# 8. Estimation of the costs and benefits of debris mitigation

Victoria Ateca-Amestoy, University of the Basque Country, Spain

Chaimaa Boukabouy, University of the Basque Country, Spain

Aitor Ciarreta, University of the Basque Country, Spain

Ignacio Eiriz, Fundación Centro de Tecnologías Aeronáuticas, Spain

María Paz Espinosa, University of the Basque Country, Spain

Space debris not only represent an environmental problem due to the emission of pollutants in outer space, they also challenge the development of the new space economy that must face escalating risks to spacecraft and new satellites.

It is a negative externality generated by human activity, and launchers and damaged satellites are already challenging the sustainability of outer space. The resulting situation can be characterised in terms of the tragedy of the commons, with the current regulation not being able to implement rigid systems of exclusion (Sandler, 2004[1]; Salter, 2016[2]). While resources seemed to be unlimited at the onset of space activity, nowadays the access and occupation of the limited geostationary (GEO) and low-earth (LEO) orbital slots are rival or substractable. These orbits are immaterial resources of outer space and poor governance and overexploitation can lead to congestion and depletion due to space debris. Given the current governance of outer space, excludability is not feasible. Space exploitation is driven by technological reasons, with a finite but increasing number of agents having the technical capacity to launch and operate artefacts into orbit. This is also the case of material resources in outer space, where property rights are incomplete and access to the resource is open. Like international fisheries, asteroid mining could be challenged by the tragedy of the commons.

The problem of space debris is receiving increasing public attention and, probably because of this social awareness, public agents operating in space and researchers have intensified their efforts to quantify the magnitude of the problem. According to a study presented in April 2021, the problem had so far been underestimated and the amount of space junk in orbit could grow 50-fold by 2100 in a worst-case scenario. The number of debris objects estimated by statistical models to be in orbit (as of January 2021) is reported by the European Space Agency to be as follows: 34 000 objects greater than 10 cm, 900 000 objects from 1 cm to 10 cm and 128 million objects from 1 mm to 1 cm (Undseth, Jolly and Olivari, 2021[3]).

Debris generation has a multiplicative effect: the more collision fragments there are, the more collisions will occur, with the risk that the entire population may be reduced to subcritical sizes. If the amount of space debris follows the tendency of recent years, it will eventually reach a tipping point, known as the Kessler Syndrome, that would prevent all space activity (Adilov, Alexander and Cunningham, 2018[4]). Apart from the negative direct impact of space debris in terms of damage, other direct operational costs to avoid collisions are also affected, e.g. satellite design, operations cost, orbit clearance cost and insurance costs (Undseth, Jolly and Olivari, 2021[3]). One could further argue that there are also indirect costs due to the impossibility to develop additional services provided by satellites, as the capacity of the orbits to host satellites would be reduced by debris.

So far, the contribution of economics to the understanding of the problem has been qualified as rather “thin” (Grzelka and Wagner, 2019[5]), with few but remarkable analyses addressing this issue. Common property and control, taxes and markets have been considered by economists to achieve socially desirable outcomes (Adilov, Alexander and Cunningham, 2015[6]; Béal, Deschamps and Moulin, 2020[7]; Macauley, 2015[8]; Rao, Burgess and Kaffine, 2020[9]; Rouillon, 2020[10]). However, further contributions from economics can bring new interesting insights, for instance the network structure of the co-operation between countries (Ateca-Amestoy et al., 2021[11]; Eiriz, 2021[12]). The modelling of strategic interaction between different firms that compete for a limited space but do not fully (or not even partially) account for the negative effects of their actions appears to be an adequate framework to study the outcomes in terms of space debris generation under different market structures. We follow this approach in this chapter.

The actual economic cost of space debris is multidimensional in the sense that it generates economic losses when incidents occur, hampering the normal functioning of satellites and further impeding the development of new opportunities, should a critical level of congestion be reached or if the capacity of orbits were to decrease. Our approach to this problem is to empirically approximate the cost of space debris when launching a satellite and to test the possibilities for policy intervention. We build a model to analyse the impact of increasing space activity, estimate the parameters of the model and obtain the external costs imposed by space activity and the benefits of space debris mitigation. Our model introduces some relevant characteristics of the new space economy. The first is the entry of a growing number of agents competing in this market due to the development of downstream services. In this respect, it is necessary to acknowledge that, while satellite operation and services is not the most highly concentrated subsector of the space commercial activity, it is still far from being a competitive market (Giannopapa et al., 2018[13]). The second is the evolution of the mass of space objects and the co-existence of bigger objects with constellations of smaller ones (Diserens, Lewis and Fliege, 2020[14]). The third is the joint consideration of the direct effect of space debris (in terms of the expected cost of collision) and the indirect effect (in terms of the limit of the capacity of orbits to host operating satellites).

We build a theoretical framework to emphasise the importance of the increasing number of players in the satellite services market. We compare the outcome under different market structures for the provision of satellite services: monopoly, oligopoly and perfect competition.

The model provides an evaluation of the external costs imposed by each firm on the rest of the market in the absence of any intervention. We show that these external costs depend on the market structure. To assess these costs, we calibrate the model using values taken from the literature to highlight the importance of the different market structures. We use data on space satellite activity to estimate the parameters of the model and the external effects. Then we test some hypothetical policy interventions that can help to reduce the new generation of mission-related debris.

In our theoretical framework, part of the cost of space debris is the expected cost of replacing the damaged spacecraft or satellite (direct effect). A second (indirect) effect of space debris is that it affects the optimal number of operating satellites.

When there is only one firm, the decision to launch an optimal number of satellites N* accounts for the effect on the probability of collision, which increases with the number of satellites in orbit. Assume that the revenue that each satellite can generate is a decreasing linear function of the total number of satellites N:

We assume that increasing space activity makes each additional satellite less profitable, since the more profitable activities are undertaken first. To simplify, we assume that satellites have an infinite lifespan and can only be destroyed by collision. In the case of a single satellite services provider, there are no external costs, since the impact on the probability of collision of the number of satellites launched is internalised. Profits are:

where D= $\frac{\delta }{1-\delta }$ is the discount factor, C is the unitary cost of replacement and ρ(N) is the expected number of spacecraft damaged by collisions in each period that must be replaced. It can be expressed as a function of the probability of collision, p(N), and the number of operating satellites, N,

An increase in the number of satellites N produces more expected space debris and consequently raises the probability of collision. Cρ(N) is the expected cost of replacement per period.

To maximise profits, the monopolist’s optimal number of satellites (N*) is defined by the following first order condition:

$\begin{array}{c}\frac{\partial \mathrm{\Pi }}{\partial N}=\frac{\delta }{1-\delta }\left(a-2bN-C\frac{d\rho \left(N\right)}{dN}\right)-C=0#\left(4\right)\end{array}$

The marginal revenue in terms of the satellite services provided has to be equal to the marginal cost, which includes not only the marginal cost of construction and launching, but also the indirect marginal expected cost of the replacement in case of collision.

Once the optimal level N* is determined, the firm will maintain it, even in the case of collision. This implies that when a satellite is destroyed, it will be replaced so that the number of operating satellites is always at the optimal level. For a single provider, the decision to launch a new satellite depends on space debris, as it raises the probability of collision and therefore the expected number to be replaced and eventually the expected profits from satellite activity.

We consider a duopolistic market. Assume two providers A and B choose simultaneously and independently the number of satellites to launch, NA and NB, respectively. The revenue per satellite is:

The profits of providers A and B are, respectively:

$\begin{array}{c}{\Pi }_{A}=\frac{\delta }{1-\delta }\left[a-b\left({N}_{A}+{N}_{B}\right)\right]{N}_{A}-C{N}_{A}-\frac{\delta }{1-\delta }C\rho \left(N,{N}_{A}\right)#\left(6\right)\end{array}$

where , , and .

The first order conditions yield the optimal number of satellites each provider will launch depending on the satellites launched by the competitor and define response functions:

$\begin{array}{c}\frac{\partial \mathrm{\Pi }}{\partial {N}_{A}}=\frac{\delta }{1-\delta }\left(a-2bN-C\frac{d\rho \left(N,{N}_{A}\right)}{d{N}_{A}}\right)-C=0#\left(8\right)\end{array}$

The optimal number of active satellites is characterised by the Nash equilibrium of the strategic situation. NA depends implicitly on NB, so firm A’s decision of how many satellites to launch depends on the number of satellites launched by firm B and vice versa.

