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Space debris collision probability analysis for proposed global broadband constellations
Acta Astronautica 151 (2018) 445–455
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Space debris collision probability analysis for proposed global broadband constellations
T
S. Le Maya,b,∗, S. Gehlya,b,1, B.A. Carterb, S. Flegela,b a b
SERC Limited, Mount Stromlo, Canberra, Australia SPACE Research Centre, RMIT University, Melbourne, Australia
A R T I C LE I N FO
A B S T R A C T
Keywords: Satellite constellation Collision probability MASTER-2009
Fragmentation events, caused by the collision of two objects in space, have been a significant source of space debris objects over a cumulative five decades of space activity. Current proposals by different commercial entities aim to launch constellations comprising thousands of satellites in Low Earth Orbit (LEO), which would result in an increase of more than five times the number of currently active satellites in a region where debris objects are most concentrated. The Inter-Agency Space Debris Coordination Committee (IADC) has already recognized the potential influence of large constellations on the LEO environment and the subsequent need to assess whether current mitigation guidelines will be adequate moving forward. Given developments for such constellations are already underway, independent research efforts ahead of any revision to current IADC guidelines could be of great value not only to the organizations involved in their operation, but also to policymakers and existing space users. This paper evaluates the probability of collisions for mega-constellations operating in the current LEO debris environment under best and worst-case implementation of current mitigation guidelines. Simulation studies are performed using the European Space Agency's (ESA) MASTER-2009 debris evolutionary model, and the specifications of the proposed OneWeb and SpaceX constellations as example mega-constellations. Multiple scenarios are then tested to assess mitigation measures and their ability to minimize the probability of fragmentation events and the creation of new debris in LEO.
1. Introduction
Outer Space (UNCOPUOS) is the central organization tasked with the development of international debris mitigation guidelines, their policies are not legally binding. In order to be effective, their recommendations must be incorporated into rules and regulations established at a national government level. As the space economy continues to develop rapidly, it is imperative that governments ensure that regulatory policies keep pace with the expanding space capabilities within the private sector [8]. Global broadband internet delivered via Non-Geostationary Satellite Orbit (NGSO) is the next emerging capability within the commercial space sector, a service which requires constellations comprising thousands of satellites in LEO. In response to this development, recent literature has investigated the potential risk associated with operating large constellations within the space debris environment. Using simulations, researchers have considered the implications of different post-mission disposal (PMD) strategies and rates of PMD success [9], variations to constellation parameters [10], “self-induced” collision probabilities [10,11], and estimates of the number of collision avoidance manoeuvres required during operations [11]. As of writing,
Space debris objects pose a substantial threat to the vast network of space infrastructure upon which society is dependant for a range of services including navigation, communication, Earth observation, security and military operations. Given the number of space launches to date, the amount of space debris in orbit, and the expected number of launches planned for the near future, it is reasonable to question the ongoing sustainability of the orbital environment for space operations. The notion that a chain of collisions between debris objects (Kessler Syndrome) could result in low Earth orbit (LEO) becoming unusable, and remaining in an unusable state for perhaps thousands of years, is a concern emphasized by many researchers [e.g. Refs. [1–5]]. There have been at least 4 reported accidental hyper-velocity collision events in LEO, one of which (the collision of Iridium 33 and Cosmos 2251) contributed 2296 catalogued objects to the debris population and hundreds of thousands of un-trackable objects less than 10 cm in size [6,7]. Although the United Nation's Committee on the Peaceful Uses of
∗
1
Corresponding author. SPACE Research Centre, RMIT University, Melbourne, Australia E-mail addresses: [email protected] (S. Le May), [email protected] (S. Gehly), [email protected] (B.A. Carter), svenfl[email protected] (S. Flegel). Now at: UNSW, Canberra, Australia.
https://doi.org/10.1016/j.actaastro.2018.06.036 Received 28 February 2018; Received in revised form 11 June 2018; Accepted 14 June 2018 Available online 19 June 2018 0094-5765/ © 2018 IAA. Published by Elsevier Ltd. All rights reserved.
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Fig. 2. MASTER-2009 output for spatial density of debris objects larger than 3 mm versus altitude for 4 September 2017.
It is also apparent that the majority of tracked objects at these altitudes are debris, not payloads, therefore there is a greater degree of uncertainty regarding their orbits. The catalogued population is based on observational data, which typically limits the catalogue to debris objects with diameters greater than 10 cm [15]. While OneWeb and SpaceX will operate in less populated regions, the spiral up and disposal phase of their missions will pass through more densely populated regions across 800 km, and will experience an increasing debris flux. However, given that the probability of collision is highest during the operational phase, due to longer residency times [11], the analysis presented in this study focuses on the 5 year operational phase of these constellations. Fig. 2 shows the MASTER-2009 spatial density output for 4 September 2017 obtained under the business as usual future scenario for debris objects larger than 3 mm. Here it is shown that explosion fragments, collision fragments and solid rocket motor (SRM) slag are the most significant contributors to the populations at the operational altitudes proposed by OneWeb and SpaceX.
Fig. 1. Number of catalogued objects in LEO (<2500 km) with proposed operational apogee altitudes for OneWeb (green) and SpaceX (blue). Data from www.space-track.org, retrieved 4 September, 2017. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
specific policies and regulations do not exist to ensure the sustainable operation of these large constellations, yet according to licensing applications made with the Federal Communications Commission (FCC), companies such as OneWeb and SpaceX have ambitions to commence launching in the near future [12,13]. Using the SpaceX and OneWeb constellations as examples, this study uses ESA's MASTER-2009 model to evaluate the collision probability associated with large satellite constellations with future projections of the debris environment, and investigates ways in which the constellation design may be altered to reduce the probability of collision. This paper is organized as follows. Section 2 provides an overview of NGSO constellations, including rationale for their deployment and technical parameters of the constellations used in this study. Section 3 provides a description of the methods used for the collision analysis, including an overview of ESA's MASTER-2009 model. Section 4 presents the results for collision probabilities associated with both the OneWeb and SpaceX constellations, and further analyses consider the impact of the constellation parameters and long-term impact of satellites which fail to perform a de-orbit manoeuvre. Closing remarks and topics for future research are provided in Section 5.
2.1. OneWeb On 22 June, 2017, OneWeb LLC (formerly WorldVu Satellites Limited) were granted access by the FCC to the US market using their proposed NGSO Fixed Satellite Service (FSS) system.2 Along with other conditions documented in the Order and Declaratory Ruling [ [16]], the FCC requires that 50% of the authorized NGSO-FSS system is launched and operational within six years of receiving authorization [17]. In December 2016, OneWeb reported their intention to launch 10 test satellites in early 2018 and, after detailed testing, the remaining 710 satellites six months later [12]. This study assumes previously reported targets by OneWeb to have their 720-satellite constellation operational from 2018 [18] which may no longer be accurate, however any delays are not expected to have a significant impact on the results presented here. Tables 1 and 2 detail the orbital and physical parameters of OneWeb's constellation satellites used for the purpose of this study.
2. Technical parameters of NGSO constellations Non-geostationary satellite orbit systems aim to provide low-latency, high-speed and high-capacity internet connectivity with global coverage to surpass the terrestrial equivalent in broadband internet services [14]. OneWeb, SpaceX and others have already put forward proposals to launch hundreds to thousands of satellites to provide global broadband internet services via new NGSO systems. The parameters of the OneWeb and SpaceX constellations used in this study have originated from the technical attachments provided by each of the respective operators' application to the FCC for operating authority within the United States [12,13]. Common to both applications are their proposed operational lifetime of five years, and selection of LEO altitudes. OneWeb has proposed to deploy their constellation at 1200 km while the SpaceX constellation makes use of multiple orbit altitudes on either side at 1100 km, 1130 km, 1150 km, 1275 km, and 1325 km. Fig. 1 shows the number of publicly catalogued objects in LEO, as of 4 September 2017, and the proposed operating altitudes for both constellations. It can be seen here that both operators have selected altitudes with relatively low populations of debris objects and payloads compared to other LEO regions, for example around 800 km.
2.2. SpaceX The application submitted to the FCC by Space Exploration Holdings (SpaceX) proposes the launch of 4425 satellites with 166 in-orbit spares operating in 83 orbital planes [13]. Tables 3 and 4 summarize the orbital configuration and physical parameters of the SpaceX constellation satellites used for this study, as provided by SpaceX in the technical 2 Since receiving authority for their 720-satellite NGSO-FSS system (used in the analysis presented in this paper), OneWeb has proposed to expand its constellation to 1980 satellites in a separate application to the FCC. The reader can estimate the mean number of expected collisions of the enlarged constellation by multiplying the fluence on a single satellite given in Table A.5 by the appropriate number.
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Table 1 OneWeb constellation parameters. Parameter
Final Deployment
Total Satellites Orbital Planes Satellites per Plane Altitude (km) Inclination (deg)
720 18 40 1200 87.9
Table 2 OneWeb satellite parameters.*Average derived using CROC from ESA's DRAMA 2.0 tool suite. Satellite Body Length (m) Width (m) Height (m) [0.5em] Solar Arrays Length (m) Width (m) Quantity [0.5em] Overall Mass (kg) Average cross-sectional area* (m2) Equivalent radius (m)
1.0 1.0 1.0 1.12 1.0 2
Fig. 3. Idealized sphere model showing approximate relative size for OneWeb spacecraft (green) and SpaceX spacecraft (blue). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
150 2.35 0.93
3. Methodology Table 3 SpaceX satellite parameters. *Average derived using CROC from ESA's DRAMA 2.0 tool suite.
Following the work of Radtke et al. [11], this paper presents an extension of the methods to derive a probability of collision P from the debris flux F on the combined cross-sectional area ( Ac ) of a spacecraft and the debris impactor. The basic terms and methods from Radtke et al. [11] are defined in Section 3.1 before introducing the extended method in Sections 3.2 and 3.3. The extended method includes the classification of collisions by energy and trackability, and uses a ‘boxwing’ approach to estimate the spacecraft geometry instead of considering the target spacecraft as a sphere.
