scenario was run without any launches after year 2040 (Fig. 12). This primarily serves to demonstrate the high
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Fig. 13. Debris mitigation policy.
endanger the life of people working in, or passing through, LEO. Orbital debris can damage critical systems on space stations, weaken heat shields on spacecraft, and even small pieces can hit astronauts during their spacewalks with tragic consequences. Today, losses of satellites due to collisions are rather rare, but, unless we change how we operate in LEO, they will become more common (or probable) with every passing year. Possibly even more alarming is the long-term effect of debris accumulation. Its inertia means we need some sort of solution sooner rather than later, lest we harm our own future, when we will most likely be even more dependent on satellites and space technology than we are now. Eventually, as we delve still deeper into the placid solitude of our solar system, we will inevitably stain our orbit with even more derelicts of our progress. This impasse, that we are literally forging ourselves, will not just fade by itself and, if left unchecked, it might even smother us. In essence, we should aim to keep this domain devoid of debris inasmuch as possible. And finally, despite its level of abstraction, this work demonstrates that system dynamics is a viable approach to modeling the Kessler Syndrome and the associated issues of accumulation of orbital debris and the threat this poses to our satellites. Compared to other models, using different methods, it is arguably more accessible and comprehensible to academics and practitioners from other, less technical fields, as well as to involved policymakers. Furthermore, it can be readily modified to include specific critical events (such as wars), changes in solar activity, rate of space launches, new industries and possible future debris mitigation attempts designed to either slow down its accumulation or even to remove certain fraction of the debris by deorbiting it. Lastly, regarding future improvements of this model, splitting up satellite population into multiple categories of different sizes and characteristics seems to be the most promising avenue.
inertia of the system and not to highlight any expected or even realistic eventuality. Counterintuitively, even with no new satellites being launched, the amount of debris in LEO keeps growing for at least another 5 years. Only another 10 years later the orbital decay removes enough debris from LEO to return the total amount back to what it was in 2040 (but still higher than what it was in the very beginning). This is caused mostly by the ongoing disintegration of already launched and inactive satellites, which essentially serve as reservoirs of future debris, ready to be scattered. 5.5. Debris mitigation The final scenario represents an attempt to mitigate the situation and somehow “fix” the debris accumulation problem via direct intervention [26]. This is modeled by removing some portion of inactive satellites from the LEO (again, starting from 2040) before they have chance to be fragmented. The model itself does not include any specific method of possible debris removal. The satellites simply get deorbited “somehow” (Fig. 13). One finds that removing 8 inactive satellites per month would nearly stabilize the debris populations. Alas, it is not purpose of this paper to describe, test and compare an entire catalogue of space debris mitigation techniques and proposals, but rather to demonstrate utility of a simple system dynamics model and its ability to quickly and easily explore and assess them. Furthermore, scenarios of this type are ideal for possible debates over various proposed strategies, techniques and policies of debris mitigation. Since all of them can easily be included into the model and simulated (whether they target inactive satellites or some other stage of the debris cycle), it is possible to estimate and compare their long-term effectiveness long before the implementation. 6. Conclusion
Acknowledgements The results show that we are not as close to a catastrophic chainreaction in LEO as it might seem. At the same time, the trend is quite clear. Moreover, even though we might not be approaching the catastrophic cascade at an accelerating rate, we are definitely making our existing and future space operations less safe and more expensive. Simply put, large amounts of debris make losses of equipment more likely. It is also conceivable that orbital collisions with debris could
This text has been written as part of the specific research project ‘Current Issues in Political Science III’ (code MUNI/A/1159/2016), undertaken at the Department of Political Science, Faculty of Social Studies, Masaryk University and was supported also by Charles University institutional funding PROGRES and SVV project number 260 453.
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Appendix. Full model stock and flow diagram
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[1] B. Weeden, 2009 Iridium-cosmos collision fact sheet. Secure world foundation, http://swfound.org/media/6575/swf_iridium_cosmos_collision_fact_sheet_updated_ 2012.pdf, (2010) , Accessed date: 30 May 2017. [2] N.L. Johnson, E. Stansbery, D.O. Whitlock, A.J. Abercromby, D. Shoots, History of On-orbit Satellite Fragmentations, fourteenth ed., NASA, Orbital Debris Program Office, 2008, http://orbitaldebris.jsc.nasa.gov/library/SatelliteFragHistory/TM2008-214779.pdf , Accessed date: 30 May 2017. [3] D.J. Kessler, B.G. Cour-Palais, Collision frequency of artificial satellites: the creation of a debris belt, J. Geophys. Res. 83 (1978) 2637–2646. [4] D.J. Kessler, N.L. Johnson, J.C. Liou, M. Matney, The Kessler Syndrome: implications to future space operations, 33rd Annual American Astronautical Society Guidance and Control Conference, 2010 http://webpages.charter.net/dkessler/ files/Kessler%20Syndrome-AAS%20Paper.pdf , Accessed date: 30 May 2017. [5] Orbital Debris Engineering Models, NASA, 2017, https://www.orbitaldebris.jsc. nasa.gov/modeling/engrmodeling.html , Accessed date: 30 May 2017. [6] Orbital Debris Evolutionary Models, NASA, 2017, https://www.orbitaldebris.jsc. nasa.gov/modeling/evolmodeling.html , Accessed date: 30 May 2017. [7] Space Debris, European Space Agency, 2017, http://www.esa.int/Our_Activities/ Operations/Space_Debris/About_space_debris , Accessed date: 30 May 2017. [8] Technical Report on Space Debris, (1999) United Nations, Scientific and Technical Subcommittee of the Committee on the Peaceful Uses of Outer Space http://www. orbitaldebris.jsc.nasa.gov/library/UN_Report_on_Space_Debris99.pdf , Accessed date: 30 May 2017. [9] S. Nikolaev, D. Phillion, H.K. Springer, W. deVries, M. Jiang, A. Pertica, J. Henderson, M. Horsley, S. Olivier, Brute force modeling of the Kessler syndrome. Lawrence Livermore national laboratory, http://www.amostech.com/ TechnicalPapers/2012/Orbital_Debris/NIKOLAEV.pdf, (2012) , Accessed date: 30 May 2017. [10] A.M. Bradley, L.M. Wein, Space debris: assessing risk and responsibility, Adv. Space Res. 43 (2009) 1372–1390. [11] Y. Barlas, System dynamics: systemic feedback modeling for policy analysis, http:// web.boun.edu.tr/ali.saysel/ESc59M/BarlasEOLSS.pdf, (2002) , Accessed date: 30 May 2017. [12] J. Duggan, A comparison of Petri net and system dynamics approaches for modelling dynamic feedback systems, https://aran.library.nuigalway.ie/bitstream/ handle/10379/4040/DUGGA171.pdf, (2006) , Accessed date: 18 January 2018.
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Contents lists available at ScienceDirect
Space Policy journal homepage: www.elsevier.com/locate/spacepol
Kessler syndrome: System dynamics model Jakub Drmolaa, Tomas Hubikb,∗ a Division of Security and Strategic Studies, Department of Political Science at the Faculty of Social Sciences of Masaryk University, Jostova 10, 602 00, Brno, Czech Republic b Department of Theoretical Computer Science and Mathematical Logic, Faculty of Mathematics and Physics, Charles University, Malostranske namesti 25, 118 00, Prague, Czech Republic
A R T I C LE I N FO
A B S T R A C T
Keywords: System dynamics Kessler syndrome Satellites Orbital debris Anti-satellite weapons Debris evolutionary model
The present paper explores the Kessler Syndrome (the potentially catastrophic accumulation of debris in the Low-Earth Orbit) through System Dynamics methodology. It models satellites and three classes of debris, their fragmentation, interactions and gradual decay over 50 years. It presents five scenarios: a) a “business as usual” approach, which leads to exponential accumulation and growing rate of satellite losses, but no catastrophic chain reaction; b) a conflict with a large-scale deployment of Anti-Satellite Weapons, leading to an accelerated accumulation and losses, but still no chain reaction; c) EMP scenario modeling loss of control over satellites en mass; d) cessation of all LEO satellite launches, illustrating high inertia of the system, which continues to produce more debris; and e) scenario representing an attempt to mitigate the situation via direct removal of some portion of inactive satellites from the LEO. All scenarios take place in 2040. The paper demonstrates the gravity of the situation and the necessity for a sustainable long-term solution, as orbital debris poses a threat to our future space operation even without triggering a catastrophic chain reaction.