This strategic interaction between providers comes, first, from the market of satellite services and the fact that revenues from a satellite depend on the number of those providing similar services and, second, from the externality generated by space debris. The optimal number of satellites decreases with the probability of collision and that probability is affected by the decisions of other providers. An important difference with the case of a single provider is that in this case, the external effects are not fully internalised.

As the number of satellite services providers increases, the market becomes more competitive. In this section, we analyse the case when each provider is small compared to the market and may have a negligible impact on π, as well as on the probability of collision p. Each firm considers π (revenue per satellite) to be fixed, as well as the probability of collision, independent of its own decisions.

Thus, each firm decides Ni to maximise profits following a price-taking behaviour and collision probability-taking behaviour:

where $\rho \left(p,{N}_{i}\right)=\sum _{j=1}^{{N}_{i}}j{\left(p\right)}^{j}{\left(1-p\right)}^{{N}_{i}-j}$

At the equilibrium of this market structure, demand equals supply and this requires the fixed probability of collision considered by firms in their optimisation problems to be consistent with the equilibrium number of active satellites N.

$\begin{array}{c}a-bN=C\left[1+\frac{\delta \rho \text{'}\left(p,N\right)}{1-\delta }\right]#\left(11\right)\end{array}$

where $\rho \text{'}\left(p,N\right)$ is the derivative of $\rho \left(p,N\right)=\sum _{j=1}^{N}\left(\begin{array}{c}N\\ j\end{array}\right){p}^{j}{\left(1-p\right)}^{N-j}$ with respect to N. Note that the private marginal cost does not take into account the effect of new launches on the probability of collision p, which is considered fixed.

Note that in this case, firms do not internalise the impact of their decisions on space debris. The supply curve for satellite services is the marginal cost of the industry. The fact that each provider i considers the probability of collision p as fixed (independent of Ni) implies that there is not even a partial internalisation.

We characterise the efficient solution then propose measures to implement it. The efficient solution corresponds to a level of N, such that the social marginal cost is equal to the social marginal value:

$\begin{array}{c}a-bN=C\left[1+\frac{\delta \rho \text{'}\left(N\right)}{1-\delta }\right]#\left(12\right)\end{array}$

where $\rho \text{'}\left(N\right)$ is the derivative of $\rho \left(N\right)=\sum _{j=1}^{N}\left(\begin{array}{c}N\\ j\end{array}\right){p\left(N\right)}^{j}{\left(1-p\left(N\right)\right)}^{N-j}$ with respect to N.

Thus, the marginal social cost of a new satellite considers the impact on the probability of collision of new launches.

To implement the efficient solution, a fiscal policy could increase the firms’ marginal cost up to the level of the social marginal cost, so that in equilibrium the number of satellites would be socially optimal.

In this and the previous sections, we have emphasised the external effects imposed on other firms through the probability of collision and the need to replace the damaged spacecraft. However, note that if the probability of collision is high enough, the space economic activity may become unfeasible or unprofitable and the corresponding social surplus would be lost. The next section focuses on the social surplus that is lost due to space debris.

To compute the loss of total surplus due to space debris, we assume a competitive market. Total surplus is the sum of consumers’ surplus and producers’ surplus

$\begin{array}{c}{\int }_{0}^{{N}^{*}}\left(a-bN-C-C\frac{\delta {\rho }^{\text{'}}\left(p,N\right)}{1-\delta }\right)dN#\left(14\right)\end{array}$

We compare the equilibrium total surplus to the total surplus that would be generated in the absence of space debris and, therefore, a negligible probability of collision. This comparison unveils the loss of value due to space debris, which has two parts: 1) the loss of space activity; and 2) the increase in cost for the replacement of the aircraft due to collision.

$\begin{array}{c}{\int }_{0}^{{N}^{**}}\left(a-bN-C\right)dN-{\int }_{0}^{{N}^{*}}\left(a-bN-C-C\frac{\delta {\rho }^{\text{'}}\left(p,N\right)}{1-\delta }\right)dN#\left(15\right)\end{array}$

To estimate the economic impact of specific space activities, previous empirical studies have based their valuation on four main indicators: 1) job creation; 2) gross domestic product/gross value added (GDP/GVA); 3) government revenues; and 4) spillover effects. Table 8.2 provides measures of impact. It estimates how much an investment of EUR 1 generates.