Satellite Body Length (m) Width (m) Height (m) [0.5em] Solar Arrays Length (m) Width (m) Quantity [0.5em] Overall Mass (kg) Average cross-sectional area* (m2) Equivalent radius (m)
4.0 1.8 1.2 6.0 2.0 2
3.1. Collision analysis method (sphere approach) 386 17.99 2.39
Flux, per square meter per annum, is obtained using ESA's MASTER2009 model. The mean number of collisions for the target satellite, Nsat , can be determined as a product of F, Ac , and the operational lifetime of the mission T;
Nsat = F ⋅Ac ⋅T
Table 4 SpaceX constellation parameters. Parameter
Initial Deployment
Final Deployment
Total Satellites Orbital Planes Satellites per Plane Spares per Plane Altitude (km) Inclination (deg)
1664 32 50 2 1150 53
1664 32 50 2 1110 53.8
416 8 50 2 1130 74
385 5 75 2 1275 81
(1)
The calculation of Ac depends on the shape of the surface being analyzed. In Radtke et al. [11], the surface of the spacecraft has been estimated as an idealized sphere (Fig. 3), therefore Ac is determined by the radius of the target spacecraft (rtar ) and the impacting debris object (rimp ).
462 6 75 2 1325 70
Ac = π (rtar + rimp)2
(2)
The probability of the spacecraft being involved in at least one collision (P≥ 1sat ) can then be determined using Poisson statistics, further described in Radtke et al. [11] and Klinkrad [15];
P≥ 1sat = 1 − e−Nsat
attachment of their FCC application [13]. SpaceX CEO, Elon Musk, announced the launch of two test satellites for their global broadband constellation on 22 February, 2018. One month later, on 29 March, 2018, the FCC granted authority for the launch and operation of their NGSO constellation [19]. Conditions of the grant are detailed in the Memorandum Opinion, Order and Authorization, and include standard requirements to comply with current and future orbital debris mitigation policies.
(3)
Results for the total constellation (Nconst and P≥ 1const ) are determined through multiplying by the total number of satellites in each deployment, and in the case of multiple deployments, summing their totals;
Nconst = F ⋅Ac ⋅T ⋅Σ
(4)
P≥ 1const = 1 − e−Nconst
(5)
where Σ is the total number of satellites in the constellation. 447
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Fig. 5. Flux versus debris impact velocity and impactor diameter for objects ≥3 mm on the OneWeb target orbit, output from MASTER-2009 under intermediate mitigation scenario. Red line indicates trackable object threshold of 10 cm. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Fig. 4. Flux versus debris impact velocity and debris impactor mass for objects ≥3 mm on the OneWeb target orbit, output from MASTER-2009 under intermediate mitigation scenario. Lines in white, from bottom to top, indicate thresholds for collisions with EMR equal to 10 kJ/kg, 100 kJ/kg and 1000 kJ/ kg, as defined by equation (6). Line in red indicates EMR equal to 40 kJ/kg, the selected critical threshold for catastrophic collisions. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
The MASTER-2009 simulations have been run under three different future scenarios that assume different levels of orbital debris mitigation measures: 1. Business-as-usual (BAU), where no mitigation measures are implemented; 2. Intermediate Mitigation (MIT1), where the release of mission-related objects are prevented and the generation of explosion fragments and solid rocket motor by-products are reduced; and 3. Full Mitigation (MIT2), which further assumes 100% successful deorbit of rocket bodies and payloads within 25 years.
Fig. 6. Simplified box-wing model showing relative size for OneWeb spacecraft (green) and SpaceX spacecraft (blue). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
minimum diameter of 10 cm are actively tracked and maintained in the current version of the Joint Space Operations Center (JSpOC) catalogue [22]. With this in mind, the new method proposes three separate classifications for collisions:
Further technical detail of the debris sources, mitigation scenarios, and models implemented by the software are given in the MASTER2009 maintenance report [20].
1. Catastrophic collisions, where EMR ≥ 40,000J/kg [21]. 2. Non-trackable collisions, where rimp < 5cm ; and 3. Catastrophic, non-trackable collisions, where both conditions of (1) and (2) apply.
3.2. Collision classification In this study, the method from Radtke et al. [11] has been extended with the aim of using additional post-processing steps to uncover greater meaning from the available MASTER-2009 dataset. It is possible to extract the relative velocity (vrel ) and mass of the debris object (Mimp ) from the MASTER-2009 output, which allows the calculation of the energy-to-mass ratio (EMR) of the predicted collision, where Mtar is the mass of the target satellite;
EMR =
In this way, the analysis is not limited to simply the probability of at least one collision involving a spacecraft, and is extended to specifically whether the collision has potential to be catastrophic. This distinction is important as a catastrophic collision is expected to result in the complete destruction of a spacecraft and, subsequently, the creation of a debris cloud. This study assumes that any impact on the spacecraft's solar panels will not result in complete destruction, hence any debris flux on the solar panels (or equivalent average area) has not been classified as catastrophic. Furthermore, identifying whether collisions involve non-trackable debris objects indicates which fraction of catastrophic collisions are effectively unavoidable. Fig. 5 shows the MASTER-2009 output for flux, diameter and impact velocity of debris objects less than 20 cm diameter using the OneWeb target orbit parameters. Not shown on this chart are objects smaller than 3 mm diameter which contribute the largest flux, totalling 197 per m2 per annum. Spacecraft are equipped with shielding to prevent damage from very small debris, but detailed information for the shielding used by the OneWeb and SpaceX constellations are not publicly available. Based on past research on the efficacy of spacecraft shielding
Mimp v 2rel 2Mtar
(6)
Collisions with EMR ≥ 40,000J/kg are considered to be catastrophic [21], having enough energy to completely destroy a spacecraft. Fig. 4 shows that despite the highest flux being concentrated around debris objects with low masses, due to very high impact velocities (around 14 km/s) a large proportion exceed the catastrophic EMR threshold. The MASTER-2009 output also provides the diameter of the debris object, such that collision events can be classified as trackable if the impactor diameter is greater than 10 cm (rimp > 5cm ) or non-trackable (rimp < 5cm ). Although there may exist the capability to detect debris objects with diameters smaller than 10 cm, only objects with a
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Fig. 7. Mean number of collisions (Nconst ) with debris objects ≥3 mm for OneWeb and SpaceX constellations under business-as-usual (BAU), intermediate mitigation (MIT1) and full mitigation (MIT2) scenarios. Study uses the sphere approach for the 5-year operational phase of the mission. Results for Nsat (single satellite) are given in Table A.5.
comparison in Section 4.1, while analyses in Sections 4.2–4.4 use the sphere-approximation of the spacecraft's surface, where Ac is determined by Equation (2).
against high impact velocity debris, it has been assumed that minimal spacecraft shielding will be adequate to mitigate any risk from objects smaller than 3 mm [23]. For this reason, a minimum size threshold of 3 mm has been selected for this study. Objects ranging 3 mm to 10 cm also make a significant contribution to the flux and those with high impact velocity may result in component damage and possible loss of spacecraft capability [24,25]. The ≥ 3mm MASTER-2009 future populations include debris from ejecta, solid rocket motor slag, sodium potassium droplets, explosion fragments and collision fragments [26], all of which have been included as sources in the simulations for this study.
4.1. N & P during operational phase Figs. 7 and 8 show the results of the sphere-study that compares Nconst (mean number of collisions) and P≥ 1const (probability of at least one collision) of different classes of collisions under different mitigation scenarios for both the OneWeb and SpaceX constellations. It is important to evaluate both Nconst and P≥ 1const concurrently as a value for P≥ 1const close to 1 considered independently will not give an indication of the total mean number of collisions projected (i.e. P≥ 1const ≃ 1 for both cases of Nconst ∼ 5 and Nconst ∼ 300 ). Overall, the mean number of total collisions projected in each scenario is substantially higher for the SpaceX constellation compared to OneWeb (Fig. 7). Despite this large difference in Nconst (Total) between the two constellations, Pconst (Total) indicates a high probability of at least one collision during the operational phase for both constellations. Across all scenarios, of particular concern are the probabilities for the occurrence of at least one catastrophic collision (BAU , P≥ 1const = 0.468) and at least one catastrophic, non-trackable collision (BAU , P≥ 1const = 0.103) in the SpaceX constellation, both are much higher than the respective results for the OneWeb constellation (BAU, P≥ 1const = 0.053 and 0.013).
3.3. Box-wing approach This study also takes advantage of the ‘oriented surface’ functionality provided by the MASTER-2009 model which supports an independent flux analysis for a single oriented surface along the trajectory of the target orbit. Using this option, it is possible to perform an approximate analysis on each of the spacecraft's eight panels (including body and solar panels), by defining their orientation based on a simplified box-wing model (Fig. 6). The spacecraft body panels are oriented relative to the Earth, to maintain a fixed nadir-pointing as in operations, while the solar panels are oriented relative to the Sun. Calculation of Ac for a rectangular panel is determined by the length (L) and width (W) of the panel, and rimp ; 2 Ac = LW + πrimp + 2rimp W + 2rimp L
(7) 4.1.1. Future scenario comparison Implementation of intermediate and full mitigation compared to a business-as-usual case (Fig. 7) reduces the projected total mean number of collisions for the SpaceX constellation by around 12%. Here, Nconst (Total) equals 304 for a business-as-usual scenario compared to 267 and 269 under the intermediate and full mitigation regimes (Fig. 7), with the slight difference between the results for mitigation scenarios being due to the statistical model underlying MASTER. Although implementing mitigation measures gives a slightly favourable outcome for both Nconst (Total) and Nconst (Non − trackable ) , it is less effective for reducing the mean number of catastrophic collisions where the improvement is less than 1% in both mitigation scenarios. With regard to the effectiveness of debris mitigation, there appears to be no significant difference in the probability results from the business-asusual scenario compared to either the intermediate or full mitigation studies for both constellations. These results can be explained by the conditions built in to the intermediate and full mitigation scenarios of the MASTER-2009 model, which implement steady reductions of debris creation from 2020 onwards [26]. Given that the operational phase
This equation is correct as it is for normal impacts. Proper incorporation of off-normal impacts requires the direction of impact relative to the rectangular panel defined through W and L. As the surface impact angle output from MASTER-2009 is given only with respect to the normal vector of the oriented surface this is not possible. As an approximation, the combined cross-sectional area Ac as per Equation (7) is multiplied with each particle's flux contribution to compute Nsat analogously to the spherically approximated spacecraft geometry, but reduced by the surface slant angle. 4. Results and discussion This section presents the results and discussion for the expected mean number of collisions and associated collision probabilities for the SpaceX and OneWeb constellations (Nconst and P≥ 1const ) during their operational phase of five years. Results for single satellite (Nsat and P≥ 1sat ) are not discussed here, but have been included for reference in Appendix A. The results of the box-wing studies are given for
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Fig. 8. Probability of at least one collision (P≥ 1const ) for the constellation with debris objects ≥3 mm for OneWeb and SpaceX under business-as-usual (BAU), intermediate mitigation (MIT1) and full mitigation (MIT2) scenarios. Study uses the sphere approach for the 5-year operational phase of the mission. Results for P≥ 1sat (single satellite) are given in Table A.5.