1. Introduction
2. Related work and goals
There are over 29,000 man-made objects greater than 10 cm in size in the orbit. These objects include defunct satellites, pieces of spacecraft, mission related debris and other pieces of space junk. The number of these objects is continuously growing due to the continuing launch activity and spontaneous space collisions and breakups [1,2]. Atmospheric drag force alone is not sufficient to stop this trend. Methods and techniques on how to stop this growth are becoming a more and more relevant topic when talking about space programs and precise tracking of these objects is critical for any space mission to avoid potentially catastrophic collision. As the number of objects in the orbit increases, the likelihood of collisions increases as well. A typical space object experiences several close flybys (i.e. within few kilometers) per day. Each close encounter is a potential collision and every collision creates more debris making the probability of future collisions even higher. It has been conjectured, that when the number of objects in the orbit is sufficiently high, a selfsustaining collisional cascading process can be formed, the so-called Kessler Syndrome, named after D. J. Kessler [3,4].
Given the importance and potential impact of the problem, several models have been built to simulate and predict the future development of space debris. These models can be generally divided into two groups – engineering models and evolutionary models. Engineering models are models trying to describe and characterize the orbital debris environment. These models are then used to assess risk related to specific missions such as spacecraft launches, ISS and others. An example of the engineering model can be ORDEM 3.0 [5]. Purpose of the evolutionary models is to predict the future of the debris environment - its evolution. They provide understanding about the behavior of the space debris and these models are invaluable tools for testing and validating various mitigation practices and scenarios. An example of a model from this category can be NASA's ThreeDimensional Orbital Debris Evolutionary Model - so called LEGEND model [6]. Model presented in this paper also fits into this category and is based on currently estimated and already modeled aggregate values for debris populations and their development divided into four groups – inactive satellites, large debris (larger than 10 cm), medium debris
∗
Corresponding author. E-mail addresses: [email protected] (J. Drmola), [email protected]ff.cuni.cz (T. Hubik).
https://doi.org/10.1016/j.spacepol.2018.03.003 Received 23 October 2017; Received in revised form 7 March 2018; Accepted 13 March 2018 0265-9646/ © 2018 Published by Elsevier Ltd.
Please cite this article as: Drmola, J., Space Policy (2018), https://doi.org/10.1016/j.spacepol.2018.03.003
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After the initial model was built, a series of iterative simulations was performed in order to tune the parameters and revise the structure until the behavior of the model matches observed data (so called reference mode). Once the model is able to replicate baseline behavior sufficiently accurately, it is possible to use it as a basis for modifications and experimentation to simulate various scenarios, test various policies and observe how these changes affect modeled behavior. In other words, the system dynamics model is used to test whether the Kessler syndrome will occur under different model setups and scenarios. One might notice that this approach is somewhat similar to Petri nets mathematical modeling language. The main difference between Petri nets and System Dynamics is that Petri nets are based on statetransition approach with discrete time - so called discrete-event simulation. System Dynamics on the other hand is based on aggregated workflows and transitions modeled continuously through sets of differential and integral equations. Generally discrete-event simulations are more analytic and focused on individual entities and events. System dynamics approach is rather holistic with emphasis on dynamic complexity - it concentrates on homogenized entities and overall behavior of system [12].