In our model, space debris limits space activity to N, instead of N∗∗. The value of the additional space activity also translates into lower employment. Spillovers refer to impacts of space activity that are not captured by GDP or employment and include other indicators such as technology development, innovation and data exploitation. The data generated are quite valuable, as they can be used by scientists, commercial users, development agencies and policy makers. Note that the spillovers vary depending on the nature of the satellites’ activities. In the case of telecommunication satellites, the spillover effect is different from that of earth observation, since the downstream revenues are generated not by the data collected, but from the broadcasting and communication services, such as consumers’ access to the Internet by satellite, communication with mobile phones, government communications, etc.

Taxes related to satellite production and launching are also part of the economic impact. Space activity generates direct government revenues for the participating countries through taxes on transactions, salaries and consumption. Several studies estimate that participating countries will indirectly recover through taxes more than 60% of the overall cost of the programmes. Adilov, Alexander and Cunningham (2015[6]) found that perfect competition between firms results in a level of satellite launches that surpasses the social optimum and investment in debris mitigation that is below the social optimum. They derived a two-part Pigouvian tax for that specific type of market context, with taxes depending on debris creation and applied per launch, and tax revenue being used to fund new debris-removal technologies. Macauley (2015[8]) also prescribed a system of launch taxes for the LEOs, the most populated orbits with the highest volume of debris. The taxes (at launch) would be refunded to companies that apply end-of life disposal measures to their satellites and spacecraft. Her approach includes rebates to satellite producers for incorporating certain ex ante debris mitigation technologies such as graveyarding, orbital manoeuvring and shielding, as these measures can also yield some spillover benefits. Rao, Burgess and Kaffine (2020[9]) highlight the fact that the mere implementation of new mitigation technologies would not end with the problem of governance, as competitors would not have the incentive to internalise their negative externalities. Last, Béal, Deschamps and Moulin (2020[7]) consider the effectiveness of different tax incentives, with more effective results in terms of recovering clean-up costs for centralised linear taxes.

According to Euroconsult (2019[16]), it is estimated that EUR 8 billion of government revenues (taxes) will be generated over the full period of analysis (2007-32) in the 22 European Space Agency (ESA) member states, plus Canada and Slovenia.

In our empirical application, we use previous studies to define several scenarios of the probability of collision as a function of satellite activity (Patera, 2001[17]; Adilov, Alexander and Cunningham, 2015[6]). To better understand the implications of the market structure model and to justify our approach, we study the evolution of competition in the market over the past decades. Figure 8.1 represents the evolution of the concentration of space activity using the Herfindahl-Hirschman Index (HHI). The volume of satellites since the first spacecraft launch – Sputnik 1 in 1957 – has escalated from around one satellite launch per year to up to 70-90 launches a year and has witnessed an increasing number of launches injecting 30 or more small satellites into orbit at once (Undseth, Jolly and Olivari, 2020[18]). This higher launch cadence and the decrease in manufacturing costs in the last two decades have affected market concentration. The market is now far more competitive with fewer entry barriers, as shown by the rise in the number of businesses, small and medium-sized, start-ups, and incubators.

The concentration by orbit type represented in Figure 8.2 shows that, for the last two decades, there has been a higher concentration in all orbits.

The data representing general information of the satellites launched in the past 40 years were collected from the Union of Concerned Scientists (UCS) Satellite Database, the usual source of information for this type of analysis. It includes more than 3 300 satellites launched since 1974. Table 8.3 represents the relevant variables, along with a brief description.