begins in 2018 for five years, most of the operational phase falls outside of the time period where mitigation scenarios are expected to show some improvement. Longer timescales considering the intermediate mitigation scenario are presented in Section 4.4 where a long-term analysis of failed satellites remaining on orbit are considered. Overall, it can be seen that the implementation of mitigation measures has less influence on the results for the OneWeb constellation compared to SpaceX, which implies that with trends toward much larger NGSO constellations, the level of compliance to mitigation policies may become increasingly significant. The full set of results across different mitigation levels and spacecraft models are provided in Appendix A. 4.1.2. Non-trackable collisions While the concern related to catastrophic collisions is due to their potential to generate a debris cloud from the total destruction of the satellite, the high Nconst and P≥ 1const results for non-catastrophic collisions are still reason for concern, as they give an indication of the exposure of constellation satellites to collisions with potential to disable their capabilities, such as communications and manoeuvrability. With regard to Nconst (Non − trackable ) and P≥ 1const (Non − trackable ) , these results are indicative of the impact of collisions that not only have the potential to be disabling, but are also unavoidable given current sensor limitations. Any collision resulting in a disabled satellite will effectively convert the active satellite into a large, high-velocity debris object in the densely populated constellation orbit regime. Such objects may become the source of cascading collisions within the remaining constellation, a concept explored further in Section 4.4. Although Nconst (Non − trackable ) is much higher for SpaceX than it is for OneWeb (Fig. 7), in the absence of a comparison to SpaceX results the projected Nconst with non-trackable objects for the OneWeb constellation (Nconst (Non − trackable ) = 5.48 under full mitigation scenario) is still reason for concern. With regards to probability, Fig. 8 shows that the probability for at least one collision with a non-trackable object is high for both OneWeb (P≥ 1const (Non − trackable ) = 0.996) and SpaceX (P≥ 1const (Non − trackable ) = 1.000 ). 4.1.3. Box-wing analysis Using the box-wing model results in an overall increase of Nconst and P≥ 1const for OneWeb, and an overall decrease for SpaceX (Fig. 9). Compared to the intermediate mitigation scenario results from the sphere study, Nconst (Total) for the SpaceX constellation is reduced by 9%–245. Conversely, Nconst (Total) for OneWeb is increased by 10% to 6.31. In all other categories, use of the box-wing model has less of an impact on the
Fig. 9. Mean number of collisions (Nconst ) and probability of at least one collision (P≥ 1const ) with debris objects ≥3 mm for OneWeb and SpaceX constellations under the intermediate mitigation scenario. Study uses the box-wing approach for the 5-year operational phase of the mission. Results for P≥ 1sat and Nsat (single satellite) are given in Table A.5.
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Fig. 10. Nconst and P≥ 1const versus EMR for debris objects ≥3 mm for the OneWeb constellation, under the intermediate mitigation scenario. Study uses the sphere approach for the 5-year operational phase of the mission.
Fig. 11. Nconst and P≥ 1const versus EMR for debris objects ≥3 mm for the SpaceX constellation, under the intermediate mitigation scenario. Study uses the sphere approach for the 5-year operational phase of the mission.
results. The changes in the total and non-trackable probabilities are less significant, with P≥ 1const still close to 1 for OneWeb (P≥ 1const (Total) = 0.997 in the sphere study compared to 0.998 in the box-wing study) and equal to 1 for SpaceX. Interestingly, there is a slight increase in Nconst and P≥ 1const for catastrophic collisions in the OneWeb constellation, with a mean of 0.055 catastrophic collisions forecast for the OneWeb constellation using the box-wing configuration compared to the result of 0.051 in the sphere study, likely attributed to statistical noise. Although the box-wing model is still simplistic, it has been shown that by moving toward a more realistic representation of the shape of the spacecraft the results can differ by ±10%. The question of the statistical significance of these differences, however, still requires further investigation. The following sections refer to results that assume the sphere-configuration and intermediate mitigation scenario, with the understanding that these assumptions can lead to different results compared against the business-as-usual or box-wing models.
draw assertions. In fact, three out of four accidental collisions that have occurred since 1990 had negligible impact on the debris environment despite exceeding this assumed threshold [5]. Figs. 10 and 11 have been prepared to investigate the distribution of Nconst and P≥ 1const across different EMR values. For both OneWeb (Fig. 10) and SpaceX (Fig. 11), selecting a critical EMR threshold above 40 kJ/kg would not significantly change the results presented in previous sections. The only significant change would result from classifying an impact with EMR of 0–5 kJ/kg as catastrophic (not shown in Figs. 10 and 11 as Nconst is higher in this category by an order of magnitude); however this would be unlikely, especially when taking into consideration that 3 of the previous 4 accidental collisions collectively contributed only 9 new debris objects to the catalog despite exceeding the generally accepted catastrophic EMR threshold of 40 kJ/kg [5]. 4.3. Effect of constellation parameters on N The results presented in Section 4.1 showed that overall the mean number of collisions projected for the OneWeb constellation are much less than for the SpaceX constellation. Comparing the parameters of both constellations, the most likely explanation for this is due to the compounding effects of both increased size of the SpaceX spacecraft
4.2. Sensitivity to EMR threshold Although an EMR of 40 kJ/kg is widely applied as the threshold for catastrophic collisions as a result of past experiments [21], the number of observed on-orbit collisions is relatively small, making it difficult to
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Fig. 12. Mean number of collisions (Nconst ) for debris objects ≥3 mm, using varied parameters of number of satellites and target radius (rtar ) in the SpaceX constellation. The sphere approach and the intermediate mitigation scenario are applied during the operational phase of 5 years. Green and blue lines indicate the proposed parameters of the OneWeb and SpaceX constellations, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Fig. 13. Mean number of collisions (Nconst ) over time for OneWeb and SpaceX constellations given an assumed percentage of constellation satellites remaining on orbit beyond operational phase due to failure. Study uses sphere approach data-set with intermediate mitigation scenario and debris objects ≥3 mm.
4.4. Long-term analysis for failed satellites
(Table 3), and increased number of satellites within the SpaceX constellation (Table 4). Fig. 12 shows that increasing the target radius of the SpaceX constellation satellites (corresponding to increased Ac per Equation (2)) results in a quadratic increase in Nconst , mean number of collisions, while increasing the number of satellites in the SpaceX constellation corresponds to a linear increase in Nconst . If SpaceX were to reduce the size of their spacecraft to a target radius equal to OneWeb's of 0.86 m, the resulting Nconst would be 36.2, which although is a substantial reduction compared to the existing results (Nconst (Total) = 267), is still more than six times greater than the OneWeb Nconst (Total) of 5.7. By keeping the same physical dimensions, but instead reducing the total number of constellation satellites to match OneWeb's total (720), Nconst (Total) for SpaceX is reduced to 41.8. The nature of FCC applications are such that operators will have applied for approval based on maximum proposed physical dimensions of their spacecraft design, therefore deviation from proposed physical dimensions to smaller dimensions are likely. Based on the results of this study, a reduction in the physical dimensions of the spacecraft resulting in a reduced cross-sectional area yields a marginally better outcome than reducing the number of satellites in the constellation.
Although Nconst (Catastrophic ) is seemingly low for both constellations (Fig. 7), both Nconst (Non − trackable ) and P≥ 1const (Non − trackable ) are very high for SpaceX (and also high for OneWeb), and therefore the potential for disabled satellites is also high. Assuming a disabled satellite is not able to perform a deorbit manoeuvre, a longer stay in orbit may entail a consequent growth of the mean number of catastrophic collisions (Equation (1)). Figs. 13 and 14 show Nconst over time for an assumed percentage (1%, 5% and 10%) of satellites within the constellation that fail to deorbit from their operational altitude. This analysis uses the annual average for a single satellite under the intermediate mitigation scenario (Nsat divided by 5) to determine Nconst (Equation (4)), for T = 0 − 50 years, where the number of failed satellites is equal to a percentage of the total constellation. The analysis does not account for any variation in the background debris flux or future launch activity, and therefore likely gives an optimistic estimate of the expected number of collisions. Assuming a worst-case scenario with a failure rate of 10%, the total mean number of collisions expected in 50 years are ∼ 35 for OneWeb and ∼ 250 for SpaceX (Fig. 13). Of these collisions, a mean of less than 1 are predicted to be catastrophic.