(between 1 and 10 cm) and small debris (smaller than 1 cm). This categorization is consistent with the one used by NASA, ESA, and other space agencies [7,8]. Naturally, every model trying to predict the future of the orbital debris faces a major limitation – uncertainty. With the power of today's sensors and supercomputers, we can rather reliably track many significant objects in the orbit, thus predicting collisions, but still not all of them. What is even more uncertain is what happens when the collision occurs. How many pieces of debris will be generated? What will be their velocity? And in which direction will the resulting fragments spread afterwards? These factors are very hard to predict and, in general, can be assessed only on aggregate level [9,10]. The aim of the model presented in this paper is not to duplicate or validate already existing models nor provide more accurate results than they do. It is arguably (and intentionally) less accurate than many aforementioned models, because it operates on a more aggregate level to better serve its purpose which is quite different. Main benefit of this specific model is that it is very easy to modify, computationally relatively undemanding, accessible to non-physicists and non-mathematicians, and therefore able to facilitate rapid and accessible evaluation of various scenarios. It can serve as a solid platform for possible policy analysis and discussions regarding space debris and its associated risks, impacts and mitigation strategies. In other words, we are building on the assumption that the above cited models are broadly correct and seek to present a simplified model, which can be easily used to explore an expanded spectrum of various possibilities. With this in mind, the paper includes several illustrative scenarios that demonstrate flexibility of the model and its wide applicability.
4. Model Primary component of the model are its feedback loops. Of primary concern (regarding the Kessler Syndrome) are the reinforcing feedback loops, meaning that the more debris there is in the space, the more collisions will occur, thus creating even more debris, which can be depicted by a heavily simplified Causal Loop Diagram focused around collisions and their effect on modeled populations These reinforcing feedback loops are noted with ‘R’ in the diagram (see Fig. 1). Arrows with plus and minus signs show the direction of causality: ‘plus’ sign means that increase (or decrease) of the variable at the start of the arrow would cause increase (or decrease) of the variable at the end of the arrow, and, conversely, the ‘minus’ sign implies that increase of first variable causes decrease of the second one (and vice versa). For example, faster orbital decay would cause the population of medium debris to decrease, which in turn causes the number of collisions to go down. The second diagram is more complex and depicts the fragmenting
3. Methodology The whole problem is highly non-linear. Resulting debris from the collisions is interacting with the rest of the system creating feedback loops. It is not possible to accurately capture this process using linear models interpolating historical behavior. To tackle the problem in an accessible manner, System Dynamics methodology was selected [11]. It is a methodology and mathematical modeling technique to describe, understand and analyze complex problems and issues and to design and discuss possible policies. The whole system is described using coupled, first-order, non-linear differential and integral equations. These equations just describe a system that is built from stocks, flows, variables, constants and connections with optional delays between those elements. Levels of stocks in the system represent a state of the system. By system we mean a set of independent elements that interact with each other, generating a behavior of the system in time. The model is usually presented not in a form of mathematical equations but in form of diagrams to be easier to read and more expressive. These diagrams are called causal loop diagrams and stock and flow diagrams. Causal loop diagram is a map of the system which consists of all entities (variables and constants) and arrows representing that one entity influences another entity. Causal loop diagram represents a structure of the system. Stock and flow diagram is more qualitative and visualizes not only system's structure, but also behavior. To do so, it is using four types of entities – stocks, flows, constants and variables. The model building process starts with definition of system boundaries and identification of system stocks (such as numbers of satellites), flows (satellites launches, orbital decay etc.), constants and variables (for example probabilities of collisions) within these boundaries. After identification of all the major elements, their mutual interactions and interferences are defined and feedback loops are created.
Fig. 1. Simplified causal loop diagram.
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Fig. 2. More detailed causal loop diagram.
solar activity (on 11-year cycle with its impact on decay times as it heats up the atmosphere and increases drag on orbiting objects) [13]. This decay is the eventual “sink” that over time removes debris from the model. This overall progression can also be visualized as a flowchart (Fig. 3) or as a simplified Stock and Flow Diagram (Fig. 4). Both diagrams show the “evolution” of satellites and the various routes they can take from being launched to either reentering the atmosphere intact or going through different stages of disintegration, thus eventually undergoing the reentry in the form of fragmented debris. Please note, that both of these diagrams, unlike the CLDs above, lack the feedback structure that cause the cycle of fragmentation in the first place. The probabilities and rates of collisions of objects from different groups were calculated using a coefficient converting the rate of collisions between objects from one group to the rate of collisions between objects from another group. The initial base rate was estimated using iterative simulations and comparison of the resulting runs with real data and outputs from other models. Detailed model built by a group of researchers from the Lawrence Livermore National Laboratory was used as a base for the calibration [see 9]. Since the major factor influencing collision probability is size, the probability increases with square of the diameter representing bigger area for possible impact. Speed would be another factor influencing the probability of impacts, but the speed depends on the distance from the Earth and is not influenced by debris size. It means that it will not vary between different debris groups and thus will not influence the collision probability conversion parameters in our model. One the most important limitations and simplifications of the model is the uncertainty of size, structure and composition of the satellites i.e. what debris the satellite will disintegrate into in case of a collision. Perhaps even more crucially, the rate of orbital decay changes significantly with the altitude and eccentricity of the trajectory. The lower the orbital altitude is or the more eccentric it is, the more drag the object experiences as it passes through the last vestiges of our atmosphere. Therefore, objects in the lower or more eccentric orbit will decay significantly faster. Thus, the actual lifetime of a piece of debris can easily vary from days to centuries. It also needs to be noted that while it may take many decades for a satellite to decay (especially from
collisions with more detail and accuracy (Fig. 2). Here it can be seen how these collisions generally destroy bigger objects and turn them into larger number of smaller ones. Interestingly, extra balancing loops (‘B’) can be seen here. These effectively act as breaks within the system, slowing down potential runaway feedback effects (but not necessarily eliminating them altogether). As was mentioned earlier, the debris populations are modeled on aggregate levels and within their respective size families are treated as homogenous (including the inactive satellites). Therefore we do not simulate their individual altitude, velocity, spin, angle of attack or composition, since doing so would increase complexity of the model immensely and would not allow for quick and easy generation of imagined scenarios and their outcomes. Instead, we assume averaged populations and then model their interactions to match previously mentioned (and computationally more intensive) models as closely as possible. It is also assumed that in order to fully fragment an object (i.e. not just render a satellite inoperable, but to fully disintegrate it) the collision must consist of objects of comparable size. In practice, this means that a modeled satellite can be fragmented only by another satellite or large piece of debris, a large object can be fragmented only by another large or medium object and a medium object can be fragmented by a medium or small object. Collision of an active satellite and medium object will disable the satellite, turning it into an inactive satellite that is not operating anymore and loses its ability to maneuver and actively avoid future collisions, which makes its future fragmentation more likely. The collision of small debris and a satellite usually does not cause any harm, as satellites are equipped with a shielding protecting them against these small fragments. Collisions of two active and fully operational satellites are not being modeled as their positions are known precisely, their trajectories plotted ahead of time, both can maneuver, and the evasion success rate is so high that such a collision has never occurred so far. Besides these spontaneous collisions, which act as debris “faucets”, the model also includes common satellite malfunctions (which are simulated as exogenous factors with parameters estimated based on realworld data) and an average orbital decay rate influenced by a variable
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Fig. 3. Flowchart of basic satellite and debris states and transitions.
trends, which are simply extended into the future. An average 1% growth rate of yearly launches of new satellites (starting at 89) is assumed, together with constant success rate in satellites' ability to actively avoid collisions with debris and other satellites, constant lifetime and failure rate. This basic model lacks any sudden events or major policy changes that would markedly influence the debris propagation. However, it serves both as a foundation for all the following scenarios and as a basis of comparison to see what the impact would be. Given high uncertainty regarding future state of the satellite industry (how many satellites will be launched per year, of what type and size, etc.), we elected to limit our simulations to 50 years. The model can certainly continue beyond this point, but the associated unknowns make the simulations progressively less useful. Running this model for its full 50 years (2016–2066) yields the expected result of perpetually growing amount of debris in the LEO. One can observe nearly 2-fold increase in the large debris (over 10 cm) and 3-fold increase in small debris (less than 1 cm) quantities (Fig. 5). The oscillations visible in the graph are caused by the aforementioned solar cycles which influence the rate of reentry for all simulated populations except the still active (i.e. powered) satellites. Also please note, that throughout the paper the graphs use quite different scales for debris populations due to the considerable variations between scenarios. Using any single scale for all graphs would render some of them unintelligible. We can see that this increase in numbers still does not result in realization of the Kessler Syndrome as most of the satellites being
the popular orbits between 500 km and 800 km), we cannot assume the same about debris. That is because while satellite orbits typically have very low eccentricity, collisions result in fragments with velocities and trajectories that vary and differ from the original intact satellite (i.e. are more eccentric and decay faster). This makes estimating rate of orbital decay of debris quite difficult, especially when combined with the ongoing laudable efforts by IADC to shorten the lifetime of satellites after they cease planned operations [14,15]. Therefore, both the orbital and structural parameters used here are (and must be) overall averages designed to represent a “general LEO satellite” and are based on previous fragmentations, of which there are but few. Furthermore, this is getting increasingly more difficult as satellites are getting progressively more diverse, especially with the ongoing boom of the miniaturized CubeSats [16]. This leads to a relatively wide and heterogeneous population of real satellites being represented by a single, homogenized stock of simulated satellites in the model. It is also uncertain and difficult to predict how exactly is this going to evolve in the far future, what proportion of launched satellites will be of which size and into which orbit they will be placed. Lacking precise information, we simply extrapolate current and expected trends.
