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The fate model aims at linking the quantity of debris released in the orbital environment to the residence time of the debris in a given orbital cell. It is quantified by the fate matrix which represents the residence time of debris in each orbital compartment, as a function of the orbital cell of emission.

The residence time of debris can be computed with the model developed by Krag et al. (2018, 2017), which assesses the survivability S of fragments >10 cm released at an altitude h (km) and still orbiting after a given time t (yrs) follows Eq. 3: S ( t , h ) = e − t α h 2 + β h + γ = e − t τ [ % ] (3)

Where coefficients α , β , and γ are empirically determined with simple least-square fit by Krag et al. (2017) and are equal to 128.3, 5.85892 × 10^–1 and 6.7 × 10^–4 respectively. The model is valid for altitudes ranging from 450 km (minimum survivability rates) to 2000 km (maximum survivability rates). Values computed for 450 km are applied to altitudes below to extend the characterisation domain until 250 km.

Within Eq. (3), the time parameter τ indicates how rapidly the exponential function decays. In our system, τ is only dependent of the initial altitude of emission (Eq. 3) and corresponds to the total retention time of debris in the orbital environment. We assume that the balance between orbital cells follows two main hypotheses:

i. A debris is systematically decaying in a lower altitude compartment (i.e. it cannot reach an upper orbital cell)

Therefore, the residence time of the debris in a given orbital cell j (FF_j, in years) can be expressed as in Eq. 4 and presented in Figure 2. F F j = τ j − τ j − 1 [ y e a r s ] (4)

The structure of the fate matrix FF is proposed in ( Eq. 5). Columns represent the emission compartments while rows represent the receiving compartments. The sum of a column represents the total time spent by a debris in the orbital environment to reach the sink (i.e. upper layer of the atmosphere). F F = [ F F j − n F F j − n F F j − n F F j − n F F j − n 0 ⋱ ⋱ ⋱ ⋮ ⋮ ⋱ F F j − 2 F F j − 2 F F j − 2 ⋮ ⋱ 0 F F j − 1 F F j − 1 0 …   0 0 F F j ] (5)

The exposure factor in a given orbital cell ( X F j ) is computed by analogy with the conventional exposure modelling in emission-related LCIA: i.e. the contact of the substance/particle from the environment to a sensitive target (Rosenbaum et al., 2018). In our case, the substance/particle is the debris emitted by the product system in the orbital environment and the sensitive target is the existing population of space objects that can collide with the debris.

We model the exposure factor for a given orbital cell (XF _j ) as the collision rate between one single debris and these space objects in the volume of a given orbital cell j per unit of time, following the analogy with the theory of gas dynamics presented by Klinkrad et al., 2006. The collision rate (c) per debris (N) in a compartment j is calculated (Eq. 6) as the product of the cumulative exposed area of both active and inactive objects within the orbital cell with the average relative velocity of collision of a debris with its target in the orbital volume. X F j = ∂ c j ∂ N = Δ ν c j ¯ ⋅ A p o p j V j [ y e a r − 1 ⋅ d e b r i s − 1 ] (6) Where ∆ v ¯ c j (m·s⁻¹) is the average relative velocity of collision in the orbital cell, V j is the volume of the orbital cell (m³) and A p o p j is the cumulative cross-section area of exposed satellites (m²). The different parameters of the exposure model are explained in the following sub-sections.

While the effect factors in LCIA usually targets human health or ecosystem quality at the endpoint level (see Figure 1), the novelty of our approach is to translate such adverse effect to final damages in the area of protection ‘resources’. Such a link between emission-related impacts and final resource damages at the endpoint level has been previously explored by Pradinaud et al. (2019) for water use. Considering the resource framework in LCA, ‘future efforts’ methods based on cost externalities are currently seen as a promising approach at the endpoint level (Berger et al., 2020; Sonderegger et al., 2020). Similarly, we propose to assess the potential damage that a collision with a debris can have from an economic perspective. We assume that the value of the orbital resource can be approximated by the future economic revenues generated by the active satellites’ population in each orbital compartment. It should be noted that this approach has been already investigated by Borelli et al. (2021). In the present study, we choose to consider the revenue associated with downstream segments (i.e., service providers), which also partly includes end-users potential applications, even if boundaries between the space downstream and the non-space activities that it enables are difficult to set (PwC, 2022). Indeed, the main economic added value of the space sector is not in the data or imagery transmitted through spacecraft, but rather in the potential downstream applications and new markets enabled by the tremendous quantity of data generated.

We adopt a mass criterion to estimate the yearly potential revenue generated by the downstream and potential end-users applications in $ per kg of an active satellite. Also, the revenue is different depending on the type of mission: earth observation and science, communications, navigation, and other application. The mass distribution according to the main missions carried out by the 4,078 active satellites in the LEO region according to the UCS database is the following: Earth observation and Earth science, 50%; communications and connectivity 49%; others 1%. It should be noted that navigation satellites are exclusively located in medium-earth orbit (MEO) which is out of our scope.

Regarding the revenues of the downstream segment according to the type of missions of each active satellite, we compile several sources of data coming from confidential market reports and other market reports focusing on Earth observation, Navigation, and Communication applications (PwC, 2019, 2022; EUSPA, 2022; OECD, 2022). The year 2030 is chosen as the reference year to estimate the potential future annual revenue per kg of active satellites depending on their mission. Indeed, satellites that were launched recently (such as Starlink constellations) will reach their maturity in several years.

Hence, the effect factor ( E F j ) for a given LEO orbital compartment j are obtained according to Eq. 8. E F j = ∑ k M k , j ⋅ r e v k , 2030 [ $$ ] (8)

Where M is the total sum of each active satellite mass m launched to fulfill a main mission k within the orbital compartment j. The coefficient r e v k , 2030 represents the specific downstream revenue per kilo in 2030 for a given mission k. The estimated values obtained following the description hereinabove are 20 k$/kg for Earth observation and Earth science, 50 k$/kg for satellite communications, and 115 k$/kg for other purposes.

Based on Eq. 2 and the methodological development above, the final characterization factors are obtained by multiplying the fate factor with the exposure and the effect (Eq. 9). C F j = F F j ⋅ X F j ⋅ E F j   [ $ ad e b r i s − 1 ] (9)

These characterization factors represent the potential damage caused by the release of one additional debris (on top of the background population) in a given orbital compartment of the LEO orbital environment. The final socio-economic damage is approximated by the potential loss of revenue at the downstream level to reflect the quality decrease of the orbital resource when additional debris is emitted.

Fate factors represent the residence time of a debris in each orbital cell and are shown in Supplementary Table S4 and Figure 3. A debris emitted above 1,600 km will spend more than 100 years in the orbital environment, while if emitted below 500 km it will reach the upper layer of the atmosphere in less than 10 years due to the drag effect.

Exposure factors represent the collision rate between a single debris and the exposed space objects in each orbital compartment. Figure 4 shows that exposure factors range from 10^–7 and 10^–2 collision·year⁻¹. It means that a debris has a probability to collide with a space object from 0.00001% to 1% depending on the orbital compartment each year. The orbital cells with the highest exposure factors are at altitudes below 700 km and inclination <100° (Supplementary Table S2) because half of the total orbital population, active and inactive, are located in this range. Few inclinations are well suited for space observation which is typically the case for sun-synchronous orbits near the pole (around 96–98°) and other around 50° are adequate for communication purpose. This can be observed thanks to the distribution of cumulative area of satellites. The average velocity of collision retrieved from Master-2009 model, slightly increases for inclination 100° while the volume is bigger for orbital cell with a higher altitude, but it does not counterbalance the important presence of satellites for smaller inclinations and altitudes (Figure 4).

Figure 5 shows the product between fate factors and exposure factors, which represents the total collision rate caused by the generation of a debris in each orbital compartment. The highest values are at high altitude because the debris generated in such compartment will cross all the downstream cells of the same inclination (as was shown with the fate factors). The potential emission of debris is very low at high altitudes because of the low flux of debris in the background. Therefore, the impact calculated with Eq. (1) are more likely to be low at high altitudes because of the low value of N_D (potential emission of debris) that does not counterbalance the high residence time of debris at high altitudes.

Figure 6 shows the effect factors, representing the total yearly revenue of each orbital compartment. Starlink constellation (communication), located at an altitude 550–600 km with a 52–54° inclination, generates more than one-third of the total yearly revenue of the orbital environment (estimated as 16.5 billion dollars/year considering our assumptions). As a result, the effect factor is the highest in this orbital environment (Figure 6). To a lesser extent, the OneWeb constellation (communication) generates high revenue at 1200km and 86°–88° inclination (estimated as 2.9 billion dollars/year). Earth observation satellites located around 98–100 (near-polar orbits) also generate a substantial revenue (i.e., nine billion dollars/year considering our assumptions). Overall, the total LEO annual revenues accounted for in the scope of our study are estimated to ca. 45.1 billions.

Final characterization factors represent the potential economic damage related to the emission of one debris in each orbital compartment (Figure 7). This is the first attempt to link the emission of a debris (modelled by the inventory) and the endpoint damage considering a full cause-effect chain with fate, exposure, and effect. However, it is to be noted that the effect factor is only a proxy for computing the economic damage caused by a collision with a debris. The effect considers that a debris collision leads to yearly revenue losses related to all the satellites in each orbital compartment. This is an overestimation of revenue losses because one debris collision would not jeopardize the entire orbital compartment. Therefore, the values of CFs should be used with caution and for relative comparison between orbital compartments rather than an absolute valuation of economic losses due to the collision with debris.

That being said, the highest CFs are located in:

- Inclination 52°–54° and altitude above 550 km because debris generated in the [550 km–2000 km] and [52°–54°] orbital band will reach the compartment Starlink constellation is located, according to our model.

The paper presents a new methodology and a set of CFs for assessing the impact of a space mission on the orbital resources within the LCA framework. The CFs represent the potential economic damages caused by the generation of debris (which is calculated in the life cycle inventory). The potential damage is computed through a cause-effect chain including the fate of debris in downstream cells, the exposure of targeted space objects, and the economic revenue loss in case of space object collision with the debris. This is in line with emission-related LCIA methodologies as depicted in Figure 1.

The characterization model is suitable for the LEO (300–2000 km) region which is the most exposed to space debris generation (ESA Space Debris Office, 2022). The methodology could also be adapted for MEO and GEO regions. The space debris pressure into MEO region seems nonetheless less important (Johnson, 2010). As for the temporal representativeness, the characterization model is based on values valid for the year 2021 concerning the satellite population (UCS database), and on forecasted economic revenues for the year 2030. The model can be updated yearly to take into account the new satellite launches which are still increasing with satellite constellations generation (ESA Space Debris Office, 2022).

Most of the satellites launched today can perform collision avoidance maneuvers for debris with a diameter >10 cm, which has been disregarded in the exposure model. However, the initial risk calculation to compute the inventory considers all the debris > 1 cm (see Supplementary File S0. Flux of debris-inventory”) meaning that a substantial part of the flow cannot be systematically tracked and avoided by space systems. Regarding secondary collisions assessed within the characterization model, the consequences in term of break-up (e.g. catastrophic collision event) are not assessed. This could be done within the EF model by estimating a representative mass of the exposed satellites (for both active and inactive population) within each orbital slot. Eqs 6–8 provided in the text document of supporting information characterise the nature of the collision while Eq. 5 gives the quantity of fragments generated. Such estimations would also require the average velocity of collision provided in Supplementary File S1 but also the estimated mass of the debris e.g. thanks to the statistic distribution proposed by the MASTER model (Klinkrad et al., 2006; Technische Universität Braunschweig, 2011; Technische Universität Braunschweig, 2014).

The proposed methodology is novel in the frame of LCA as it concerns impacts and damages (considering fate, exposure, effect) on resources (i.e., orbits) and not on ecosystem quality or human health. However, further studies should investigate the economic losses generated by collision with space debris with more accuracy. It is to be noted that the proposed effect factor is a first proxy: we consider that a collision with a debris damages the full orbital compartment where the collision occurs. This leads to an overestimation of the economic losses since not all satellites of the orbital compartment will break up after a collision. On the other hand, the potential economic losses are underestimated since the total revenue per cell is computed for 1 year, while the average lifetime of a satellite in LEO ranges from 5 to 10 years. It should be noted that the direct economic cost of the satellites (including R&D, manufacturing and launch expenses) are not covered by this proxy which focuses only on the “service” delivered by space systems. This upstream direct revenue, including spacecraft manufacturing and launch services, represents around 10% of the total amount against ca. 85% for downstream application (Euroconsult, 2022). Potential insurance costs for company, estimated around $ 500 k-1million for a small LEO satellites (Hussain and Cohn, 2021) are not included neither. In our study, the downstream revenues generated for 1 year ($45.1 b) seems in the same order of magnitude than Euroconsult estimations (Euroconsult, 2022) when navigation satellites in MEO (51% of the total revenue), as well as GEO communication satellites are excluded. This is because both categories are not part of our scope which focuses on LEO activities.

Quantification of endpoint damage for the ‘resources’ area of protection in LCIA is still under debate in the LCA community. Economic valuation (such as done here) seems promising since it may enable to directly compare and possibly integrate the damage on different natural resources. However, some natural resources (e.g. minerals) are evaluated and traded in the markets, while others (e.g. orbits, freshwater, soil) differ from free markets trade mechanisms (UNEP/SETAC Life Cycle Initiative, 2021). Therefore, the economic valuation of natural resources can include different scopes in the valuation (such as use value and non-use value) depending on the adopted approaches. The economic valuation as proposed in this paper could be adapted as a function of the methodological advances in the field.

The current methodology only takes into account the impact related to space debris. Space systems launched in the orbital regions also generate space congestion which can lead to competition with other users to access the same orbital resource. This impact pathway has already been explored by Maury et al. (2019) but would deserve deeper investigations in the future.

The potential environmental impact of one space mission on the orbital environment could be determined by the proposed characterization model. Going further, it appears possible to rank or compare each space mission by adopting a unit of comparison related to the amount of data they generate. Hence, the orbital resource intensity required to generate a certain amount of data by type of mission could be derived A similar approach has been already investigated in the LCA community with the absolute environmental sustainability assessment (AESA) methodology proposed by Bjørn et al. (2019) and based on the physical carrying capacity of ecosystems. An outer space carrying capacity seems an appropriate way to offer a common basis of comparison, e.g. via a normalization factor. (Bjørn and Hauschild, 2015; Bjørn et al., 2020). This approach fits well with the concept of space capacity which is already widely discussed in the aerospace community (Letizia et al., 2020, 2021; Trozzi et al., 2021). The space capacity for each orbital compartment could complement our proposed characterization model via a normalization factor. To ensure consistency with the LCA framework, only parameters related to the space environment should be considered (such as the maximum additional debris that could be emitted before reaching the Kessler syndrome in a given orbital compartment (Miraux, 2022). However, a distance-to-target approach could also be an option for a “composite indicator” not reflecting only environmental mechanisms. In such a case, the normalisation factor for each characterised orbital compartment can be based on international political consensus as proposed by Krag et al. (2017), Krag et al. (2018) and Letizia et al. (2021) or theoretical socio-economic threshold (Rouillon, 2020) allowing normalisation of each space mission contribution and based on international political consensus could be a relevant option.

Even if the computation of the CFs could appear rather simple compared to the ones published by the aerospace experts community (Letizia et al., 2020; Colombo et al., 2021; Letizia and Lemmens, 2021), the impact assessment model allows the calculus of easy-to-handle factors. This is typical of the parsimonious perspective adopted for other LCIA models already available, e.g. in the toxicology field (Rosenbaum et al., 2008).

The fate factor is based on the temporal survivability of the debris in the orbital environment and is only dependent on the altitude in our model. More complete approaches based on a density model of the cloud of debris based on a probabilistic approach could be considered in further development to characterise the most likely behaviour of a fragment at any point in space and time (Letizia et al., 2015; Letizia et al., 2016; Letizia et al., 2017; Frey et al., 2017; Frey et al., 2019).

The exposure factor is mainly dependent of the orbital population composed of both active and inactive spacecraft. The total exposed area provided in the paper represents a picture of the “recent past” based on both launch and space debris databases. Therefore, the exposed area should be regularly updated to obtain representative XFs. A forecast of future launches and orbital population -considering future fragmentation (i.e. collision and break up), could be implemented. This would allow the computation of prospective XFs taking into account the evolution of the orbital environment. This approach has already been proposed in LCA e.g. to characterise water resource scarcity (Baustert et al., 2022).

The methodology to assess the EF factors via the revenue of each type of satellite mission (earth observation, communication, etc.) should be further refined according to a more robust economic valuation method, as already discussed in the previous sub-section.

Finally, potential discrepancies could occur when retrieving the orbital parameters of both active and inactive orbital populations. For instance, this can be the case when recent satellites are inventoried in the UCS database but do not have reached yet their operating orbits. Some potential mismatch between both sources of datasets (UCS and DISCOS databases) could be solved by favouring the exclusive use of the DISCOS database where the active population is regularly updated by the ESA.

This methodology is mainly targeted to LCA practitioners studying the environmental impact of space systems. The developed CFs can be applied for the LCA related to any space system (such as a satellite or launcher) that is located in the LEO region. A prerequisite is to know the potential debris emission (life cycle inventory) which can be computed with the methodology in the SI, and also available in Maury et al. (2019). The number of potential debris N_D can be multiplied by the CF of the environment where the debris is generated (see Eq. (1)) in order to compute potential economic damage.

The results can be then integrated into the full LCA of a space system, along with other environmental impacts (such as climate change, toxicity, mineral resource use, etc.). This is useful for comparing the impacts of different scenarios for a space mission, e.g., using different propellants for satellite re-entry. In this case, propellant with higher theoretical efficiency implies the possibility of re-entry of the spacecraft at the end of life and therefore its associated exposure to space debris (Maury et al., 2020). Such scenarios can be compared to typical environmental impacts related to the production of propellants, but also on the emission, fate, exposure, and effect of debris potentially generated during the use and the end-of-life of the satellite thanks to the present methodology. Other relevant studies can include the selection of orbital location for a space system depending on the environmental and orbital impacts.

The characterisation model developed in the paper could represent a good starting point to complete the environmental footprint of space activities based on the EC-recommended product environmental footprint (PEF) methodology (EC, 2021). In the coming years, the European space sector could define and agree on sector-specific common guidelines for environmental footprint such as Product Environmental Footprint Categories Rules (PEFCRs) for space activities (Pinto, 2022). In such a case, a robust environmental indicator, compliant with the LCA framework might be needed to cover environmental impacts occurring in outer space. A generic methodological framework is proposed by Zampori and Pant (2019) and has been successfully deployed in recent years for other sectors, i.e. energy storage with lithium-ion batteries.