Beyond Mitigation: New Metrics for Space Sustainability Assessment ^†

Abstract

The escalating volume of space operations and the proliferation of satellites underscore the urgent need for a pivotal shift towards sustainable space use. This paper highlights the importance of addressing space sustainability through a holistic framework. Robust international commitments, aligned with the United Nations Sustainable Development Goals (SDGs) 12 (Responsible Consumption and Production) and 13 (Climate Action), alongside the implementation of legislative measures, are essential for fostering responsible and sustainable practices in space activities. Furthermore, innovative technology advancements can potentially convert this space sustainability problem into an opportunity for the space sector. Mitigating the risk of debris is no longer sufficient. This article advocates for prioritizing sustainability in the design phase of the new missions and constellations. To achieve this objective, it is crucial to develop a comprehensive understanding of how various design parameters—such as orbital altitude, the number of satellites, the inclusion or exclusion of inter-satellite links, system interoperability, and reconfigurability—impact the sustainability of space systems. Hence, the investigation suggests creating innovative Key Performance Indicators (KPIs) that specifically target space sustainability. These KPIs would enable the evaluation of specific missions/constellations and the comparison of different design alternatives. The absence of current research on these KPIs requires the creation of new ones. This research introduces a preliminary framework for establishing these novel metrics, which can be vital for governments and companies to develop and oversee a sustainable future in space. By implementing a holistic strategy combining robust policy frameworks with cutting-edge technology solutions, we can guarantee the ongoing, secure, and environmentally responsible space utilization for future generations.

1. Introduction

The rapid proliferation of satellites in Low Earth Orbit (LEO) has raised significant concerns regarding space sustainability, compelling stakeholders to reevaluate current practices and frameworks governing space activities [1,2]. As global interest in space exploitation intensifies, the associated risks—particularly the growing menace of space debris—pose substantial threats to the safety of space activities. There is an urgent necessity for responsible resource management and proactive measures to mitigate environmental impacts, aligning with the ethical imperatives of modern space endeavours. The current paradigm, which predominantly focuses on debris risk mitigation, is insufficient for addressing the complex challenges of sustainable space exploitation. A paradigm shift is needed that prioritizes sustainability from the onset of mission design [3,4,5,6,7]. In this framework, to enable an optimized constellation/mission design able to trade system performance and impact the long-term sustainability of space activities, the definition of novel KPIs would play a crucial role. Such KPIs could enable a more nuanced understanding of how different design alternatives impact long-term sustainability, allowing for systematic comparisons and informed decision-making. As a matter of fact, there has been some effort in the direction of measuring the impact of constellations/missions in terms of space sustainability, such as the initiative of the Space Sustainability Rating (SSR) [8]. The SSR uses a tiered scoring system that takes a series of metrics based on models previously published by agencies and academic institutes that serve to quantify and measure sustainability decisions taken by operators, without disclosing confidential mission data and proprietary information. A rated entity will receive a Tier Score that will determine the rating level between Bronze, Silver, Gold or Platinum. The SSR utilizes a composite indicator of modules. Selected modules take into account the level of harmful physical interference caused by the planned design and mission operations, the ability to detect, identify and track small objects that might be operational but cannot usually be reliably tracked and identified, collision avoidance capabilities, data sharing between operator and various communities, and the adoption of standardization concepts in design and operations where possible. However, the SSR is a certification that a company obtains after submitting their mission, and it is unsuitable for this paper, which provides system designers with a flexible tool to optimize their design, meeting the best trade-off between performance and long-term space sustainability. With this objective, this work introduces a preliminary framework for establishing a novel KPI that takes into account in a compact way the main parameters and design choices that might impact the space sustainability of the designed constellation/mission. A key characteristic of such KPI is that it also takes into account the performance requirements of the specific mission, thus giving higher scores to the design that achieves the best trade-off between performance and impact on space sustainability.

The paper is organized as follows: Section 2 presents the concept of space sustainability by design; Section 3 introduces the proposed methodology for building a novel KPI that could play an important role in the design phase of any space mission; using the proposed methodology, Section 4 show the comparison of two of the most important current satellite mega-constellations, namely OneWeb and Starlink, for global broadband communications. KPIs are also used to better understand the impact of different design choices on space sustainability; finally, conclusions are drawn in Section 5.