5. Scenarios and simulation results 5.1. Business as usual and beyond The baseline scenario represents a continuation of the current
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Fig. 4. Simplified stock and flow diagram (see Appendix for complete SFD).
Fig. 5. Satellites and debris during “business as usual” run.
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Fig. 6. Graph of diminishing launch efficiency defined as < satellites launched/satellites lost to collisions > .
This negative development of increasingly risky and costly operation of satellites can also be highlighted and visualized in a graph by comparing the number of satellites launched to the number of satellites lost (to collisions as well as malfunctions) in each given year (Fig. 6). This ratio shows diminishing efficiency of the system, where number of losses per launch increases. After fully acknowledging limitations stemming from inherent uncertainties, we can also try to “make things expectedly worse” by doubling the growth rate of yearly launches (to what it perhaps might end up being due to the boom in satellites industry because of
launched remain intact for their full expected service life. However, it comes with a considerable increase in risk to satellites, which is manifested by their higher yearly losses, making satellites operations riskier and more expensive for governments and private companies alike. This increased amount of debris in LEO combined with the larger number of active satellites makes it approximately twice as likely that an active satellite will suffer a disabling hit or a total disintegration during its lifetime. It should be noted, that this risk might possibly be offset by future improvements in satellite reliability, debris tracking and navigation [17].
Fig. 7. Extended graph for run with doubled growth of yearly launch rate.
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Fig. 8. Satellites and debris during run with assumed conflict.
collapse of sorts around the year 2163. However, it does not look like a suddenly triggered chain reaction leading to widespread fragmentation of the entire LEO, but rather like a gradually reached point at which LEO is so full of debris and the rate of active satellite fragmentation is so high (almost one every day) that the launches cannot keep up anymore. This is consistent with the findings reported by LaFleur and Finkelman, who found the debris system to be unconditionally stable [18,19].
increasing privatization of space, growing demand for communication satellites, etc.) and also extending the simulation timeframe to 200 years (Fig. 7). It must be stressed, that the model was not designed with such long outlooks in mind and many of the assumptions will certainly not hold over the next 200 years (such as static launch rate growth, size and structure of the satellites, their lifetime, evasion rates, lack of mitigation and many others). But in the overwhelmingly unlikely case that these assumptions stay true, the simulated outcome seems to suggest a
Fig. 9. Satellites and debris during run with assumed conflict with relaunch.
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Fig. 10. Graph of diminishing launch efficiency - comparative graph of ASAT scenario variants.
method of destruction (a collision of a missile with a satellite) leads to extensive fragmentation and creation of large debris clouds. A prime example of this was the Chinese 2007 ASAT test which destroyed China's own decommissioned weather satellite FengYun-1C. This hypervelocity collision created around 3000 pieces of medium to large debris and tens of thousands of smaller pieces, most of which will remain in orbit for decades, thus considerably contributing to overall risk of future orbital collisions [20]. As much as occasional tests of ASATs are increasing the amount of debris in the LEO, a greater danger by far is the possibility of a large-
5.2. ASAT scenario Apart from the usual collisional risks that satellites face in the LEO, there has been growing concern regarding the development of antisatellite weapon systems (ASATs) by several world powers (namely China, Russian Federation and the US). These weapons are designed to intercept and destroy orbiting satellites and are, for the most part, descended from the anti-ballistic missile defense systems. While there are some alternative designs under development, the current generation mostly takes form of a boosted missile with a kinetic kill vehicle. This
Fig. 11. Satellite loss due to EMP.