The probability of collision is one of the most important metrics for collision avoidance measures. Alfano and Oltrogge (2018[19]) provide a computational form for the probability of collision pc(N ), which can be expressed as follows:

$\begin{array}{c}{p}_{c}\left(N\right)=\frac{1}{2\pi \sigma x\sigma y}{\int }_{-r}^{r}{\int }_{-\sqrt{{r}^{2}-{x}^{2}}}^{\sqrt{{r}^{2}-{x}^{2}}}{e}^{-\frac{1}{2}}\left[{\left(\frac{x-xm}{\sigma x}\right)}^{2}+{\left(\frac{y-ym}{\sigma y}\right)}^{2}\right]dydx#\left(16\right)\end{array}$

where r is the combined object radius, x lies along the covariance ellipse minor axis, y lies along the major axis, xm and ym are the respective components of the projected miss distance, and σx and σy are the corresponding standard deviations. In this model, the probability of collision is very sensitive to inputs (object size, shape and orientation) and it is, therefore, crucial to determine the independent variables with precision, otherwise the model would yield high errors in the probability of collision. It further relies on the following assumptions: motion of the conjunction objects is fast enough (assumed linear); errors are zero-mean, Gaussian and uncorrelated; the covariances (between size, shape, orientation) are assumed to be constant; and objects are modelled as spheres.

We estimate pc(N ) as a function of volume (kg) and size, based on Alfano and Oltrogge (2018[19]). We obtain:

where α includes the size of the object, represented by the following equation: with $AR>1$

AR is the covariance aspect ratio (shape), d is the miss distance (the maximum distance at which the explosion of a missile head can be expected to damage a target, from Kumar, De Remer and Marshall (2005[20])). Figure 8.3 shows the estimated probability of collision for different shapes, sizes and distances, based on the Alfano and Oltrogge (2018[19]) nomogram. The centre panel illustrates how the lower the distance in kilometres (km) between the objects, the higher the probability of collision. For the second graph to show the impact of the AR (shape) and the size (r) of the objects on the probability of collision, we have fixed the distance at 1 km. With a fixed distance, we can conclude that the larger the size and the more sizeable the shape, the more likely the objects are to collide.

Mitigation measures play an essential role in preserving the outer space environment and guaranteeing its sustainability. The debris present a menace to new launch missions and the functioning of existing spacecraft and satellites, and to some extent a high risk to crew safety and also a hazard to Earth in case of atmospheric re-entry. The debris technical mitigation measures could be broadly classified into two main categories: short-term and long-term measures. The short-term policies involve reducing the number of collisions and the generation of debris related to new missions (avoidance manoeuvres and passivation). The long-term measures are based, first, on deorbiting and removing spacecraft and launch vehicles that are no longer of use from very populated and operational orbits and, second, on compliance with guidelines. The United Nations Office for Outer Space Affairs has developed a framework (guidelines) that should be followed in the early stages of planning, manufacturing and design and later for launching and disposal. The guidelines can be summarised as: limiting space activity (spacecraft and launch vehicles) in LEO and GEO; avoiding intentional destruction and minimising post-mission break-ups (stored energy); and limiting the debris released and collision in orbit (through separation mechanisms and deployment).

So far, according to data from the ESA, the only measures used are collision manoeuvres and passivation. The collision manoeuvres vary depending on the orbit type of the spacecraft. For instance, for LEO, the only possible and recommended disposal is re-entry into the Earth’s atmosphere. For other orbits, the graveyarding technique is the most effective manoeuvre to date: a spacecraft has to re-orbit at an altitude no less than 300 km above the GEO ring to ensure that objects cannot collide or interfere. The passivation technique is implemented at the early stages of the manufacturing (energy reservoirs). It consists of removing all forms of energy sources to avert explosions while in the orbital stage. Such energy can be residual propellants and charged batteries.

Active debris removal brings about new concepts developed by space agencies to clean space at a rate of five to ten objects per year. Some of these concepts (based on the International Interdisciplinary Space Debris Congress Report (2012[21])) are: momentum exchange or electrodynamics (LEO only) tether; attaching a deboost motor, a balloon (for LEO only) or adding a device to the object to increase drag; deploying a reusable tug that grapples and moves; and retrieval (return to Earth, recycling in space) of the object. The main constraint when it comes to active debris removal is that it should be cost-effective.

Based on our model under the perfect competition set-up, we consider a tax per launched satellite (equation 1.15) equal to:

$\begin{array}{c}\tau =C\frac{\delta }{1-\delta }\left[{\rho }^{\text{'}}\left(N\right)-\rho \text{'}\left(p,N\right)\right]#\left(18\right)\end{array}$

A tax set at this level would make the operators internalise the external effects they cause and therefore contribute to the mitigation of the space debris problem. Note that the tax is not fixed, but changes with the number of satellites already in orbit, with the cost of spacecraft replacement and the probability of collision. This last result derived from the model could be estimated for different values of the parameters, as done in the previous subsection to estimate the cost of replacement. Countries could use the revenue of such a tax to invest in R&D for effective technical mitigation measures, e.g. debris removal measures, or to pool collected taxes to provide resources for international research. In the case of already established international co-operative institutions, such as the ESA, these funds could be added to countries’ voluntary contributions (see Ateca-Amestoy et al., (2020[22]); Eiriz (2021[12])).