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MASTER-2009 model does have limitations, including no quantified uncertainty associated with the flux output. The results of this study represent the mean collisional behaviour of the system, and are not strictly a prediction of the future. When the collision probability is derived from discrete random particles, the chance of having an accurate result increases with sample size and probability of collision. Both of these are higher for the SpaceX constellation compared with the OneWeb constellation. The differences observed between the results for the sphere and box-wing for the Total results for SpaceX thus have the highest chance of not being due to statistical noise. In statistics, the likelihood for the difference between two results being due to statistical noise is called statistical significance [28]. Similarly, for both constellations the results for Nconst (Total) and Nconst (Non − Trackable ) may have greater statistical significance than Nconst (Catastrophic ) and Nconst (Catastrophic, Non − trackable ) as the flux is derived from a larger number of particles. Quantifying statistical significance in this context would require a more robust statistical analysis, recommended for future work. OneWeb's Orbital Debris Mitigation Plan reports that the probability of a OneWeb satellite becoming disabled as a result of collisions with small debris is 0.003, as computed using NASA's ORDEM3 model and taking the minimum hazardous debris size as 1 cm. In comparison, this study used ESA's MASTER model and a minimum size threshold of 3 mm to determine the probability of collision for a single OneWeb satellite. The resulting probability is around 0.008 (Table A.5), a value which aligns well with OneWeb's own study. In response to the FCC's request to provide an analysis of collision risk, SpaceX reported that there is “approximately a 1% chance per decade that any failed SpaceX satellite would collide with a piece of tracked debris”.3 Although this specific case wasn't explored in Section 4.4, our analysis for the probability of collision of one failed satellite with trackable debris (not shown here) agrees with this statement. However, it does not take into account the collision probabilities associated with non-trackable objects, determined to be P≥ 1sat = 0.124 after 10 years using the sphere model. The results of this study show that implementation of the mitigation measures in MASTER did not significantly reduce the probability of at least one collision during the five year operational phase of either the OneWeb or SpaceX constellation. The MASTER-2009 model's intermediate and full mitigation scenarios implement steady reductions of debris creation from 2020 onwards and therefore have very little impact on the first generation of the OneWeb and SpaceX constellations which cease operation in 2023. Additional measures may be required to ensure the safe and sustainable operation of such constellations, including but not limited to reducing the size and number of satellites launched. Due to imminent launch dates and because of the potential value such constellations have for the global community, in particular developing economies, the question of how to ensure safe and sustainable operations alongside constellations of this scale still needs to be addressed.
Fig. 14. Mean number of catastrophic collisions (Nconst (Catastrophic ) ) over time for OneWeb and SpaceX constellations given an assumed percentage of constellation satellites remaining on orbit beyond operational phase due to failure. Study uses sphere approach data-set with intermediate mitigation scenario and debris objects ≥3 mm.
Although this work only investigates the projected mean number of collisions between failed satellites and debris, because the intention of both operators is to replenish their constellations at the same altitude [12,13], failed satellites have the potential to initiate accidental collisions with future generations of the constellation. High velocity collisions involving two intact spacecraft from two different orbital planes will generate two debris clouds. Assuming similar altitudes of both orbital planes, as is the case in both the OneWeb and SpaceX constellation parameters (Tables 1 and 4), work by Radtke et al. [11] shows the respective debris clouds will increase the collision risk of all spacecraft in the affected orbit altitude. For this reason, a high PostMission Disposal (PMD) success rate is desirable at altitudes where atmospheric drag is low or non-existent, where in the absence of active disposal, spacecraft will remain indefinitely [27].
Acknowledgements The authors extend their thanks to Christopher Kebschull (Institute of Space Systems, TU Braunschweig) who provided valuable insight, expertise and feedback that assisted in this research project. The authors would also like to acknowledge the support of the Cooperative Research Centre for Space Environment Management (SERC Limited) through the Australian Governments Cooperative Research Centre Programme. This research was also supported by the Australian Research Council Linkage grant (project LP160100561) awarded to BAC.
5. Summary and conclusion The results of this study indicate a high probability for the occurrence of at least one collision for both the proposed OneWeb and SpaceX constellations during an operational phase of 5 years. It was found that the probability of there being at least one catastrophic collision involving a spacecraft within the OneWeb constellation is 5.0%, and for SpaceX much higher at 45.8%. It must be noted that the
3
In correspondence from William M. Wiltshire (Counsel to SpaceX) to Jose P. Albuquerque, IBFS File No. SAT-LOA-20161115-00118 (April 20, 2017).
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Appendix A. Table of results Table A.5 Summary of results for N and P≥ 1 for a single satellite (sat) and accross the whole constellation (const) for the OneWeb (720 satellites) and SpaceX (4591 satellites) constellations. Mitigation Scenarios include Business-as-Usual (BAU), Intermediate Mitigation (MIT1) and Full Mitigation (MIT2). Classes of collisions include catastrophic, where EMR ≥ 40kJ / kg , and non-trackable, where rimp < 5cm . Constellation
Surface
Scenario
Class
Nsat
P≥ 1, sat
Nconst
Pconst
OneWeb
Box-Wing
MIT1
Sphere
BAU
Total Catastrophic Non-trackable Catastrophic, Non-trackable Total Catastrophic Non-trackable Catastrophic, Non-trackable Total Catastrophic Non-trackable Catastrophic, Non-trackable Total Catastrophic Non-trackable Catastrophic, Non-trackable Total Catastrophic Non-trackable Catastrophic, Non-trackable Total Catastrophic Non-trackable Catastrophic, Non-trackable Total Catastrophic Non-trackable Catastrophic, Non-trackable Total Catastrophic Non-trackable Catastrophic, Non-trackable
8.76E-03 7.67E-05 8.64E-03 1.31E-05 9.23E-03 7.59E-05 9.16E-03 1.80E-05 7.91E-03 7.15E-05 7.84E-03 1.51E-05 7.69E-03 7.13E-05 7.62E-03 1.50E-05 5.33E-02 1.09E-04 5.30E-02 1.26E-05 6.63E-02 1.37E-04 6.60E-02 2.34E-05 5.81E-02 1.34E-04 5.78E-02 2.11E-05 5.87E-02 1.35E-04 5.84E-02 2.23E-05
8.72E-03 7.67E-05 8.61E-03 1.31E-05 9.19E-03 7.59E-05 9.12E-03 1.80E-05 7.88E-03 7.15E-05 7.81E-03 1.51E-05 7.66E-03 7.13E-05 7.59E-03 1.50E-05 5.19E-02 1.09E-04 5.16E-02 1.26E-05 6.41E-02 1.37E-04 6.39E-02 2.34E-05 5.64E-02 1.34E-04 5.62E-02 2.11E-05 5.70E-02 1.35E-04 5.68E-02 2.23E-05
6.31 E+00 5.52E-02 6.22 E+00 9.47E-03 6.64 E+00 5.46E-02 6.59 E+00 1.29E-02 5.70 E+00 5.15E-02 5.65 E+00 1.08E-02 5.53 E+00 5.14E-02 5.48 E+00 1.08E-02 2.45 E+02 4.99E-01 2.43 E+02 5.78E-02 3.04 + E02 6.30E-01 3.03 E+02 1.07E-01 2.67 E+02 6.13E-01 2.66 E+02 9.71E-02 2.69 E+02 6.19E-01 2.68 E+02 1.02E-01
9.98E-01 5.37E-02 9.98E-01 9.42E-03 9.99E-01 5.32E-02 9.99E-01 1.29E-02 9.97E-01 5.02E-02 9.96E-01 1.08E-02 9.96E-01 5.01E-02 9.96E-01 1.08E-02 1.00 E+00 3.93E-01 1.00 E+00 5.62E-02 1.00 E+00 4.68E-01 1.00 E+00 1.02E-01 1.00 E+00 4.58E-01 1.00 E+00 9.25E-02 1.00 E+00 4.62E-01 1.00 E+00 9.73E-02
MIT1
MIT2
SpaceX
Box-Wing
MIT1
Sphere
BAU
MIT1
MIT2
1016/j.actaastro.2016.03.034 https://doi.org/10.1016/j.actaastro.2016.03.034. [10] H.G. Lewis, J. Radtke, A. Rossi, J. Beck, M. Oswald, P. Anderson, B. Bastida Virgili, H. Krag, Sensitivity of the space debris environment to large constellations and small satellites, JBIS - Journal of the British Interplanetary Society 70 (2–4) (2017) 105–117. [11] J. Radtke, C. Kebschull, E. Stoll, Interactions of the space debris environment with mega constellations - using the example of the OneWeb constellation, Acta Astronaut. 131 (May 2016) (2017) 55–68, http://dx.doi.org/10.1016/j.actaastro. 2016.11.021 https://doi.org/10.1016/j.actaastro.2016.11.021. [12] R.J. Barnett, OneWeb Non-geostationary Satellite System: Technical Information to Supplement Schedule S - Attachment to FCC Application SAT-LOI-2016042800041, (2016). [13] Space Exploration Holdings, SpaceX Non-geostationary Satellite System Attachment to FCC Application SAT-LOA-20161115-00118, (2016). [14] J. Garrity, C. Lasalle, R. Pepper, A. Salem Al Ruwais, H. Johnson, R. Möller, K. Wallstedt, E. Weidman-Grunewald, J. Emery-Jones, C. Roisse, E. Schnitzler, F. Alves, B. Barlett, K. Martin, B. Moore, The State of Broadband 2016: Broadband Catalyzing Sustainable Development, Broadband Commission for Sustainable Development, International Telecommunication Union, Geneva, Switzerland, 2016. [15] H. Klinkrad, Space Debris, John Wiley & Sons, Ltd, 2010, http://dx.doi.org/10. 1002/9780470686652.eae325 https://doi.org/10.1002/9780470686652.eae325. [16] FCC, Order and Declaratory Ruling, (2017) IBFS File No. SAT-LOI20160428–00041. [17] A. Pai, M.L. Clyburn, M. O'Rielly, B. Carr, Update to parts 2 and 25 concerning nongeostationary, fixed-satellite service systems and related matters, https://apps.fcc. gov/edocs_public/attachmatch/FCC-17-122A1.pdf, (2017). [18] OneWeb, OneWeb Announces $1.2 billion in funded capital from SoftBank group and other investors, http://oneweb.net/press-releases/2016/oneweb-announces-1. 2-billion-in-funded-capital-from-softbank-group, (2016).