2. Space Sustainability by Design—Backward and Forward Compatibility

The issue of the sustainable use of space and its protection has become very urgent. Space operations have become challenging as the margin of error for maintaining separation between satellites becomes reduced and the consequent higher probability of collisions leads to further debris increase. Beyond debris, there are other issues that urgently need to be addressed, such as interference with astronomical observations, radio frequency interference with other communication systems, and challenging spectrum management. Several recent initiatives and projects are ongoing to face the space sustainability challenge. Most of the initiatives and research activities are focused on mitigating the damages caused by the wild use of satellite orbits and an uncontrolled generation of space garbage. However, just mitigating the already-made damages will not guarantee long-term space sustainability and safe use of space. We must start designing novel systems with sustainability in mind from the beginning. The Space Sustainability by Design approach places the space sustainability requirements at the start of the design phase or even during the planning stage. A sustainable system should take into account what is already available in space, before sending new hardware out, and also ensure that it is possible to upcycle any of pre-existing ones. This capability would indicate that a system is backward-compatible, meaning it can reuse already deployed space infrastructure. On the other hand, a sustainable system should also be flexible enough to be used for different missions in the future and even for different purposes. In the last case, the designed mission/constellation is forward-compatible. Such by-design flexibility would allow a reduction in the space/aerial nodes to be launched and a more efficient use of the platforms, payload, and links that are involved, thus making a real, more sustainable Space. Key enabling technologies have been identified, such as softwarization pervasiveness, high data rate Inter Satellite Links (ISLs) and interlayer links at millimeter waves, optical and THz frequencies and the use of AI and ML tools [3]. However, to provide system designers with a flexible tool to optimize their design to meet the best trade-off between performance and long-term space sustainability, novel KPIs must be identified to measure the impact on space sustainability of different design choices.

3. Proposed Approach Towards the Definition of a Space Sustainability Index

This Section presents the proposed preliminary framework for establishing a novel KPI that takes into account in a compact way the main parameters and design choices that have an impact on the space sustainability of the designed constellation/mission. A key characteristic of such a KPI is that it also takes into account the performance requirements of the specific mission, thus giving higher scores to the design that achieves the best trade-off between performance and impact on space sustainability.

The Space Sustainability Index (SSI) is defined as an integrated metric comprising three key components:

$$SSI=w_1{e}_{debris}+w_2{e}_p+w_3{e}_{bf}$$

(1)

where

• $e_{debris}$ is a measure of how the designed constellation manages to keep low the probability of further increasing the space debris.
• $e_p$ is the efficiency related to the performance, i.e., a constellation is well designed from the space sustainability point of view, if it manages to meet the performance requirements of the specific service for which it is designed, with a low number of satellites.
• $e_{bf}$ represents the degree to which the designed constellation aligns with the compatibility of BW or FW, as detailed in Section 2.
• $w_i$ parameters are weights, with unitary norm, used to properly tailor the impact of the previously described metrics on SSI.

The parameters $e_{debris}$ and $e_{bf}$ are associated with the characteristics of the constellation, including the number of satellites, orbital configurations, and altitude. These parameters also account for mechanisms aimed at mitigating the probability of exacerbating space debris, such as debris removal systems and deorbiting strategies, as well as ensuring BW and FW compatibility, for instance, through the implementation of ISLs or a software-defined payload. In contrast, $e_p$ refers to the specific service being provided. In the following sections, we define the three components of the SSI under the assumption that the service in question is broadband communications. For this scenario, the primary performance metrics considered are data rate and coverage.

3.1. Space Debris-Related Component

$$e_{debris}=u_1(1-P_{coll})+u_{2}col{l}_{av}+u_{3}retr+u_4\widehat{t_{do}}$$

(2)

where

• $P_{coll}$ is the probability of one or more collisions between the satellites of a constellation and space debris.
• $col{l}_{av}$ refers to the presence or absence of a collision avoidance system onboard the satellites. In case satellites are equipped with an advanced CA system, its value will be set $col{l}_{av}=1$; if they are equipped with a simple CA system, $col{l}_{av}=0.5$; when there is no CA system, $col{l}_{av}=0$.
• $retr$ is the retrieval possibility, i.e, the presence of grapple fixtures on each satellite to allow future active debris removal operations. $retr=1$ if the necessary hardware is present on board and operational, and $retr=0.5$ if it is present but not operational; $retr=0$ if it is absent.
• $\widehat{t_{do}}$ is a number between 0 and 1 proportional to the time needed for a proactive controlled deorbit of a satellite.
• $u_i$ are weighting factors, with unitary norm, for the previously introduced parameters.