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Fig. 12. Satellites and debris with no launches after year 2040.
5.3. EMP scenario
scale ASAT deployment during an armed conflict between two or more major, technologically advanced powers. Given the reliance of modern militaries on satellites for intelligence, communication and navigation, it is generally presumed that the initial phase of any such conflict would involve mutual destruction of each other's satellites in order to blind the enemy and hinder their offensive operations [21,22]. Such opening salvos could involve immediate destruction of dozens of satellites, thus creating massive clouds of debris threatening the remaining satellites and possibly leading to cascading disintegration across the entire orbit. This kind of hypothetical event is simulated in the second scenario, where an imaginary major military conflict erupts in the year 2040, during which roughly half of all military satellites is destroyed by intentional kinetic impacts using Anti-Satellite weapons. With military and dual-use satellites generally representing a little over one third of all satellites [23] (depending on criteria and the operating country), this results in some 200 satellites destroyed by ASATs in 2040 (Fig. 8). However, even this sudden event is not enough to trigger a chain reaction of satellites disintegrating in LEO, at least according to this model. Nevertheless, the number of collisions with active satellites ends up nearly twice as high at the end of the simulation (i.e. 25 years after the conflict and ASAT strikes) when compared to the previous run. This shows that the damage would be long-term and would negatively affect satellite operations (including commercial and scientific ones) for many years after any conflict involving ASATs. And again, much like in previous chapter, we can make bad situation even worse by imagining a more destructive initial volley of ASATs (double) and by adding some aftereffects. In this case, it is a rapid relaunch of even more satellites to replace the lost military capacity. Therefore, 400 satellites are shot down and then replaced by 800 new ones (Fig. 9). Of course, we have no way of knowing how such a conflict would really unfold. Maybe even more satellites would be targeted, or maybe the attack would be more gradual. Shown here are only some examples, but the model allows one to simulate whatever scenario one might imagine. Impact of these scenarios and the sudden decrease in operational safety of even civilian satellites can be made apparent by plotting their launch efficiency in a single graph (Fig. 10). Two more variants of this scenarios are added for further comparison and to fill in the continuum between the two described above. Gradual return to “standard” levels can be also observed.
The third custom scenario (Fig. 11) is modeling a high-altitude electro-magnetic pulse (EMP) going off, leading to a loss of control over satellites en mass. These kinds of blasts are mostly associated with nuclear weapons and, more specifically, with the high-altitude nuclear weapons tests which were conducted before they were banned by the Partial Test Ban Treaty [24] signed in 1963. Considering the perpetually growing dependence of our civilization on information and communication technology, the EMP (in the form of nuclear bomb or some other device) remains a potential threat. The exact effect that the EMP would have on LEO satellites would depend greatly on the weapon, shielding used and the location of its deployment. Contrary to popular belief, EMP of this type does not necessarily lead to an instantaneous shutdown of all electronic equipment in range, but rather creates a belt of lingering radiation, which damages the equipment as it passes through. Herein modeled EMP attack is based on the Starfish Prime nuclear weapon test, which was conducted by United States on July 9, 1962, 400 km above Pacific Ocean with an approximate yield equivalent to 1.4 megatons of TNT. It led to a gradual failure of roughly one third of all LEO satellites at the time [25]. This is notably less catastrophic (from the debris point of view) than using ASATs. Even though the total number of affected satellites is larger than in the ASAT scenario, the impact on the LEO environment is comparatively mild. This is because the disabled satellites remain intact and do no disintegrate into many thousands of pieces. At least until they collide with something, but even that is comparatively less likely, as tracking and evading hundreds of inactive satellites is simpler task than doing the same with potentially millions of small fragments. We could also compare multiple variants of this scenario (multiple EMPs, relaunches, etc.) but the effect of EMP on LEO debris populations is markedly less pronounced than what we observed in the ASAT scenario, thus making such comparisons (beyond already described difference between the effect of EMP versus that of ASAT volley) relatively unenlightening. 5.4. Cessation of launches Next, a hypothetical scenario was run without any launches after year 2040 (Fig. 12). This primarily serves to demonstrate the high
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Fig. 13. Debris mitigation policy.