A safe space, considered to be a global public good, and the market opportunities related to the exploitation and exploration of outer space, represented by the services derived from data, communications and navigation, must be made compatible by properly addressing the space debris problem. Human activity in outer space creates negative externalities, some of which are related to the use of the commons, others to the large fixed costs related to space activity and manufacturing leading to underinvestment; other problems are related to the limited spillover effects that only a few countries benefit from. In the limiting case, collision cascading could reduce the realised value of certain earth orbits to zero. Many scientists and space agencies estimate more debris generation and ultimately a non-accessible outer space due to the higher probability of collision that increases with every new launch mission.

This chapter studied the impact of increasing space activity under different market structures: monopoly, oligopoly and perfect competition, by valuating the debris in outer space and its cost. The model allows studying the effect of a policy intervention that can help reduce the new generation of mission-related debris. We illustrated an approach to quantify the cost of debris based on firm profits and the probability of collision under three market structures. The result is that there is no external cost in the case of a monopolistic satellite services provider, since the impact on the probability of collision of the number of satellites launched is internalised. In contrast, in more fragmented market structures, the firms do not fully internalise the impact of their decisions on space debris. The internalisation of externalities related to space activity or debris can be represented by an enforced liability. On the basis of an (reformed) outer space treaty, the damages caused by debris could be assigned to the country or organisation responsible for launching and operating the satellite.

The debris mitigation measures already implemented have had little effect on the rate of debris generation and removal. The reason for this is that the guidelines that need to be followed only refer to the design, manufacturing and launching stages. However, the volume of debris from previous space activities needs to be eliminated. This chapter argued that a suitable approach would be a Pigouvian taxation system of ex ante launch taxes that would reduce debris per satellite launched. This fiscal policy could increase firms’ marginal cost up to the level of the social marginal cost, so that in equilibrium, the number of satellites would be socially optimal.

The pervasiveness of technological risk, uncertainties on property rights and other global governance issues in outer space, which lead to the accumulation of space debris among other problems, are market failures that call for public intervention. As in other cases where negative externalities of production are involved, increased competition in the market for services provided by orbital satellites leads to a situation in which social welfare tends to decrease if the negative externality is not promptly addressed. Competition in this market has indeed increased a lot, as can be observed in the evolution of the market concentration (HHI) index.

Without a global regulatory intervention, the welfare loss will start to explode because of cascades of collisions and incidents created by objects launched. The main lesson from our analysis is that the best time to act is now, as the recent irruption of cubesats and mega-constellations of satellites can dramatically change the magnitude of the problem (Béal, Deschamps and Moulin, 2020[7]). Twenty years ago the technology enabled the shift into a more competitive market, but still the number of countries and agencies that have access to the launch and operation of satellites is limited, which makes it relatively easy to implement a new governance system that introduces regulation. Such regulation should ensure that actors in this market have the proper incentives to internalise the negative externalities of their activity. This opens a window of opportunity. While the incentives and the tools to implement that new governance system should be negotiated and agreed upon, the urgency of the intervention is clear and past research suggests that we cannot only rely on the progress of technical solutions, such as improvement in deorbiting, to tackle the problem (Undseth, Jolly and Olivari, 2020[18]; Rao, Burgess and Kaffine, 2020[9]). If a new governance of satellite launches and space activity is not implemented, current actors and new entrants will still have the incentive to neglect the negative externality imposed on an increasing number of third parties. The proposed space governance will not be easy, but can we afford the welfare losses and the risk of depletion of the commons?

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[18] Undseth, M., C. Jolly and M. Olivari (2020), “Space sustainability: The economics of space debris in perspective”, OECD Science, Technology and Industry Policy Papers, No. 87, OECD Publishing, Paris, https://doi.org/10.1787/a339de43-en.

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