The mean number of collisions for all the objects having the same altitude and inclination in the selected constellation is given by [9]:

$$N_{\alpha }=F·A_c·T·\alpha$$

(3)

where $\alpha$ is the number of satellites; the term F is the flux provided by MASTER8 [10], a tool provided by ESA for the characterization of the space debris environment and its future evolution. The flux is determined by the motion of the object through a stationary medium of uniform particle density at a constant speed, it is measured in ${\mathrm{m}}^2/\mathrm{yrs}$ and it is inversely proportional to the diameter of the debris. T is the considered time frame and it is set to 5 years.

The term $A_c$ is the cross-sectional area and can be calculated using the radii of one satellite of the constellation (the target), $r_{tar}$, and the one of space debris (the impactor), $r_{imp}$: $A_c=\pi {(r_{imp}+r_{tar})}^2$.

The probability of collision can be calculated using Poisson statistics:

$$P_{i=n}={\displaystyle \frac{N_{\alpha }^n}{n!}}·e^{N_{\alpha }}$$

(4)

where n is the number of impacts. Therefore, the probability of one or more impacts will be:

$$P_{i\ge 1}=1-e^{-N\alpha }$$

(5)

Finally, the probability of one or more collisions in a constellations with $\alpha$ satellites is then given by:

$$P_{coll}=P_{i\ge \alpha }=1-e^{-N_{\alpha }}$$

(6)

The term related to the deorbiting time is defined as:

$$\widehat{t_{do}}=\left\{\begin{array}{cc}0,\hfill & \mathrm{if}{t}_{do}\ge 60,\hfill \\ 0.2,\hfill & \mathrm{if}36<t_{do}<60,\hfill \\ 0.5,\hfill & \mathrm{if}12<t_{do}\le 36,\hfill \\ 0.8,\hfill & \mathrm{if}6<t_{do}\le 12,\hfill \\ 1,\hfill & \mathrm{if}{t}_{do}\le 6.\hfill \end{array}\right.$$

(7)

where $t_{do}$ is the deorbiting time in months; its maximum value is set to 60, because this is the average estimated time for an LEO satellite to passively deorbit due to atmospheric drag.

3.2. BW/FW Compatibility Efficiency

The degree of BW and FW compatibility is measured by:

$$e_{bf}=0.5{\eta }_{BW}+0.5{\eta }_{FW}$$

(8)

The parameter ${\eta }_{BW}$ is related to the backward compatibility efficiency, i.e., a value of ${\eta }_{BW}=1$ would imply that the mission or service of the system under design can be carried out without the launch of any additional hardware; on the other hand, ${\eta }_{BW}=0$ is an indicator of the fact the mission or service can not exploit any backward compatibility with currently operating systems. The parameter ${\eta }_{FW}$ is a measure of forward compatibility efficiency, i.e., ${\eta }_{FW}=1$ would indicate that all future missions or services could take advantage of the system under design; ${\eta }_{FW}=0$ represents the fact that no future mission could exploit resources from this system.

Although this component of the SSI, closely related to the concept of sustainability by design, represents a crucial element to identify design choices that could contribute to a more sustainable constellation/mission, the exact expression for $e_{bf}$ has not been derived in this work. A more comprehensive understanding of the key technological solutions required to ensure BW/FW compatibility is necessary and will be addressed in future research.

3.3. Performance-Related Efficiency

The efficiency related to system performance has no unique standard definition, being related to the particular service provided. In the frame of this work, we will focus on satellite services for broadband user internet access; under this assumption, we can state that the performance efficiency consists of two main components:

• Coverage efficiency, $e_{cov}$, which has a value of 1 when the coverage requirement is met with the minimum number of satellites; this value decreases when the constellation is oversized (i.e., the coverage requirement is met with a number of satellites higher than the minimum one). The coverage efficiency has a value equal to 0 when the coverage requirement is not met.
• Data rate efficiency, $e_{rate}$, which has its maximum value when the designed constellation manages to serve the planned number of users (according to the business plans) with the minimum required data rate; it is 0 when it does not manage to serve the planned users with the minimum data rate.

Therefore, the performance-related efficiency will be a combination of these two efficiencies, properly weighted, namely:

$$e_p=0.5\left(e_{cov}\right)+0.5\left(e_{rate}\right)$$

(9)

In the rest of this section, the above efficiencies are defined.