endanger the life of people working in, or passing through, LEO. Orbital debris can damage critical systems on space stations, weaken heat shields on spacecraft, and even small pieces can hit astronauts during their spacewalks with tragic consequences. Today, losses of satellites due to collisions are rather rare, but, unless we change how we operate in LEO, they will become more common (or probable) with every passing year. Possibly even more alarming is the long-term effect of debris accumulation. Its inertia means we need some sort of solution sooner rather than later, lest we harm our own future, when we will most likely be even more dependent on satellites and space technology than we are now. Eventually, as we delve still deeper into the placid solitude of our solar system, we will inevitably stain our orbit with even more derelicts of our progress. This impasse, that we are literally forging ourselves, will not just fade by itself and, if left unchecked, it might even smother us. In essence, we should aim to keep this domain devoid of debris inasmuch as possible. And finally, despite its level of abstraction, this work demonstrates that system dynamics is a viable approach to modeling the Kessler Syndrome and the associated issues of accumulation of orbital debris and the threat this poses to our satellites. Compared to other models, using different methods, it is arguably more accessible and comprehensible to academics and practitioners from other, less technical fields, as well as to involved policymakers. Furthermore, it can be readily modified to include specific critical events (such as wars), changes in solar activity, rate of space launches, new industries and possible future debris mitigation attempts designed to either slow down its accumulation or even to remove certain fraction of the debris by deorbiting it. Lastly, regarding future improvements of this model, splitting up satellite population into multiple categories of different sizes and characteristics seems to be the most promising avenue.
inertia of the system and not to highlight any expected or even realistic eventuality. Counterintuitively, even with no new satellites being launched, the amount of debris in LEO keeps growing for at least another 5 years. Only another 10 years later the orbital decay removes enough debris from LEO to return the total amount back to what it was in 2040 (but still higher than what it was in the very beginning). This is caused mostly by the ongoing disintegration of already launched and inactive satellites, which essentially serve as reservoirs of future debris, ready to be scattered. 5.5. Debris mitigation The final scenario represents an attempt to mitigate the situation and somehow “fix” the debris accumulation problem via direct intervention [26]. This is modeled by removing some portion of inactive satellites from the LEO (again, starting from 2040) before they have chance to be fragmented. The model itself does not include any specific method of possible debris removal. The satellites simply get deorbited “somehow” (Fig. 13). One finds that removing 8 inactive satellites per month would nearly stabilize the debris populations. Alas, it is not purpose of this paper to describe, test and compare an entire catalogue of space debris mitigation techniques and proposals, but rather to demonstrate utility of a simple system dynamics model and its ability to quickly and easily explore and assess them. Furthermore, scenarios of this type are ideal for possible debates over various proposed strategies, techniques and policies of debris mitigation. Since all of them can easily be included into the model and simulated (whether they target inactive satellites or some other stage of the debris cycle), it is possible to estimate and compare their long-term effectiveness long before the implementation. 6. Conclusion
Acknowledgements The results show that we are not as close to a catastrophic chainreaction in LEO as it might seem. At the same time, the trend is quite clear. Moreover, even though we might not be approaching the catastrophic cascade at an accelerating rate, we are definitely making our existing and future space operations less safe and more expensive. Simply put, large amounts of debris make losses of equipment more likely. It is also conceivable that orbital collisions with debris could
This text has been written as part of the specific research project ‘Current Issues in Political Science III’ (code MUNI/A/1159/2016), undertaken at the Department of Political Science, Faculty of Social Studies, Masaryk University and was supported also by Charles University institutional funding PROGRES and SVV project number 260 453.
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Appendix. Full model stock and flow diagram
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References
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