PEDAS1-0012-10 Modeling the Space Debris Environment with MASTER-2009 and ORDEM2010 Sven Flegel a, Paula Krisko b, Gelhaus J. a, Wiedemann C. a, Möckel M. a, Vörsmann P. a, Krag H. c, Klinkrad H. c, Xu Y.-L. b, Horstman M.F. b, Opiela J.N. b, Matney M. b a Institute of Aerospace Systems, Technische Universität Braunschweig, Hermann-Blenk-Str. 23, 38108 Braunschweig, Germany b ESCG, Mail Code JE104, 2224 Bay Area Blvd., Houston, TX 77058, USA c Space Debris Office, ESA/ESOC, Robert-Bosch-Str. 5, 64293 Darmstadt, Germany Abstract The two software tools MASTER-2009 and ORDEM2010 are the ESA and NASA reference software tools respectively which describe the earth s debris environment. The primary goal of both programs is to allow users to estimate the object flux onto a target object for mission planning. The current paper describes the basic distinctions in the model philosophies. At the core of each model lies the method by which the object environment is established. Central to this process is the role played by the results from radar/telescope observations or impact fluxes on surfaces returned from earth orbit. The ESA Meteoroid and Space Debris Terrestrial Environment Reference Model (MASTER) is engineered to give a realistic description of the natural and the man-made particulate environment of the earth. Debris sources are simulated based on detailed lists of known historical events such as fragmentations or solid rocket motor firings or through simulation of secondary debris such as impact ejecta or the release of paint flakes from degrading spacecraft surfaces. The resulting population is then validated against historical telescope/radar campaigns using the ESA Program for Radar and Optical Observation Forecasting (PROOF) and against object impact fluxes on surfaces returned from space. The NASA Orbital Debris Engineering Model (ORDEM) series is designed to provide reliable estimates of orbital debris flux on spacecraft and through telescope or radar fields-of-view. Central to the model series is the empirical nature of the input populations. These are derived from NASA orbital debris modeling but verified, where possible, with measurement data from various sources. The latest version of the series, ORDEM2010, compiles over two decades of data from NASA radar systems, telescopes, in-situ sources, and ground tests that are analyzed by statistical methods. For increased understanding of the application ranges of the two programs, the current paper provides an overview of the two models main program features and the methods by which simulation results are presented. This paper is written in a combined effort by ESA and NASA. Keywords: MASTER-2009, ORDEM2010, space debris 1. Introduction Email addresses: s.flegel@tu-bs.de (Sven Flegel), paula.krisko-1@nasa.gov (Paula Krisko) The current paper is part of an ongoing effort between ESA s Space Debris Office and NASA s Orbital Debris Program Office. The aim of this Preprint submitted to Elsevier August 24, 2010
work is to increase mutual understanding of the two major space debris software tools namely ESA s MASTER (Meteoroid and Space Debris Terrestrial Environment Reference) and NASA s ORDEM (Orbital Debris Engineering Model). The work was spurred by previous publications which revealed significant differences in the populations of both models. Most notibly, Fukushige et al./4/ published a paper in which the results from OR- DEM2000, MASTER-2001 and MASTER-2005 were shown to deviate significantly in the debris size range of 1 mm to 1 cm. This size range poses a special challenge as the amount of measurement data is extremely scarce. The ORDEM2010 model which is currently in the final stages of developement is the first model to incorporate radar measurements for these sizes. The first two chapters of this paper give a detailed introduction into the generation processes of the debris populations of the two models. Example diagrams exemplify the methods by which the two populations are created and validated. A specific comparison of the two processes identifies basic characteristics and gives possible causes for deviations in the resulting populations. The final chapter gives a brief overview of some of the program features. The conclusion reviews the major findings of the effort thus far. It also offers proposals for specific tasks which could help in determining the true nature of the debris population between 1 mm and 1 cm. 2. MASTER-2009 The philosophy of the population generation process of MASTER-2009 is outlines in the following paragraph: Statistical debris models mimic all known debris creation mechanisms in as much detail as possible. The ultimate goal is for the debris models to create a population which agrees with measurement data without the requirement of postsimulation processing. 2 2.1. Modeling overview The entire process of population generation can be divided into the following steps: 1. Historical population generation 2. Large object validation 3. Small object validation The most important features of this process are detailed in Figure 1. For the historical population generation, TLE data and simulation data are merged to form a space debris population reaching down to 1µm. For the validation of the created large object population, measurement campaigns with radars and telescopes are simulated with the ESA Program for Radar and Optical Observation Forecasting (PROOF). These simulations use the complete generated population as basis. Differences between the simulated and real measurement campaigns give information about incongruencies in the population generation process which is then modified to minimize these differences. The small particle validation is based on impact data from surfaces returned from space such as the Hubble Space Telescope solar arrays. The exposure of these surfaces to the debris environment is simulated using MASTER and the results are compared based on the number of impacts over crater diameter or a derived ballistic limit. The pure simulation models for ejecta and solid rocket motor slag underestimate the true impacts and thus are scaled to match the measurement data. These processes are detailed in the following sections. 2.2. Historical population generation The trackable size range above 5-10 cm and non-trackable size ranges down to 1µm are described in the MASTER space debris environment. Tracked objects are merged with simulated objects to form the large object MASTER-population. The untrackable size range of the MASTER-population relies on simulated debris particles alone. The historical population generation process can be roughly described by the three steps a) data acquisition&processing, b) debris simulation and c)
Figure 1: MASTER-2009 population generation schematic. data merging. During data acquisition & processing, data for tracked objects is merged from different sources. Momentary orbit data and object properties are stored in quarterly population snapshots from 1957 onwards. For the same time frame, the entire debris environment is simulated using the Program for Orbital Debris Environment Modeling (POEM). The data is stored in the same format as that of the tracked objects as quarterly population snapshots since 1957. The final step then merges the acquired & processed quarterly data with the simulated data, substituting acquired objects for simulated objects where parameters are sufficiently similar. In practice, the debris simulation step divides into further steps. The ejecta for instance simulate the impact of small particles on larger objects. 3 This can only be simulated once all other sources have been acquired, processed and merged with simulated objects. A schematic of the population generation process is given in Figure 2. 2.2.1. Object data acquisition and processing Information on all objects which have been cataloged since 1957 is compiled. The data consists of orbit parameters at quarterly epochs along with object mass, diameter and mass-to-area ratio. The cataloged objects include payloads, rocket bodies, mission related objects and collision and explosion fragments. The sources for this data are the USSTRATCOM s Satellite Situation Report and the Two Line Elements (TLE) which are both obtained from the Space Track website/9/, ESA s
Figure 2: Schematic of historical population generation in MASTER. FRAG - fragmentation debris; PL - payloads; RB - rocket bodies; MRO - mission related objects; LMRO - launch and mission related objects; COLL - collision fragments; EXPL - explosion fragments; WFN - Westford Needles; NaK - sodium-potassium droplets; SRMS - solid rocket motor slag; SRMD - solid rocket motor dust; MLIX - multi-layer insulation from explosion; MLID - multi-layer insulation from deterioration; EJEC - ejecta; PAFL - paint flakes Database and Information System Characterising Objects in Space (DISCOS)/2/ and Jonathan Mc- Dowell s Satellite Catalog/7/. Satellites, rocket bodies and mission related objects are stored as launch- and mission related objects (LMRO). Fragments are later divided into explosion and collision fragments and are merged with the simulation results. 2.2.2. Debris simulation and data merging The simulation of all debris sources is performed with POEM. This program is in essence a compendium of individual debris generation mechanisms which can be used to simulate any selection of debris sources. Two types of debris models are distinguished: a) list based debris models and b) continuous debris models. Figure 3 lists all space debris sources included in the MASTER software 4 with the contributing size ranges. List based debris models. For the debris sources cluster (Westford Needles), explosions and collisions, sodium-potassium droplets, solid rocket motor firings and fragmentation driven multi-layer insulation, comprehensive lists are maintained which contain parameters detailing each event since the beginning of human space activities in 1957. These parameters include in all cases the epoch, orbit and location of the event. The release of the sodiumpotassium droplets and solid rocket motor firings use additional directional information for the ejection of the debris. The fidelity of the list based debris models depends on the completeness of these lists and the accuracy of the models coded in POEM. The quality of the lists benefits from the validation process. Invaluable insight is obtained
Figure 3: MASTER-2009 space debris sources. into individual events by direct comparison of measurement data with the simulation results. Continuous debris models. Paint flakes, ejecta and delamination of multi-layer insulation are produced continuously. Ejecta are furthermore unique in that they are the result of small debris particles impacting larger structures. All other debris sources must therefore have been completely simulated, before ejecta can be created with POEM. The two models for paint flakes and delamination of multi-layer insulation both succesively analyze the LMRO objects given at defined epochs starting from 1957. The evaluation process uses the population snapshots produced during the data acquisition&processing step. Each object is evaluated according to model specific parameters. In addition to size and orbit type, other factors are considered such as age or solar flux. In this manner, debris objects are produced at statistical epochs according to developed probabilty distributions/8/. 5 Data fusion. The clusters (Westford Needles) are considered launch- and mission related objects and are stored along with the acquired payloads, rocket bodies and mission related objects. At this stage, two data sets are given for explosion and collision objects: quarterly snapshots from data acquisition & processing with objects down to a few centimeters in size and fragments from debris simulation ranging from several meters down to 1µm. A correlation tool merges the objects from these two sources independently for each quarterly snapshot. The tool substitutes TLE objects for simulated objects with similar parameters. In the event that no matching simulated object is found, the TLE object is omitted. In MASTER-2009, merging parameters were selected which resulted in a correlation rate of 95 %. 2.3. Large object validation The large object validation uses data from radar and telescope detection campaigns. The PROOF tool simulates these detection campaigns based on a large number of specific radar or telescope properties and the created historical population.
The detection results from the real and simulated campaigns are then compared using scatter plots for doppler inclination and range and histograms for number of detections over different object parameters. Differences between the reality and the simulations show where the models for the large objects require adjusting or certain events have previously gone undetected. Inclination [deg] 20 15 10 5 ESA-SDT-2001 PROOF Debris clouds from individual events can sometimes be made visible, if orbit parameters from measurements are plotted as scatter plots. Other information which is used includes radar cross section against altitude. The number of detected objects is compared on the basis of histograms. Using these plots in combination with the scatter plots, the size of individual events and the background population can be evaluated. Examples of a scatter plot and a histogram plot are given in Figure 4. In the past, measurement campaigns from the ESA-Space Debris Telescope (ESA-SDT) on Tenerife and the Tracking & Imaging Radar (TIRA) in Wachtberg, Germany have been used for validation. For MASTER-2009, results from the European Incoherent Scatter (EISCAT) on Svalbard have been added especially for validation of the fragment clouds of the Feng-Yun 1C event and the Iridium-33 and Cosmos 2251 fragment clouds. The ESA-SDT performs scans of the GEO and GTO region while the two other sensors perform LEO measurements. In all, the MASTER-2009 large object population has been validated against seven years of ESA-SDT observations, eight TIRA campaigns and observation data over extended periods of time during 2007/2008 and 2009 from EISCAT. 2.4. Small object validation The small object validation starts at object sizes of about 1 mm and is based on impact data from surfaces retrieved from space. These missions are simulated with the MASTER software. The data collected from the returned surfaces is then 6 Detection Rate [1/h] 0 0 50 100 150 200 250 300 350 4 3.5 3 2.5 2 1.5 1 0.5 RAAN [deg] TIRA 2001 Campaign 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Altitude [km] TIRA PROOF Figure 4: Example of scatter plot (left) and histogram plot (right) used for MASTER large object validation. compared to the simulations based on the impact number over impact crater size for individual surfaces. On the software side, damage equations are implemented in MASTER which convert simulated impacts based on user defined equation parameters into crater diameters or ballistic limits. Chemical analyses of the impacts give information on the possible origin of the impactor and allow a more detailed validation of individual debris models. Objects which have been used for the small size validation are the solar arrays of the Hubble Space Telescope (HST), the Long Duration Exposure Facility (LDEF) and the European Retrievable Carrier (EuReCa). In all, 14 surfaces were used for validation of MASTER-2009 over a cumulated in-orbit time of almost 20 years. A typical comparison is
Semi major axis / km LDEF mission profile for MASTER 2009 simulation 6880 6860 6840 6820 6800 6780 6760 6740 6720 6700 1984 1986 1988 1990 Time / Years Flux [1/m 2 /a] 10000 1000 100 10 1 0.1 0.01 0.001 0.0001 1e-05 1e-05 0.0001 0.001 SRM Dust SRM Slag Paint Fragments Ballistic Limit [m] Ejecta Meteoroids Debris Flux (Model) Debris Flux (Data) Figure 5: Example of orbit evolution and resulting impacts over crater size plot for MASTER small object validation for LDEF south face. shown in the right hand plot in Figure 5. Cumulated impacts on the south face of LDEF are shown over the crater diameters. Due to the lack of chemical analysis of the impactors, the debris impact data was obtained by subtraction of simulated meteroid impacts from the total number of impacts. The top figure demonstrates LDEF s orbit evolution and the discretized simulation steps chosen. 3. ORDEM2010 The ORDEM2010 population generation philosphy can be summarized as follows: Supporting debris source models provide an initial population matrix which matches the true population with respect to orbits and object types in quality but not necessarily in quantity. Statistical methods are applied to then match the simulated populations to measurement data with respect to quantity. 3.1. Modeling overview The entire process of population generation can be divided into the following steps: 1. Initial population simulation 2. Large object data matching 3. Small object data matching 7 Figure 6 is a schematic of the population generation process. Selected debris mechanisms are simulated to create an initial population of intacts and debris. This population serves as an initial matrix which is then matched to given measurement data via an iterative process using Bayesian statistics/11/. The large object population is matched to data from radars and telescopes. The small object validation is matched to data from impacts on space shuttle surfaces. The large object population is matched by adjusting the initially simulated population. The small object population matching process involves adjusting the production rate of degradation/ejecta in the debris model. The creation processes are detailed in the following section. 3.2. Initial population generation For the initial debris population, four object sources are simulated: intacts, fragmentations, NaK-droplets and degradation/ejecta particles. The debris is further distinguished by material density. Fragments are divided into low, medium and high density objects. Degradation/ejecta are split into medium and high density objects. These four sources are briefly discussed here. Intacts. Intacts include payloads, rocket bodies, mission related objects. These are simulated
Figure 6: ORDEM2010 population generation schematic. by LEGEND (LEO-to-GEO Environment Debris Model)/6/ for the time frame 1957 to 2035. For the historical time frame, these objects are included based on a NASA internal database/10/. For the future time frame, LEGEND simulates payloads and associated objects according to defined launch profiles. Objects with diameters roughly 10 cm and larger are produced. No post-simulation scaling is required to match the simulated population to actual measurements. 8 Fragments. All fragmentation events since 1957 and up to 2035 are simulated using LEGEND. The simulated debris is used for sizes above 1 mm. The fragmentation events are simulated using the basic NASA Breakup model without adjustment to the individual events. Post-simulation scaling is used to match the population matrix to measurement data. Large events such as the anti-satellite test on the Feng-Yun 1C satellite are modelled individually. The scaling of sizes larger than 2 mm uses data from Haystack, HAX, SSN and MOD- EST. For LEO fragments, the initial population is reduced by a factor three. Highly eccentric objects are scaled by a factor of 1.15 approximately. Centimeter size objects are reduced in number to match observations. NaK-droplets. An NaK-Module simulates the release of sodium-potassium droplets. The covered size range is 1 mm to some centimeters in size. The applied distribution is based on observation data from the Haystack radar/3, 5/. Degradation/Ejecta. An independent model simulates continuous production of small particles. The
population is created by derivation of a constant production rate at different debris sizes for each in orbit intact. For the historical time frame, the objects from the SSN catalog are used while for the future time frame objects simulated with LEGEND are utilized. 3.3. Large object data matching The large object regime is represented through payloads, rocket bodies and mission related objects in addition to sodium-potassium droplets and fragmentation debris. The payloads, rocket bodies and mission related objects are simulated by the tool LEGEND. Sodium-potassium droplets are simulated by an external NaK-Module. Both sources give a one-to-one representation of the measurement data and do not require further adjustment. LEGEND also simulates all historical fragmentation events which are scaled to match the measurement data from radar and telescope campaigns. The process by which the simulated fragmentation objects are matched to the observation data is exemplified here using radar measurements. Data obtained by radars consists of range, range-rate and radar cross section (RCS). The RCS is transformed into an object diameter using the NASA size-estimation model (SEM) /1, 12/. For one measurement campaign, this data is sorted into two-dimensional arrays of range and range-rate. Each array holds the detections for all objects larger than a certain diameter. The diameter limits used for ORDEM2010 are 0.316 cm, 1 cm, 3.16 cm, 10 cm, 31.6 cm and 1 m. To account for uncertainties in the detections, each array entry (also referred to as bin ) is assigned an indiviual poisson distribution (see Figure 7). To be able to compare the simulated population with the measured data, the simulated population is brought into the same format as the measurement data. This requires simulating the measurement campaigns. The simulation uses the epoch of the measurement campaigns along with the orientation, field-of-view and detection range 9 and minimum object size limits of the observation platform. The differences between the simulated and measured data are fed into a Bayesian statistical approach. The return value of this approach is a new set of parameters for the scaling of the simulated population. This procedure is iterative and converges towards a best estimate for the scaling of the population. In practice, the population is matched to measurement data starting at the largest diameter of 1 m. Once the population above this diameter correlates with the data, the entire population above the next lower diameter of 31.6 cm is matched. In this step, the previously validated population is considered frozen so that only the population in the size range 31.6 cm to 1 m is scaled. This process is repeated down to the lowest sizes for which data is available. The application of poisson distributions to the data results in a measure of uncertainty between the simulated and the measured data. An example of the detection arrays which are used for data matching to radar campaigns is given in Figure 7. The figure shows an overlay of Haystack detections of NaK-droplets as white cross signs over simulated detection rates for NaKdroplets. 3.4. Small object data matching The debris population below 1 mm in size is simulated by modeling surface degradation processes. Measurement data consists of impacts on the space shuttle windows and radiators for a total of 38 missions. The data is given in terms of number of impacts vs. crater depth for space shuttle windows and number of impacts vs. crater diameter for space shuttle radiators. For the comparison of simulated data with measurement data, the space shuttle missions are simulated. Crater depth and diameter are derived for all simulated impacts using damage equations. Due to the short duration of the space shuttle missions the number of impacts per mission are too few to be used individually. For the small object matching, the impacts for all STS missions are combined into a single cumulative distribution over impact
Figure 7: Left: Schematic of radar data discretization for data matching. Right: Example of range vs. range-rate plot for OR- DEM2010 large object matching. The white cross signs are detections from the Haystack radar. The background is the simulated detection rate. feature size. Two example plots are given in Figure 8. The left hand plot shows the cumulated impacts from all STS missions split into medium and high density space debris impacts. The right hand plot shows the matched model data against measurement data. The small object matching consists of two iteration cycles. In Figure 6, these are represented by the Model adjusting (or outer) cycle and the Comparison block (or inner cycle). The initial model assumes that one surface degradation object is produced per week and per square meter of surface area for all in-orbit payloads and rocket bodies. The debris flux vs. impact features which results from the simulated population is the so-called model matrix. During the inner iteration process, the model matrix remains unchanged. The goal of the inner iteration is the derivation of scaling parameters for the debris production rates at different size ranges. In ORDEM2010 Bayesian statistics are used in a converging process which minimizes differences between simulated results and given data by scaling of the base-line model matrix. Individual best estimates are derived using this method for the size ranges 10-31.6 µm, 31.6-100 µm, 10 100-316µm, and 316µm - 1 mm. The four discrete estimated scaling factors are used as a basis for adjusting the production rates in these four size ranges. Within the size groups, linear interpolation is performed to avoid discontinuities in the production rates over diameter. The outer cycle is thus entered wherein the reference population is resimulated using the new model parameters and the model matrix is again derived. The inner cycle is run again until the statistical approach converges to a new set of the four discrete adjustment factors. This entire process is repeated until the simulation results match the measurement data sufficiently well, i.e. the four discrete scaling factors are all close to 1. 4. Comparison of Population Creation Mechanisms This chapter compares the two modeling processes with a special emphasis on the size range 1 mm to 1 cm. This size regime is crucial as only extremely limited measurement data exists to date for this size range and marked differences between the MASTER-2005 and ORDEM2000
Figure 8: Example of crater depth plot for ORDEM2010 small object matching for window impacts combined from all Space Shuttle missions. models have been perceived/4/. Comparing the model philosophies, an important difference can be recognized: Both models have to make assumptions at different points during the population generation process. For MASTER-2009, these apply to the models mimicing the creation mechanisms themselves. Whereever processes are not well understood or data is scarce or controversial, assumptions are used. If no model parameter setting is found during model validation, which results in sufficient correlation of simulated and measured data, time invariant scaling parameters are applied. This measure is currently applied to ejecta, which are scaled by a factor 1000 below 200µm and to solid rocket motor slag which is scaled by a factor of 50 below about 300 µm. The scaling is reduced to one for both sources at 1 mm diameter. The debris source with the highest contribution at the millimeter to centimeter size range in MASTER is solid rocket motor slag. In ORDEM2010, a gap-free population can 11 only be created if continuous measurement data across all epochs and diameter ranges is available. For the crucial size range, some measurement data is available from the Haystack and Goldstone radars (see Table 1). The population matrix for this size range is created by LEGEND. The small size population below 1 mm is then extended upward to 3.16 mm and the large object population above 3.16 mm down to 1 mm. For the two different populations, the scaling parameters from the adjacent half decadal size ranges are initially extended into the region 1 mm to 3.16 mm. It is assumed that a realistic representation of this regime is found, if the two overlapping populations can be brought into agreement with one another with only limited change to the initial scaling factors for both populations. An overview of additional important differences between the modeling approaches is given in Table 1. Common data has been used in the past on selected occasions only such as for the NASA and ESA NaK-models. This could account for some additional differences in the populations.
Table 1: Listing of Model population generation features for MASTER-2009 and ORDEM2010. MASTER-2009 ORDEM2010 General Properties Validation data for objects> 10 cm TIRA, EISCAT, ESA-SDT Haystack, HAX, SSN, MODEST Validation data for objects > 2 mm Haystack (> 5.5 mm), Goldstone (> 2 mm) Validation data for objects < 1 mm LDEF, HST-solar arrays, Eu- ReCa Space Shuttle windows and radiators Payloads, rocket bodies and mission related objects Included from catalogs Included from historical database using LEGEND Considered orbital perturbations: - Zonal geopotential deformations J 2,0, J 3,0, J 4,0, J 5,0 J 2,0 - Air drag MSIS-2000 below 1500 km - Sun & Moon gravity Yes Yes - Solar radiation pressure Yes - without earth shadow Yes 5. Comparison of Program Features Table 2 contains an overview of features of both models which are briefly discussed in this section. 5.1. Object Flux on Space Craft Both tools allow the user to define a spacecraft target orbit. In ORDEM2010, the target orbit may be given in the form of a TLE data set. While MASTER-2009 does not have this capability, it is able to handle multiple successive orbits for a single target to simulate a mission profile. Both models produce a direction dependent flux on the target. The MASTER model has the advantage of determining the flux on oriented surfaces (e.g. sun-oriented solar pannels), on a tumbling plate or a sphere. The oriented surfaces enable the evaluation of flux over impact angle. The format of the plots which present the information vary between the models. Both models are capable of presenting the results in 2D and 3D 12 plots. The ORDEM tool offers the results in terms of impact fluence over impact velocity and impact direction. Different plotting options include polar and cartesian coordinates. The MASTER tool presents the results in cartesian coordinates only. In addition to impact fluence over velocity and impact direction, a number of other information can be plotted for the target such as fluence over impact altitude, right ascension or declination. Information on the impactors can be evaluated in detail by fluence plots for individual debris sources over mass or diameter or the orbit parameters of the impactors. Post processing of the plots in MASTER is possible via direct access to the underlying gnuplot drivers. The graphical user interface in MASTER offers simple options for differential, cumulative or reverse cumulative plotting. Detailed analyses of the resulting information is however best performed by processing the automatically produced output files. ORDEM offers a large suite of tools within the graphical user interface which enable a
Table 2: Listing of Model features for MASTER-2009 and ORDEM2010. MASTER-2009 ORDEM2010 General Properties Population time frame 1957-2060 1995-2035 Debris size range 1 µm 10 µm (LEO-MEO) 10 cm (GEO) Object Flux on Space Craft User defined orbit Yes Yes Orbit parameters from TLE No Yes Multiple orbit sets Yes No Directional flux Yes Yes Orientated surfaces Yes No 2D-plots Yes Yes 3D-plots Yes Yes Plot postprocessing via gnuplot driver via graphical interface Telescope/Radar Mode Implementation managed by PROOF software built in ability Geometrical filter Yes Yes Radar-/Telescope performance model Yes No detailed analysis of the results without additional simulation time or the requirement of using additional software. 5.2. Telescope/Radar Mode Observation of the debris environment using radars or telescopes can be simulated in ORDEM with a built in function. This function relies on a geometry filter which analyses objects which pass a user defined field of view. For MASTER, this option is supplied through a standalone program: ESA s Program for Radar and Optical Observation Forecasting (PROOF). The ESA PROOF tool is a powerful software which combines radar- and telescope performance models with geometrical filters. Ground based as well as space based observation platforms can be simulated. 6. Conclusion The MASTER-2009 population is created by simulation of every known debris creation mechanism and event using nine independent debris models. The initially simulated debris 13 population requires only limited adjustment to the models so that individual parameters can be manually adjusted. Post-simulation scaling is used only if the population cannot be brought into agreement with measurement data by adjusting of model parameters. This is currently applied to two sources: ejecta and SRM-slag. The debris source with the highest contribution to the critical size regime between 1 mm and 1 cm is solid rocket motor slag. Resolving the uncertainties relating to the SRM-slag creation is seen as a vital step in bringing insight into the true nature of the millimeter size regime. ORDEM2010: Statistical debris creation mechanisms simulate a subset of all known debris sources. Iterative scaling cycles match the simulated fragmentation debris and the debris production rates for the degradation/ejecta to measurement data. The matching process is performed for a large number of parameters (material density, debris sizes, orbit parameters) and incorporates poisson distributions for the measured data. The iterative cycles apply Bayesian statistics to derive
model parameters and population scaling parameters. The basic idea behind the iterative scaling cycles is that all debris orbits of unknown sources are completely represented by a limited number of debris sources. The true quantity of objects on the respective orbits is derived by matching the simulated population to measurement data. By applying poisson distributions to the measurement data, a measure of uncertainty can be derived which represents the differences between the model population and the measurement data. The basic requirement is that continuous data must be available for the simulated time frame over all covered size ranges. In ORDEM, determining the debris source with the highest contribution in this size range could compliment sparse measurement data in this region. The current work has resulted in a greater mutual understanding of the two models ORDEM and MASTER. Insight has been gained into the modeling processes of the two models especially in view of the critical size range between 1 mm to 1 cm. Uncertainties with respect to the modelling in this size range remain on both sides. 7. Acknowledgement The authors wish to thank Mr. Nicholas Johnson of the NASA Orbital Debris Program Office and Mr. Heiner Klinkrad of ESA s Space Debris Office for making the current close collaboration possible. 3. Foster James L. Jr., Krisko Pala H., Matney Mark J., Stansbery Eugene G., NaK Droplet Source Modeling, presented at Space Debris Space Traffic Management 2003, published in Science and Technology Series Vol. 109, pp. 113-124, 2004 4. Fukushige Shinya, Akahoshi Yasuhiro, Kitazawa Yukuhito, Goka Tateo, Comparison of Debris Environment Models; ORDEM2000, MASTER2001 and MAS- TER2005, IHI Engineering Review Vol. 40 No. 1, February 2007 5. Krisko P.-H., Foster J.L., Modeling the sodium potassium droplet interactions with the low earch orbit space debris environment, published by Elsevier Ltd. in Acta Astronautica Vol 60, 2007, pp. 939-945, doi:10.1016/j.actaastro.2006.10.015 6. Liou J.-C., Hall D.T., Krisko P.H., Opiela J.N., LEG- END - a three-dimensional LEO-to-GEO debris evolutionary model, published by Elsevier Ltd. in Advances in Space Research Vol. 34, 2004, doi:10.1016/j.asr.2003.02.027 7. Jonathan McDowell, Jonathan McDowell s Personal Home Page, http://planet4589.org/jcm/jmcdowell.html 8. Oswald M., Stabroth S., Wiedemann C., Wegener P., Martin C., Klinkrad H., Upgrade of the MASTER Model - Final Report, ESA contract number 18014/03/D/HK(SC), April 26, 2006 9. