Advances in Space Research 34 (2004) 969–974 www.elsevier.com/locate/asr
The sensitivity of the ESA DELTA model C. Martin a b
a,*
, R. Walker a, H. Klinkrad
b
Space Department, QinetiQ, Cody Technology Park, Ively Road, Farnborough, Hampshire GU14 0LX, UK European Space Operations Centre (ESA/ESOC), Robert-Bosch-Strasse, 5, D-64293, Darmstadt, Germany Received 19 October 2002; received in revised form 24 January 2003; accepted 4 February 2003
Abstract The debris environment long term analysis (DELTA) model, developed by QinetiQ for the European Space Agency (ESA), allows the future projection of the debris environment throughout Earth orbit. To ensure a sound basis for such future projections, and consequently for assessing the effectiveness of various mitigation measures, it is essential that the sensitivity of the model is examined. This paper discusses the sensitivity of the DELTA model to changes in key model parameters and assumptions. Specifically, the variation in future traffic rates, including the deployment of satellite constellations, and the variation in the break-up model and criteria used to simulate future explosion and collision events. 2004 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Space debris; DELTA model
1. Introduction Long-term debris environment models play a vital role in furthering our understanding of the future debris environment, and in aiding the determination of a strategy to preserve the Earth orbital environment for future use. By their very nature these models have to make certain assumptions to enable informative future projections to be made. Examples of these assumptions include the projection of future traffic, including launch and explosion rates, and the methodology used to simulate break-up events. To ensure a sound basis for future projections, and consequently for assessing the effectiveness of various mitigation measures, it is essential that the sensitivity of these models to variations in key assumptions is examined. The recently upgraded debris environment long term analysis (DELTA) model, developed by QinetiQ for the European Space Agency (ESA), models the evolution of the debris environment and associated collision risks throughout Earth orbit (Martin et al., 2002). Extensive *
Corresponding author. Tel.: +44-1252-397-066; fax: +44-1252-396320. E-mail address:
[email protected] (C. Martin).
analyses with this model have been performed under the auspices of an ESA contract to update the ESA Space Debris Mitigation Handbook. This paper draws on these analyses to present the sensitivity of the DELTA model to changes in key model parameters and assumptions. Specifically the paper will address the variation in future traffic rates, including the deployment of satellite constellations, and the variation in the break-up model and criteria used to simulate future explosion and collision events.
2. Baseline scenario To enable an assessment of the sensitivity of the DELTA model a baseline scenario must be run for comparative purposes. This scenario, commonly denoted ‘business as usual’, applies default model parameters and assumptions to produce, essentially, the best available forecast of the future debris environment. The baseline scenario and all of the sensitivity studies presented in this paper share the following set-up: • 100 year studies of the LEO debris environment. • The MASTER’99 model reference population for debris objects >1 mm in size is used as input to the model.
0273-1177/$30 2004 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2003.02.028
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• Orbit perturbation models of Earth gravity (J2 , J3 , J22 ), atmospheric drag, luni-solar gravity and solar radiation pressure are used to propagate the debris population. • No mitigation measures are implemented at any point in the simulation. • All of the results are an average of 10 Monte Carlo runs. For further discussion of a LEO ‘business as usual’, or baseline, scenario refer to Walker et al. (2001). The baseline scenario assumptions that will be varied in turn during the sensitivity studies are: • Launch, explosion and solid rocket motor (SRM) firing rate. The average launch and explosion rates, in the period 1991–1998 inclusive, were approximately 75 launches (generating a corresponding number of SRM firing events) and 5.5 explosions per year. These rates are considered constant in the baseline scenario. • Satellite constellations. No new constellations are deployed in the baseline scenario. • Collision fragmentation threshold. The impactor energy to target mass ratio, above which a collision is treated as catastrophic, is taken to be 40 J g 1 in the baseline scenario. • Break-up model. The baseline scenario employs the MASTER’99 break-up model (Battelle Model), including the Reynolds low intensity explosion law derived from an Atlas fragmentation.
3. Future traffic An essential driver for the future collision rate and correspondingly the evolution of the debris environment is the amount of mass on orbit. This is dictated by the number of launches, and the balance between these new satellites and the number of objects that re-enter the Earth’s atmosphere. The simulation of future launch activity over the next century is a significant source of uncertainty for long-term evolution models. Consequently, it is important to model a number of different traffic scenarios to enable possible future behaviour to be bounded.
3.1. Launch and explosion rates If the methods and technologies used today continue to be used in the future, it is reasonable to assume that any changes in the launch rate will produce a corresponding change in the explosion and solid rocket motor firing rates. To reflect this, the scenarios modelled and presented here consider equivalent variations in all three rates. Three scenarios are modelled and compared to the baseline scenario. These are: • Step in traffic. Continuation of recent historical launch, explosion and SRM firing activity until the year 2020, followed by a smooth increase between 2020 and 2030, reaching a level double that of the baseline scenario. On aggregate, this is 75% higher than the baseline scenario. • Doubling traffic. A gradual linear increase in the traffic rates over the 100 year simulation, finally reaching a level double that of the baseline scenario. On aggregate, this is 50% higher than the baseline scenario. • Halving traffic. A gradual linear decrease in the traffic rates over the 100 year simulation, finally reaching a level half that of the baseline scenario. On aggregate, this is 25% lower than the baseline scenario. The variation in the scenarios is designed to broadly represent the diversity of possible future traffic. In particular, the Step in traffic scenario is included to simulate a possible technological advance that may ease access to space. The effect of variations in the future traffic on the debris environment is shown in Fig. 1. As expected in the absence of mitigation measures, the collision rate increases. This is illustrated in Fig. 1(a), which shows a non-linear, increasing trend in the cumulative number of collisions in all cases. When the traffic rate is at its highest (Step in traffic) a general exponential trend can be deduced, and the total number of collisions over the 100 year period is more than double that in the baseline scenario. The collision rate is observed to increase even if the traffic rate steadily decreases over the next 100 years, because the number of objects on orbit continues to grow. The correspondence between the traffic rate and
Fig. 1. (a) The cumulative number of collisions and (b) Evolution of the number of objects >10 cm in size for the different future traffic scenarios.
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the number of collisions is non-linear due to the contribution of feedback collisions – collisions involving fragments from earlier break-up events. In the baseline scenario the balance between the new objects launched into orbit (occurring at a constant rate) and the number of objects removed due to atmospheric drag results in a linear increase in the decimetre population (Fig. 1(b)). In contrast, the scenarios with varying traffic rates show a non-linear evolution in the number of decimetre objects. Halving traffic means the number of objects removed by drag begins to increase relative to the number of satellites placed on orbit, and the population growth slows down. However, the higher traffic rates (Step in traffic and Doubling traffic) show an exponential growth in the number of objects larger than ten centimetres in size. As a whole these results show that varying the traffic between the lowest and highest rates modelled here gives a threefold increase in the total number of catastrophic collisions and more than doubles the decimetre debris population. 3.2. Satellite constellations The benefits of using multiple satellite constellation systems have been recognised in recent years in both the telecommunications and remote sensing fields. However, recent and well-documented difficulties have, perhaps, placed the future of satellite constellation systems in doubt, at least in the near-term. The introduction of satellite constellations into the low Earth orbit environment, and their subsequent effect on the debris population, has been studied by several
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research groups (van der Ha, 1998; Krisko et al., 2001). These studies have demonstrated the need to perform an analysis of the sensitivity of DELTA to the inclusion of satellite constellation systems in future launch traffic. To this end, two scenarios are modelled: • Constellation traffic. Deploying three generations each of the Iridium, Globalstar, Orbcomm, Teledesic and Skybridge constellations within a 25 year period. These constellations are those already deployed or those proposals considered more concrete at the time of the analysis. • Large constellation. Deploying three generations of a very large constellation into the most crowded LEO region, over a period of 25 years. These two scenarios are thought to represent a moderate, realistic case (Constellation traffic) and a theoretical, worst case (Large constellation). Details of the constellation design and component satellites are given in Table 1. Before considering the influence of satellite constellations on the debris environment, it is important to examine the evolution of the constellations themselves, Fig. 2 shows the satellite constellation histories in each of the two modelled scenarios. The initial deployment of the three generations is observable in the early years of the evolution and is followed by the decay of the low altitude constellations. This decay is evident by step reductions in the number of satellites as each generation reenters the Earth’s atmosphere. When all operational and non-operational satellites are on orbit there will be many constellation satellites within narrow altitude bands. This is particularly the case in the Large constellation
Table 1 Summary of constellation design and component satellite specification Name
a (km)
i ()
No. satellites
Mass (kg)
Area (m2 )
Life (yrs)
Iridium Globalstar Orbcomm Teledesic Skybridge Large constellation
7158 7792 7203 7753 7847 7178
86.4 52 45 84.7 53 82
66 + 6 spare 48 + 4 spare 28 + 8 spare 288 + 36 spare 80 1000
689 450 42 1400 1250 700
4.3 10 3 12 12 10
5 7.5 10 10 8 7
Fig. 2. Evolution of the number of constellation satellites in Earth orbit for (a) Constellation traffic and (b) Large constellation.