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Space debris collision probability analysis for proposed global broadband constellations
T
S. Le Maya,b,∗, S. Gehlya,b,1, B.A. Carterb, S. Flegela,b a b
SERC Limited, Mount Stromlo, Canberra, Australia SPACE Research Centre, RMIT University, Melbourne, Australia
A R T I C LE I N FO
A B S T R A C T
Keywords: Satellite constellation Collision probability MASTER-2009
Fragmentation events, caused by the collision of two objects in space, have been a significant source of space debris objects over a cumulative five decades of space activity. Current proposals by different commercial entities aim to launch constellations comprising thousands of satellites in Low Earth Orbit (LEO), which would result in an increase of more than five times the number of currently active satellites in a region where debris objects are most concentrated. The Inter-Agency Space Debris Coordination Committee (IADC) has already recognized the potential influence of large constellations on the LEO environment and the subsequent need to assess whether current mitigation guidelines will be adequate moving forward. Given developments for such constellations are already underway, independent research efforts ahead of any revision to current IADC guidelines could be of great value not only to the organizations involved in their operation, but also to policymakers and existing space users. This paper evaluates the probability of collisions for mega-constellations operating in the current LEO debris environment under best and worst-case implementation of current mitigation guidelines. Simulation studies are performed using the European Space Agency's (ESA) MASTER-2009 debris evolutionary model, and the specifications of the proposed OneWeb and SpaceX constellations as example mega-constellations. Multiple scenarios are then tested to assess mitigation measures and their ability to minimize the probability of fragmentation events and the creation of new debris in LEO.
1. Introduction
Outer Space (UNCOPUOS) is the central organization tasked with the development of international debris mitigation guidelines, their policies are not legally binding. In order to be effective, their recommendations must be incorporated into rules and regulations established at a national government level. As the space economy continues to develop rapidly, it is imperative that governments ensure that regulatory policies keep pace with the expanding space capabilities within the private sector [8]. Global broadband internet delivered via Non-Geostationary Satellite Orbit (NGSO) is the next emerging capability within the commercial space sector, a service which requires constellations comprising thousands of satellites in LEO. In response to this development, recent literature has investigated the potential risk associated with operating large constellations within the space debris environment. Using simulations, researchers have considered the implications of different post-mission disposal (PMD) strategies and rates of PMD success [9], variations to constellation parameters [10], “self-induced” collision probabilities [10,11], and estimates of the number of collision avoidance manoeuvres required during operations [11]. As of writing,
Space debris objects pose a substantial threat to the vast network of space infrastructure upon which society is dependant for a range of services including navigation, communication, Earth observation, security and military operations. Given the number of space launches to date, the amount of space debris in orbit, and the expected number of launches planned for the near future, it is reasonable to question the ongoing sustainability of the orbital environment for space operations. The notion that a chain of collisions between debris objects (Kessler Syndrome) could result in low Earth orbit (LEO) becoming unusable, and remaining in an unusable state for perhaps thousands of years, is a concern emphasized by many researchers [e.g. Refs. [1–5]]. There have been at least 4 reported accidental hyper-velocity collision events in LEO, one of which (the collision of Iridium 33 and Cosmos 2251) contributed 2296 catalogued objects to the debris population and hundreds of thousands of un-trackable objects less than 10 cm in size [6,7]. Although the United Nation's Committee on the Peaceful Uses of
∗
1
Corresponding author. SPACE Research Centre, RMIT University, Melbourne, Australia E-mail addresses: [email protected] (S. Le May), [email protected] (S. Gehly), [email protected] (B.A. Carter), svenfl[email protected] (S. Flegel). Now at: UNSW, Canberra, Australia.
https://doi.org/10.1016/j.actaastro.2018.06.036 Received 28 February 2018; Received in revised form 11 June 2018; Accepted 14 June 2018 Available online 19 June 2018 0094-5765/ © 2018 IAA. Published by Elsevier Ltd. All rights reserved.
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Fig. 2. MASTER-2009 output for spatial density of debris objects larger than 3 mm versus altitude for 4 September 2017.
It is also apparent that the majority of tracked objects at these altitudes are debris, not payloads, therefore there is a greater degree of uncertainty regarding their orbits. The catalogued population is based on observational data, which typically limits the catalogue to debris objects with diameters greater than 10 cm [15]. While OneWeb and SpaceX will operate in less populated regions, the spiral up and disposal phase of their missions will pass through more densely populated regions across 800 km, and will experience an increasing debris flux. However, given that the probability of collision is highest during the operational phase, due to longer residency times [11], the analysis presented in this study focuses on the 5 year operational phase of these constellations. Fig. 2 shows the MASTER-2009 spatial density output for 4 September 2017 obtained under the business as usual future scenario for debris objects larger than 3 mm. Here it is shown that explosion fragments, collision fragments and solid rocket motor (SRM) slag are the most significant contributors to the populations at the operational altitudes proposed by OneWeb and SpaceX.
Fig. 1. Number of catalogued objects in LEO (<2500 km) with proposed operational apogee altitudes for OneWeb (green) and SpaceX (blue). Data from www.space-track.org, retrieved 4 September, 2017. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
specific policies and regulations do not exist to ensure the sustainable operation of these large constellations, yet according to licensing applications made with the Federal Communications Commission (FCC), companies such as OneWeb and SpaceX have ambitions to commence launching in the near future [12,13]. Using the SpaceX and OneWeb constellations as examples, this study uses ESA's MASTER-2009 model to evaluate the collision probability associated with large satellite constellations with future projections of the debris environment, and investigates ways in which the constellation design may be altered to reduce the probability of collision. This paper is organized as follows. Section 2 provides an overview of NGSO constellations, including rationale for their deployment and technical parameters of the constellations used in this study. Section 3 provides a description of the methods used for the collision analysis, including an overview of ESA's MASTER-2009 model. Section 4 presents the results for collision probabilities associated with both the OneWeb and SpaceX constellations, and further analyses consider the impact of the constellation parameters and long-term impact of satellites which fail to perform a de-orbit manoeuvre. Closing remarks and topics for future research are provided in Section 5.
2.1. OneWeb On 22 June, 2017, OneWeb LLC (formerly WorldVu Satellites Limited) were granted access by the FCC to the US market using their proposed NGSO Fixed Satellite Service (FSS) system.2 Along with other conditions documented in the Order and Declaratory Ruling [ [16]], the FCC requires that 50% of the authorized NGSO-FSS system is launched and operational within six years of receiving authorization [17]. In December 2016, OneWeb reported their intention to launch 10 test satellites in early 2018 and, after detailed testing, the remaining 710 satellites six months later [12]. This study assumes previously reported targets by OneWeb to have their 720-satellite constellation operational from 2018 [18] which may no longer be accurate, however any delays are not expected to have a significant impact on the results presented here. Tables 1 and 2 detail the orbital and physical parameters of OneWeb's constellation satellites used for the purpose of this study.
2. Technical parameters of NGSO constellations Non-geostationary satellite orbit systems aim to provide low-latency, high-speed and high-capacity internet connectivity with global coverage to surpass the terrestrial equivalent in broadband internet services [14]. OneWeb, SpaceX and others have already put forward proposals to launch hundreds to thousands of satellites to provide global broadband internet services via new NGSO systems. The parameters of the OneWeb and SpaceX constellations used in this study have originated from the technical attachments provided by each of the respective operators' application to the FCC for operating authority within the United States [12,13]. Common to both applications are their proposed operational lifetime of five years, and selection of LEO altitudes. OneWeb has proposed to deploy their constellation at 1200 km while the SpaceX constellation makes use of multiple orbit altitudes on either side at 1100 km, 1130 km, 1150 km, 1275 km, and 1325 km. Fig. 1 shows the number of publicly catalogued objects in LEO, as of 4 September 2017, and the proposed operating altitudes for both constellations. It can be seen here that both operators have selected altitudes with relatively low populations of debris objects and payloads compared to other LEO regions, for example around 800 km.
2.2. SpaceX The application submitted to the FCC by Space Exploration Holdings (SpaceX) proposes the launch of 4425 satellites with 166 in-orbit spares operating in 83 orbital planes [13]. Tables 3 and 4 summarize the orbital configuration and physical parameters of the SpaceX constellation satellites used for this study, as provided by SpaceX in the technical 2 Since receiving authority for their 720-satellite NGSO-FSS system (used in the analysis presented in this paper), OneWeb has proposed to expand its constellation to 1980 satellites in a separate application to the FCC. The reader can estimate the mean number of expected collisions of the enlarged constellation by multiplying the fluence on a single satellite given in Table A.5 by the appropriate number.
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Table 1 OneWeb constellation parameters. Parameter
Final Deployment
Total Satellites Orbital Planes Satellites per Plane Altitude (km) Inclination (deg)
720 18 40 1200 87.9
Table 2 OneWeb satellite parameters.*Average derived using CROC from ESA's DRAMA 2.0 tool suite. Satellite Body Length (m) Width (m) Height (m) [0.5em] Solar Arrays Length (m) Width (m) Quantity [0.5em] Overall Mass (kg) Average cross-sectional area* (m2) Equivalent radius (m)
1.0 1.0 1.0 1.12 1.0 2
Fig. 3. Idealized sphere model showing approximate relative size for OneWeb spacecraft (green) and SpaceX spacecraft (blue). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
150 2.35 0.93
3. Methodology Table 3 SpaceX satellite parameters. *Average derived using CROC from ESA's DRAMA 2.0 tool suite.
Following the work of Radtke et al. [11], this paper presents an extension of the methods to derive a probability of collision P from the debris flux F on the combined cross-sectional area ( Ac ) of a spacecraft and the debris impactor. The basic terms and methods from Radtke et al. [11] are defined in Section 3.1 before introducing the extended method in Sections 3.2 and 3.3. The extended method includes the classification of collisions by energy and trackability, and uses a ‘boxwing’ approach to estimate the spacecraft geometry instead of considering the target spacecraft as a sphere.
Satellite Body Length (m) Width (m) Height (m) [0.5em] Solar Arrays Length (m) Width (m) Quantity [0.5em] Overall Mass (kg) Average cross-sectional area* (m2) Equivalent radius (m)
4.0 1.8 1.2 6.0 2.0 2
3.1. Collision analysis method (sphere approach) 386 17.99 2.39
Flux, per square meter per annum, is obtained using ESA's MASTER2009 model. The mean number of collisions for the target satellite, Nsat , can be determined as a product of F, Ac , and the operational lifetime of the mission T;
Nsat = F ⋅Ac ⋅T
Table 4 SpaceX constellation parameters. Parameter
Initial Deployment
Final Deployment
Total Satellites Orbital Planes Satellites per Plane Spares per Plane Altitude (km) Inclination (deg)
1664 32 50 2 1150 53
1664 32 50 2 1110 53.8
416 8 50 2 1130 74
385 5 75 2 1275 81
(1)
The calculation of Ac depends on the shape of the surface being analyzed. In Radtke et al. [11], the surface of the spacecraft has been estimated as an idealized sphere (Fig. 3), therefore Ac is determined by the radius of the target spacecraft (rtar ) and the impacting debris object (rimp ).
462 6 75 2 1325 70
Ac = π (rtar + rimp)2
(2)
The probability of the spacecraft being involved in at least one collision (P≥ 1sat ) can then be determined using Poisson statistics, further described in Radtke et al. [11] and Klinkrad [15];
P≥ 1sat = 1 − e−Nsat
attachment of their FCC application [13]. SpaceX CEO, Elon Musk, announced the launch of two test satellites for their global broadband constellation on 22 February, 2018. One month later, on 29 March, 2018, the FCC granted authority for the launch and operation of their NGSO constellation [19]. Conditions of the grant are detailed in the Memorandum Opinion, Order and Authorization, and include standard requirements to comply with current and future orbital debris mitigation policies.
(3)
Results for the total constellation (Nconst and P≥ 1const ) are determined through multiplying by the total number of satellites in each deployment, and in the case of multiple deployments, summing their totals;
Nconst = F ⋅Ac ⋅T ⋅Σ
(4)
P≥ 1const = 1 − e−Nconst
(5)
where Σ is the total number of satellites in the constellation. 447
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Fig. 5. Flux versus debris impact velocity and impactor diameter for objects ≥3 mm on the OneWeb target orbit, output from MASTER-2009 under intermediate mitigation scenario. Red line indicates trackable object threshold of 10 cm. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Fig. 4. Flux versus debris impact velocity and debris impactor mass for objects ≥3 mm on the OneWeb target orbit, output from MASTER-2009 under intermediate mitigation scenario. Lines in white, from bottom to top, indicate thresholds for collisions with EMR equal to 10 kJ/kg, 100 kJ/kg and 1000 kJ/ kg, as defined by equation (6). Line in red indicates EMR equal to 40 kJ/kg, the selected critical threshold for catastrophic collisions. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
The MASTER-2009 simulations have been run under three different future scenarios that assume different levels of orbital debris mitigation measures: 1. Business-as-usual (BAU), where no mitigation measures are implemented; 2. Intermediate Mitigation (MIT1), where the release of mission-related objects are prevented and the generation of explosion fragments and solid rocket motor by-products are reduced; and 3. Full Mitigation (MIT2), which further assumes 100% successful deorbit of rocket bodies and payloads within 25 years.
Fig. 6. Simplified box-wing model showing relative size for OneWeb spacecraft (green) and SpaceX spacecraft (blue). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
minimum diameter of 10 cm are actively tracked and maintained in the current version of the Joint Space Operations Center (JSpOC) catalogue [22]. With this in mind, the new method proposes three separate classifications for collisions:
Further technical detail of the debris sources, mitigation scenarios, and models implemented by the software are given in the MASTER2009 maintenance report [20].
1. Catastrophic collisions, where EMR ≥ 40,000J/kg [21]. 2. Non-trackable collisions, where rimp < 5cm ; and 3. Catastrophic, non-trackable collisions, where both conditions of (1) and (2) apply.
3.2. Collision classification In this study, the method from Radtke et al. [11] has been extended with the aim of using additional post-processing steps to uncover greater meaning from the available MASTER-2009 dataset. It is possible to extract the relative velocity (vrel ) and mass of the debris object (Mimp ) from the MASTER-2009 output, which allows the calculation of the energy-to-mass ratio (EMR) of the predicted collision, where Mtar is the mass of the target satellite;
EMR =
In this way, the analysis is not limited to simply the probability of at least one collision involving a spacecraft, and is extended to specifically whether the collision has potential to be catastrophic. This distinction is important as a catastrophic collision is expected to result in the complete destruction of a spacecraft and, subsequently, the creation of a debris cloud. This study assumes that any impact on the spacecraft's solar panels will not result in complete destruction, hence any debris flux on the solar panels (or equivalent average area) has not been classified as catastrophic. Furthermore, identifying whether collisions involve non-trackable debris objects indicates which fraction of catastrophic collisions are effectively unavoidable. Fig. 5 shows the MASTER-2009 output for flux, diameter and impact velocity of debris objects less than 20 cm diameter using the OneWeb target orbit parameters. Not shown on this chart are objects smaller than 3 mm diameter which contribute the largest flux, totalling 197 per m2 per annum. Spacecraft are equipped with shielding to prevent damage from very small debris, but detailed information for the shielding used by the OneWeb and SpaceX constellations are not publicly available. Based on past research on the efficacy of spacecraft shielding
Mimp v 2rel 2Mtar
(6)
Collisions with EMR ≥ 40,000J/kg are considered to be catastrophic [21], having enough energy to completely destroy a spacecraft. Fig. 4 shows that despite the highest flux being concentrated around debris objects with low masses, due to very high impact velocities (around 14 km/s) a large proportion exceed the catastrophic EMR threshold. The MASTER-2009 output also provides the diameter of the debris object, such that collision events can be classified as trackable if the impactor diameter is greater than 10 cm (rimp > 5cm ) or non-trackable (rimp < 5cm ). Although there may exist the capability to detect debris objects with diameters smaller than 10 cm, only objects with a
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Fig. 7. Mean number of collisions (Nconst ) with debris objects ≥3 mm for OneWeb and SpaceX constellations under business-as-usual (BAU), intermediate mitigation (MIT1) and full mitigation (MIT2) scenarios. Study uses the sphere approach for the 5-year operational phase of the mission. Results for Nsat (single satellite) are given in Table A.5.
comparison in Section 4.1, while analyses in Sections 4.2–4.4 use the sphere-approximation of the spacecraft's surface, where Ac is determined by Equation (2).
against high impact velocity debris, it has been assumed that minimal spacecraft shielding will be adequate to mitigate any risk from objects smaller than 3 mm [23]. For this reason, a minimum size threshold of 3 mm has been selected for this study. Objects ranging 3 mm to 10 cm also make a significant contribution to the flux and those with high impact velocity may result in component damage and possible loss of spacecraft capability [24,25]. The ≥ 3mm MASTER-2009 future populations include debris from ejecta, solid rocket motor slag, sodium potassium droplets, explosion fragments and collision fragments [26], all of which have been included as sources in the simulations for this study.
4.1. N & P during operational phase Figs. 7 and 8 show the results of the sphere-study that compares Nconst (mean number of collisions) and P≥ 1const (probability of at least one collision) of different classes of collisions under different mitigation scenarios for both the OneWeb and SpaceX constellations. It is important to evaluate both Nconst and P≥ 1const concurrently as a value for P≥ 1const close to 1 considered independently will not give an indication of the total mean number of collisions projected (i.e. P≥ 1const ≃ 1 for both cases of Nconst ∼ 5 and Nconst ∼ 300 ). Overall, the mean number of total collisions projected in each scenario is substantially higher for the SpaceX constellation compared to OneWeb (Fig. 7). Despite this large difference in Nconst (Total) between the two constellations, Pconst (Total) indicates a high probability of at least one collision during the operational phase for both constellations. Across all scenarios, of particular concern are the probabilities for the occurrence of at least one catastrophic collision (BAU , P≥ 1const = 0.468) and at least one catastrophic, non-trackable collision (BAU , P≥ 1const = 0.103) in the SpaceX constellation, both are much higher than the respective results for the OneWeb constellation (BAU, P≥ 1const = 0.053 and 0.013).
3.3. Box-wing approach This study also takes advantage of the ‘oriented surface’ functionality provided by the MASTER-2009 model which supports an independent flux analysis for a single oriented surface along the trajectory of the target orbit. Using this option, it is possible to perform an approximate analysis on each of the spacecraft's eight panels (including body and solar panels), by defining their orientation based on a simplified box-wing model (Fig. 6). The spacecraft body panels are oriented relative to the Earth, to maintain a fixed nadir-pointing as in operations, while the solar panels are oriented relative to the Sun. Calculation of Ac for a rectangular panel is determined by the length (L) and width (W) of the panel, and rimp ; 2 Ac = LW + πrimp + 2rimp W + 2rimp L
(7) 4.1.1. Future scenario comparison Implementation of intermediate and full mitigation compared to a business-as-usual case (Fig. 7) reduces the projected total mean number of collisions for the SpaceX constellation by around 12%. Here, Nconst (Total) equals 304 for a business-as-usual scenario compared to 267 and 269 under the intermediate and full mitigation regimes (Fig. 7), with the slight difference between the results for mitigation scenarios being due to the statistical model underlying MASTER. Although implementing mitigation measures gives a slightly favourable outcome for both Nconst (Total) and Nconst (Non − trackable ) , it is less effective for reducing the mean number of catastrophic collisions where the improvement is less than 1% in both mitigation scenarios. With regard to the effectiveness of debris mitigation, there appears to be no significant difference in the probability results from the business-asusual scenario compared to either the intermediate or full mitigation studies for both constellations. These results can be explained by the conditions built in to the intermediate and full mitigation scenarios of the MASTER-2009 model, which implement steady reductions of debris creation from 2020 onwards [26]. Given that the operational phase
This equation is correct as it is for normal impacts. Proper incorporation of off-normal impacts requires the direction of impact relative to the rectangular panel defined through W and L. As the surface impact angle output from MASTER-2009 is given only with respect to the normal vector of the oriented surface this is not possible. As an approximation, the combined cross-sectional area Ac as per Equation (7) is multiplied with each particle's flux contribution to compute Nsat analogously to the spherically approximated spacecraft geometry, but reduced by the surface slant angle. 4. Results and discussion This section presents the results and discussion for the expected mean number of collisions and associated collision probabilities for the SpaceX and OneWeb constellations (Nconst and P≥ 1const ) during their operational phase of five years. Results for single satellite (Nsat and P≥ 1sat ) are not discussed here, but have been included for reference in Appendix A. The results of the box-wing studies are given for
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Fig. 8. Probability of at least one collision (P≥ 1const ) for the constellation with debris objects ≥3 mm for OneWeb and SpaceX under business-as-usual (BAU), intermediate mitigation (MIT1) and full mitigation (MIT2) scenarios. Study uses the sphere approach for the 5-year operational phase of the mission. Results for P≥ 1sat (single satellite) are given in Table A.5.
begins in 2018 for five years, most of the operational phase falls outside of the time period where mitigation scenarios are expected to show some improvement. Longer timescales considering the intermediate mitigation scenario are presented in Section 4.4 where a long-term analysis of failed satellites remaining on orbit are considered. Overall, it can be seen that the implementation of mitigation measures has less influence on the results for the OneWeb constellation compared to SpaceX, which implies that with trends toward much larger NGSO constellations, the level of compliance to mitigation policies may become increasingly significant. The full set of results across different mitigation levels and spacecraft models are provided in Appendix A. 4.1.2. Non-trackable collisions While the concern related to catastrophic collisions is due to their potential to generate a debris cloud from the total destruction of the satellite, the high Nconst and P≥ 1const results for non-catastrophic collisions are still reason for concern, as they give an indication of the exposure of constellation satellites to collisions with potential to disable their capabilities, such as communications and manoeuvrability. With regard to Nconst (Non − trackable ) and P≥ 1const (Non − trackable ) , these results are indicative of the impact of collisions that not only have the potential to be disabling, but are also unavoidable given current sensor limitations. Any collision resulting in a disabled satellite will effectively convert the active satellite into a large, high-velocity debris object in the densely populated constellation orbit regime. Such objects may become the source of cascading collisions within the remaining constellation, a concept explored further in Section 4.4. Although Nconst (Non − trackable ) is much higher for SpaceX than it is for OneWeb (Fig. 7), in the absence of a comparison to SpaceX results the projected Nconst with non-trackable objects for the OneWeb constellation (Nconst (Non − trackable ) = 5.48 under full mitigation scenario) is still reason for concern. With regards to probability, Fig. 8 shows that the probability for at least one collision with a non-trackable object is high for both OneWeb (P≥ 1const (Non − trackable ) = 0.996) and SpaceX (P≥ 1const (Non − trackable ) = 1.000 ). 4.1.3. Box-wing analysis Using the box-wing model results in an overall increase of Nconst and P≥ 1const for OneWeb, and an overall decrease for SpaceX (Fig. 9). Compared to the intermediate mitigation scenario results from the sphere study, Nconst (Total) for the SpaceX constellation is reduced by 9%–245. Conversely, Nconst (Total) for OneWeb is increased by 10% to 6.31. In all other categories, use of the box-wing model has less of an impact on the
Fig. 9. Mean number of collisions (Nconst ) and probability of at least one collision (P≥ 1const ) with debris objects ≥3 mm for OneWeb and SpaceX constellations under the intermediate mitigation scenario. Study uses the box-wing approach for the 5-year operational phase of the mission. Results for P≥ 1sat and Nsat (single satellite) are given in Table A.5.
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Fig. 10. Nconst and P≥ 1const versus EMR for debris objects ≥3 mm for the OneWeb constellation, under the intermediate mitigation scenario. Study uses the sphere approach for the 5-year operational phase of the mission.
Fig. 11. Nconst and P≥ 1const versus EMR for debris objects ≥3 mm for the SpaceX constellation, under the intermediate mitigation scenario. Study uses the sphere approach for the 5-year operational phase of the mission.
results. The changes in the total and non-trackable probabilities are less significant, with P≥ 1const still close to 1 for OneWeb (P≥ 1const (Total) = 0.997 in the sphere study compared to 0.998 in the box-wing study) and equal to 1 for SpaceX. Interestingly, there is a slight increase in Nconst and P≥ 1const for catastrophic collisions in the OneWeb constellation, with a mean of 0.055 catastrophic collisions forecast for the OneWeb constellation using the box-wing configuration compared to the result of 0.051 in the sphere study, likely attributed to statistical noise. Although the box-wing model is still simplistic, it has been shown that by moving toward a more realistic representation of the shape of the spacecraft the results can differ by ±10%. The question of the statistical significance of these differences, however, still requires further investigation. The following sections refer to results that assume the sphere-configuration and intermediate mitigation scenario, with the understanding that these assumptions can lead to different results compared against the business-as-usual or box-wing models.
draw assertions. In fact, three out of four accidental collisions that have occurred since 1990 had negligible impact on the debris environment despite exceeding this assumed threshold [5]. Figs. 10 and 11 have been prepared to investigate the distribution of Nconst and P≥ 1const across different EMR values. For both OneWeb (Fig. 10) and SpaceX (Fig. 11), selecting a critical EMR threshold above 40 kJ/kg would not significantly change the results presented in previous sections. The only significant change would result from classifying an impact with EMR of 0–5 kJ/kg as catastrophic (not shown in Figs. 10 and 11 as Nconst is higher in this category by an order of magnitude); however this would be unlikely, especially when taking into consideration that 3 of the previous 4 accidental collisions collectively contributed only 9 new debris objects to the catalog despite exceeding the generally accepted catastrophic EMR threshold of 40 kJ/kg [5]. 4.3. Effect of constellation parameters on N The results presented in Section 4.1 showed that overall the mean number of collisions projected for the OneWeb constellation are much less than for the SpaceX constellation. Comparing the parameters of both constellations, the most likely explanation for this is due to the compounding effects of both increased size of the SpaceX spacecraft
4.2. Sensitivity to EMR threshold Although an EMR of 40 kJ/kg is widely applied as the threshold for catastrophic collisions as a result of past experiments [21], the number of observed on-orbit collisions is relatively small, making it difficult to
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Fig. 12. Mean number of collisions (Nconst ) for debris objects ≥3 mm, using varied parameters of number of satellites and target radius (rtar ) in the SpaceX constellation. The sphere approach and the intermediate mitigation scenario are applied during the operational phase of 5 years. Green and blue lines indicate the proposed parameters of the OneWeb and SpaceX constellations, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Fig. 13. Mean number of collisions (Nconst ) over time for OneWeb and SpaceX constellations given an assumed percentage of constellation satellites remaining on orbit beyond operational phase due to failure. Study uses sphere approach data-set with intermediate mitigation scenario and debris objects ≥3 mm.
4.4. Long-term analysis for failed satellites
(Table 3), and increased number of satellites within the SpaceX constellation (Table 4). Fig. 12 shows that increasing the target radius of the SpaceX constellation satellites (corresponding to increased Ac per Equation (2)) results in a quadratic increase in Nconst , mean number of collisions, while increasing the number of satellites in the SpaceX constellation corresponds to a linear increase in Nconst . If SpaceX were to reduce the size of their spacecraft to a target radius equal to OneWeb's of 0.86 m, the resulting Nconst would be 36.2, which although is a substantial reduction compared to the existing results (Nconst (Total) = 267), is still more than six times greater than the OneWeb Nconst (Total) of 5.7. By keeping the same physical dimensions, but instead reducing the total number of constellation satellites to match OneWeb's total (720), Nconst (Total) for SpaceX is reduced to 41.8. The nature of FCC applications are such that operators will have applied for approval based on maximum proposed physical dimensions of their spacecraft design, therefore deviation from proposed physical dimensions to smaller dimensions are likely. Based on the results of this study, a reduction in the physical dimensions of the spacecraft resulting in a reduced cross-sectional area yields a marginally better outcome than reducing the number of satellites in the constellation.
Although Nconst (Catastrophic ) is seemingly low for both constellations (Fig. 7), both Nconst (Non − trackable ) and P≥ 1const (Non − trackable ) are very high for SpaceX (and also high for OneWeb), and therefore the potential for disabled satellites is also high. Assuming a disabled satellite is not able to perform a deorbit manoeuvre, a longer stay in orbit may entail a consequent growth of the mean number of catastrophic collisions (Equation (1)). Figs. 13 and 14 show Nconst over time for an assumed percentage (1%, 5% and 10%) of satellites within the constellation that fail to deorbit from their operational altitude. This analysis uses the annual average for a single satellite under the intermediate mitigation scenario (Nsat divided by 5) to determine Nconst (Equation (4)), for T = 0 − 50 years, where the number of failed satellites is equal to a percentage of the total constellation. The analysis does not account for any variation in the background debris flux or future launch activity, and therefore likely gives an optimistic estimate of the expected number of collisions. Assuming a worst-case scenario with a failure rate of 10%, the total mean number of collisions expected in 50 years are ∼ 35 for OneWeb and ∼ 250 for SpaceX (Fig. 13). Of these collisions, a mean of less than 1 are predicted to be catastrophic.
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MASTER-2009 model does have limitations, including no quantified uncertainty associated with the flux output. The results of this study represent the mean collisional behaviour of the system, and are not strictly a prediction of the future. When the collision probability is derived from discrete random particles, the chance of having an accurate result increases with sample size and probability of collision. Both of these are higher for the SpaceX constellation compared with the OneWeb constellation. The differences observed between the results for the sphere and box-wing for the Total results for SpaceX thus have the highest chance of not being due to statistical noise. In statistics, the likelihood for the difference between two results being due to statistical noise is called statistical significance [28]. Similarly, for both constellations the results for Nconst (Total) and Nconst (Non − Trackable ) may have greater statistical significance than Nconst (Catastrophic ) and Nconst (Catastrophic, Non − trackable ) as the flux is derived from a larger number of particles. Quantifying statistical significance in this context would require a more robust statistical analysis, recommended for future work. OneWeb's Orbital Debris Mitigation Plan reports that the probability of a OneWeb satellite becoming disabled as a result of collisions with small debris is 0.003, as computed using NASA's ORDEM3 model and taking the minimum hazardous debris size as 1 cm. In comparison, this study used ESA's MASTER model and a minimum size threshold of 3 mm to determine the probability of collision for a single OneWeb satellite. The resulting probability is around 0.008 (Table A.5), a value which aligns well with OneWeb's own study. In response to the FCC's request to provide an analysis of collision risk, SpaceX reported that there is “approximately a 1% chance per decade that any failed SpaceX satellite would collide with a piece of tracked debris”.3 Although this specific case wasn't explored in Section 4.4, our analysis for the probability of collision of one failed satellite with trackable debris (not shown here) agrees with this statement. However, it does not take into account the collision probabilities associated with non-trackable objects, determined to be P≥ 1sat = 0.124 after 10 years using the sphere model. The results of this study show that implementation of the mitigation measures in MASTER did not significantly reduce the probability of at least one collision during the five year operational phase of either the OneWeb or SpaceX constellation. The MASTER-2009 model's intermediate and full mitigation scenarios implement steady reductions of debris creation from 2020 onwards and therefore have very little impact on the first generation of the OneWeb and SpaceX constellations which cease operation in 2023. Additional measures may be required to ensure the safe and sustainable operation of such constellations, including but not limited to reducing the size and number of satellites launched. Due to imminent launch dates and because of the potential value such constellations have for the global community, in particular developing economies, the question of how to ensure safe and sustainable operations alongside constellations of this scale still needs to be addressed.
Fig. 14. Mean number of catastrophic collisions (Nconst (Catastrophic ) ) over time for OneWeb and SpaceX constellations given an assumed percentage of constellation satellites remaining on orbit beyond operational phase due to failure. Study uses sphere approach data-set with intermediate mitigation scenario and debris objects ≥3 mm.
Although this work only investigates the projected mean number of collisions between failed satellites and debris, because the intention of both operators is to replenish their constellations at the same altitude [12,13], failed satellites have the potential to initiate accidental collisions with future generations of the constellation. High velocity collisions involving two intact spacecraft from two different orbital planes will generate two debris clouds. Assuming similar altitudes of both orbital planes, as is the case in both the OneWeb and SpaceX constellation parameters (Tables 1 and 4), work by Radtke et al. [11] shows the respective debris clouds will increase the collision risk of all spacecraft in the affected orbit altitude. For this reason, a high PostMission Disposal (PMD) success rate is desirable at altitudes where atmospheric drag is low or non-existent, where in the absence of active disposal, spacecraft will remain indefinitely [27].
Acknowledgements The authors extend their thanks to Christopher Kebschull (Institute of Space Systems, TU Braunschweig) who provided valuable insight, expertise and feedback that assisted in this research project. The authors would also like to acknowledge the support of the Cooperative Research Centre for Space Environment Management (SERC Limited) through the Australian Governments Cooperative Research Centre Programme. This research was also supported by the Australian Research Council Linkage grant (project LP160100561) awarded to BAC.
5. Summary and conclusion The results of this study indicate a high probability for the occurrence of at least one collision for both the proposed OneWeb and SpaceX constellations during an operational phase of 5 years. It was found that the probability of there being at least one catastrophic collision involving a spacecraft within the OneWeb constellation is 5.0%, and for SpaceX much higher at 45.8%. It must be noted that the
3
In correspondence from William M. Wiltshire (Counsel to SpaceX) to Jose P. Albuquerque, IBFS File No. SAT-LOA-20161115-00118 (April 20, 2017).
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Appendix A. Table of results Table A.5 Summary of results for N and P≥ 1 for a single satellite (sat) and accross the whole constellation (const) for the OneWeb (720 satellites) and SpaceX (4591 satellites) constellations. Mitigation Scenarios include Business-as-Usual (BAU), Intermediate Mitigation (MIT1) and Full Mitigation (MIT2). Classes of collisions include catastrophic, where EMR ≥ 40kJ / kg , and non-trackable, where rimp < 5cm . Constellation
Surface
Scenario
Class
Nsat
P≥ 1, sat
Nconst
Pconst
OneWeb
Box-Wing
MIT1
Sphere
BAU
Total Catastrophic Non-trackable Catastrophic, Non-trackable Total Catastrophic Non-trackable Catastrophic, Non-trackable Total Catastrophic Non-trackable Catastrophic, Non-trackable Total Catastrophic Non-trackable Catastrophic, Non-trackable Total Catastrophic Non-trackable Catastrophic, Non-trackable Total Catastrophic Non-trackable Catastrophic, Non-trackable Total Catastrophic Non-trackable Catastrophic, Non-trackable Total Catastrophic Non-trackable Catastrophic, Non-trackable
8.76E-03 7.67E-05 8.64E-03 1.31E-05 9.23E-03 7.59E-05 9.16E-03 1.80E-05 7.91E-03 7.15E-05 7.84E-03 1.51E-05 7.69E-03 7.13E-05 7.62E-03 1.50E-05 5.33E-02 1.09E-04 5.30E-02 1.26E-05 6.63E-02 1.37E-04 6.60E-02 2.34E-05 5.81E-02 1.34E-04 5.78E-02 2.11E-05 5.87E-02 1.35E-04 5.84E-02 2.23E-05
8.72E-03 7.67E-05 8.61E-03 1.31E-05 9.19E-03 7.59E-05 9.12E-03 1.80E-05 7.88E-03 7.15E-05 7.81E-03 1.51E-05 7.66E-03 7.13E-05 7.59E-03 1.50E-05 5.19E-02 1.09E-04 5.16E-02 1.26E-05 6.41E-02 1.37E-04 6.39E-02 2.34E-05 5.64E-02 1.34E-04 5.62E-02 2.11E-05 5.70E-02 1.35E-04 5.68E-02 2.23E-05
6.31 E+00 5.52E-02 6.22 E+00 9.47E-03 6.64 E+00 5.46E-02 6.59 E+00 1.29E-02 5.70 E+00 5.15E-02 5.65 E+00 1.08E-02 5.53 E+00 5.14E-02 5.48 E+00 1.08E-02 2.45 E+02 4.99E-01 2.43 E+02 5.78E-02 3.04 + E02 6.30E-01 3.03 E+02 1.07E-01 2.67 E+02 6.13E-01 2.66 E+02 9.71E-02 2.69 E+02 6.19E-01 2.68 E+02 1.02E-01
9.98E-01 5.37E-02 9.98E-01 9.42E-03 9.99E-01 5.32E-02 9.99E-01 1.29E-02 9.97E-01 5.02E-02 9.96E-01 1.08E-02 9.96E-01 5.01E-02 9.96E-01 1.08E-02 1.00 E+00 3.93E-01 1.00 E+00 5.62E-02 1.00 E+00 4.68E-01 1.00 E+00 1.02E-01 1.00 E+00 4.58E-01 1.00 E+00 9.25E-02 1.00 E+00 4.62E-01 1.00 E+00 9.73E-02
MIT1
MIT2
SpaceX
Box-Wing
MIT1
Sphere
BAU
MIT1
MIT2
1016/j.actaastro.2016.03.034 https://doi.org/10.1016/j.actaastro.2016.03.034. [10] H.G. Lewis, J. Radtke, A. Rossi, J. Beck, M. Oswald, P. Anderson, B. Bastida Virgili, H. Krag, Sensitivity of the space debris environment to large constellations and small satellites, JBIS - Journal of the British Interplanetary Society 70 (2–4) (2017) 105–117. [11] J. Radtke, C. Kebschull, E. Stoll, Interactions of the space debris environment with mega constellations - using the example of the OneWeb constellation, Acta Astronaut. 131 (May 2016) (2017) 55–68, http://dx.doi.org/10.1016/j.actaastro. 2016.11.021 https://doi.org/10.1016/j.actaastro.2016.11.021. [12] R.J. Barnett, OneWeb Non-geostationary Satellite System: Technical Information to Supplement Schedule S - Attachment to FCC Application SAT-LOI-2016042800041, (2016). [13] Space Exploration Holdings, SpaceX Non-geostationary Satellite System Attachment to FCC Application SAT-LOA-20161115-00118, (2016). [14] J. Garrity, C. Lasalle, R. Pepper, A. Salem Al Ruwais, H. Johnson, R. Möller, K. Wallstedt, E. Weidman-Grunewald, J. Emery-Jones, C. Roisse, E. Schnitzler, F. Alves, B. Barlett, K. Martin, B. Moore, The State of Broadband 2016: Broadband Catalyzing Sustainable Development, Broadband Commission for Sustainable Development, International Telecommunication Union, Geneva, Switzerland, 2016. [15] H. Klinkrad, Space Debris, John Wiley & Sons, Ltd, 2010, http://dx.doi.org/10. 1002/9780470686652.eae325 https://doi.org/10.1002/9780470686652.eae325. [16] FCC, Order and Declaratory Ruling, (2017) IBFS File No. SAT-LOI20160428–00041. [17] A. Pai, M.L. Clyburn, M. O'Rielly, B. Carr, Update to parts 2 and 25 concerning nongeostationary, fixed-satellite service systems and related matters, https://apps.fcc. gov/edocs_public/attachmatch/FCC-17-122A1.pdf, (2017). [18] OneWeb, OneWeb Announces $1.2 billion in funded capital from SoftBank group and other investors, http://oneweb.net/press-releases/2016/oneweb-announces-1. 2-billion-in-funded-capital-from-softbank-group, (2016).
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