3.3.1. Coverage Efficiency

The coverage efficiency $e_{cov}$ is defined as follows:

$$e_{cov}=\left\{\begin{array}{cc}rati{o}_{sat}\hfill & \mathrm{if}rati{o}_{sat}\le 1\hfill \\ 0\hfill & \mathrm{if}rati{o}_{sat}>1\hfill \end{array}\right.$$

(10)

where $rati{o}_{sat}$ is equal to:

$$rati{o}_{sat}={\displaystyle \frac{mi{n}_{sat}}{n_{sat}}}$$

(11)

The minimum number of satellites $mi{n}_{sat}$ needed to cover the desired area is defined as follows:

$$mi{n}_{sat}=A_{cov}/A_{hex}$$

(12)

where $A_{cov}$ refers to the area on Earth that a certain constellation covers with its satellites and it is calculated using the Maximum North Latitude, ${\varphi }_1$, and the Maximum South Latitude, ${\varphi }_2$, at which it can operate and Earth’s radius $R_e$:

$$A_{cov}=2\pi R_e^2[sin\left({\varphi }_1\right)-sin(-{\varphi }_2)]$$

(13)

To calculate the hexagonal area of a cell we first find the radius of the field of view of a single satellite, $r_{FoV}$, given its altitude, h, the Earth’s radius, $R_e$, and the value of its minimum elevation of the user terminal, ${\epsilon }_{\mathrm{UT}}$:

$$r_{FoV}=R_e\left({\displaystyle \frac{\pi }{2}}-{\epsilon }_{\mathrm{UT}}-arcsin\left({\displaystyle \frac{R_e\left(sin\left(\frac{\pi }{2}+{\epsilon }_{\mathrm{UT}}\right)\right)}{R_e+h}}\right)\right)$$

(14)

Therefore, the area of the hexagonal cell is:

$$A_{hex}={\displaystyle \frac{3\sqrt{3}}{2}}{r}_{FoV}^2$$

(15)

3.3.2. Data Rate Efficiency

We define the efficiency $e_{rate}$ as:

$$e_{rate}=\left\{\begin{array}{cc}rati{o}_{users}\hfill & \mathrm{if}rati{o}_{users}\le 1\hfill \\ 0\hfill & \mathrm{if}rati{o}_{users}>1\hfill \end{array}\right.$$

(16)

where the ratio $r_{users}$ is defined as the number of subscribers $N_{sub}$ divided by the number of serviceable users $N_{users}$:

$$rati{o}_{users}={\displaystyle \frac{N_{sub}}{N_{users}}}$$

(17)

The number of serviceable users $N_{users}$ can be defined as:

$$N_{users}={\displaystyle \frac{N_{sat}{T}_{sat}{\eta }_{addr}{\eta }_{serv}{\zeta }_{div}}{B_{user}}}$$

(18)

where $N_{sat}$ represents the number of satellites in a constellation and $B_{user}$ is the bandwidth allocated to each user; ${\eta }_{serv}$ is the service load, i.e., the amount of data that is being used or required by each satellite at a given time; ${\zeta }_{div}$ is the overbooking factor which refers to oversubscription which is when a provider allocates more customers than can be served at the same time; ${\eta }_{addr}$ is the addressability, i.e., the percentage of satellite capacity effectively utilized for serving customers and $T_{sat}$ is the average throughput of each satellite and the maximum data rate per satellite, $T_{max}$, assuming multiple beams and only the downlink path from space to earth.

The Simpson distribution $f_u\left({ϵ}_u\right)$ is used to model the density of a user having a particular minimum elevation; it is defined between the minimum elevation of the User Terminal (UT), ${ϵ}_{UT}$, and the maximum elevation, $\pi /2$, by:

$$f_u\left({ϵ}_u\right)={\displaystyle \frac{2({ϵ}_u-{ϵ}_{UT})}{{(\pi /2-{ϵ}_{UT})}^2}}$$

(19)

Therefore, $T_{sat}$ will be calculated as the following integral:

$$T_{sat}={\int }_{{ϵ}_{UT}}^{\pi /2}{f}_u\left({ϵ}_u\right)T_{max}\left({ϵ}_u\right)d{ϵ}_u$$

4. Satellite Constellation Comparison: Starlink vs. OneWeb

In this section, we first compare two of the main mega constellations already deployed, namely Starlink and OneWeb using the defined SSI. For the purpose of the comparison, we only consider the two terms of the SSI related to the debris and to the performance requirements.

Table 1. Constellation-specific parameters.

Parameters	Starlink	Oneweb
No. of Satellites	6416	650
h	550 km	120 km
${ϵ}_{UT}$	${25}^{\circ }$	${40}^{\circ }$
F	$0.3342\times {10}^{-3}$	$0.1195\times {10}^{-3}$
$r_{sat}$	$2.39$ m	$0.93$ m
T	5 yrs	5 yrs
${\varphi }_1$	55	85
${\varphi }_2$	$-55$	$-85$
$T_{max}$	$19.7$ Gbps	$9.97$ Gbps
$N_{sub}$	$2.2$ mil	$0.2$ mil

shows the parameters that have been used for both constellations. Moreover, for both constellations, the value of the addressability ${\eta }_{addr}$ is assumed to be $30\%$, the value of the service load ${\eta }_{serv}=50\%$ and the value of the overbooking factor ${\xi }_{div}=50$ [11]. For both constellations, we assume the bandwidth $B=100$ Mbps. The flux F measured in [1/${\mathrm{m}}^2$/yr] is derived from the ESA’s MASTER8 tool [10]. The tool requires specifying the the radius of the impactor debris in a collision, which has been assumed to equal $0.005$ m as we have decided to consider all debris with diameter $>1$ cm. Moreover, in the calculation, we have considered that Starlink has an advanced CA mechanism while Oneweb a simple one.

Let us note that in the calculation of $e_{debris}$, we have given more weight to the low probability of collision and hence we have chosen the following weights: $u_1=0.55$, $u_2=15$, $u_3=0.15$, $u_4=0.15$. From

Table 2. SSI for Starlink and Oneweb.

Parameters	Starlink	Oneweb
$e_{cov}$	$0.0283$	$0.2541$
$e_{rate}$	$0.2321$	$0.4179$
$e_{debris}$	$0.2850$	$0.3424$
$SSI\%$	$24.50\%$	$30.61\%$

it is possible to conclude that Oneweb is slightly more sustainable than Starlink. However, it is important to better understand this conclusion. From the comparison of the single terms, we can conclude that Starlink is oversized with respect to the current number of subscribers (it could serve more users) and the considered coverage area. Moreover, Starlink has a slighter higher probability of increasing the debris. In order to better analyze those results, we have made the comparison between the two constellations without considering the added technology needed for collision avoidance and debris retrivial. From the results shown in

Table 3. Comparison without considering collision avoidance/retrivial and assited deorbiting.

Parameters	Starlink	Oneweb
$e_{cov}$	$0.0283$	$0.2541$
$e_{rate}$	$0.2321$	$0.4179$
$e_{debris}$	$0.0$	$0.1924$
$SSI\%$	$5.258\%$	$23.11\%$

it is possible to conclude that for Starlink the advanced collision avoidance system plays a key role in making the constellations more space sustainable. The SSI of Oneweb is only slightly decreased. Finally, to outline the importance of the altitude of the satellites, we have compared two constellations characterized by the same parameters such as the same number of satellites N = 640, the same radius of the satellite, the same number of subscribers (0.2 mil), and the same maximum capacity per satellite (9.97 Gbps) but different altitudes of 550 km and 1200 km. Results are shown in

Table 4. Comparison assuming one constellation, with equal parameters and different altitudes.

Parameters	h = 550 km	h = 1200 km
$e_{cov}$	$0.2840$	$0.2541$
$e_{rate}$	$0.4179$	$0.4179$
$e_{debris}$	$0.02916$	$0.1924$
$SSI\%$	$7.189\%$	$23.11\%$

. Results clearly show the importance of the choice of the altitude of the constellation when space sustainability is considered as a requirement.

5. Conclusions

This work has proposed a preliminary framework for the development of a novel KPI that encapsulates, in a concise manner, the primary parameters and design decisions influencing the space sustainability of a given constellation or mission. The essential components of the KPI have been defined and their mathematical expressions have been derived as functions of key constellation and service parameters. To illustrate its applicability, the proposed Space Sustainability Index (SSI) has been utilized to compare two prominent, currently operational mega constellations, Starlink and OneWeb. The findings underscore the critical role of orbital altitude in determining space sustainability.

The SSI aspires to serve as an instrumental tool for optimizing the design of future constellations, with a specific emphasis on integrating sustainability considerations. The next stage in refining this KPI involves incorporating terms related to bandwidth and frequency compatibility, accounting for enabling technologies such as network softwarization, high data-rate inter-orbit and intra-orbit links, and autonomous system capabilities.