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Fig. 3. (a) The cumulative number of collisions and (b) Evolution of the number of objects >1 cm in size for the different constellation scenarios.
scenario. Note that the gradual decrease in the number of satellites of the large constellation, prior to the first generation decay, is due to collision break-ups. Fig. 3 shows the evolution of the LEO debris environment when satellite constellations are included in the future traffic. The Constellation traffic scenario results in a 50% increase in the total number of collisions in the simulation, whereas the Large constellation scenario produces a four-fold increase (Fig. 3(a)). The correspondence between the collision profile and the number of satellites on orbit can be noted – the highest collision rate occurs when 3000 satellites are in the most heavily populated altitude region. In the latter years of the simulation, as the constellation satellites decay to lower altitudes and eventually re-enter the Earth’s atmosphere, the collision rate begins to reduce. A corresponding profile can be observed in the evolution of the number of debris objects, where the presence of satellite constellations produces a steep growth in the centimetre population, shown in Fig. 3(b). The number of objects >1 cm in size in the Large constellation scenario is double that of the baseline case by the end of the simulation.
sured using the ratio of impactor energy to target mass. To determine the effect this parameter has on the number of collisions predicted in a long-term evolution, two scenarios are modelled: • 30 J g 1 . Reducing the fragmentation threshold to the lower limit determined from ground-based tests. • 60 J g 1 . Increasing the fragmentation threshold to the upper limit determined from ground-based tests. Fig. 4 shows the evolution of the number of objects larger than 10 cm in size for each of the modelled
4. Break-up modelling
Fig. 4. The evolution of the number of objects >10 cm in size for the different fragmentation thresholds.
An important component of the future debris population is the fragments generated by on-orbit break-up events. Consequently the ability to model different fragmentation events is a vital part of a long-term debris environment model. For each type of event, be it explosion or collision related, many models are available in the literature (Williams et al., 2002). However, the use of different models can lead to varying predictions of the future environment, and thus it is important to consider how the DELTA model long-term projections are effected by using a different set of break-up equations. 4.1. Collision fragmentation threshold When modelling future collision events the threshold above which a complete fragmentation occurs is mea-
Fig. 5. Fragment number versus size distribution for the different break-up models.
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Fig. 6. (a) The cumulative number of collisions and (b) Evolution of the number of objects >1 cm in size for the different break-up models.
fragmentation thresholds. It illustrates that this parameter has only a minimal influence on the evolution of the future debris environment. Indeed, the differences from the baseline scenario are within the error bounds of the DELTA model. 4.2. Break-up model The aim of a break-up model is to represent the distribution of fragments after an explosion or collision event. A new model has been derived from extensive analysis of on-orbit fragmentation events and the SOCIT ground based test, and implemented in the NASA EVOLVE 4.0 model (Johnson et al., 2001). The approach of this break-up model differs significantly from that used in the DELTA baseline scenario as illustrated in Fig. 5. The NASA model generally produces more fragments with a lower dispersion, which are subject to stronger atmospheric drag. To learn the effect the NASA break-up model has on the DELTA environment predictions, a scenario was modelled using the NASA relationships. The differences in the long-term projections are shown in Fig. 6. The predicted number of catastrophic collisions differs by just a few events over 100 years (Fig. 6(a)). The NASA breakup model does generate more decimetre fragments but this is balanced by the higher orbital decay rate (areato-mass ratio) of these objects. Although the collision rate remains similar, the increase in the centimetre population in the NASA scenario is substantial (Fig. 6(b)), reaching double the level of the baseline scenario. Debris in this size range may not be able to cause numerous feedback collisions but the damage they can do to onorbit assets is significant and, consequently, the importance of this trend cannot be neglected.
5. Discussion The sensitivity analyses performed here confirm that future traffic is critical to the forecasting of the debris
environment and can thus be a source of significant uncertainty in long-term models such as DELTA. The number of launches is dictated by political and economic as well as technical considerations. Perhaps more sophisticated future traffic models are needed to thoroughly study the influences of technological and market trends on the launch traffic rate (Johnson, 2000). Such technological trends include the deployment of satellite constellations into Earth orbit. Although these systems have an uncertain future they undoubtedly can play an important role in the evolution of the debris environment and should not be neglected. The analyses have also demonstrated the importance of the break-up models chosen to simulate future explosion and collision events. Careful consideration must be given to the role these models play in predicting the evolution of the debris environment. The work presented here has placed the DELTA long-term projections of the future debris population into context by considering the sensitivity of the model to variations in key parameters. This knowledge strengthens the validity of long-term debris modelling and helps assess the suitability of mitigation measures that have been proposed to help preserve Earth orbit.
Acknowledgements The work presented in this paper was performed as part of the ESA/ESOC contract ‘Update of the ESA Space Debris Mitigation Handbook’.
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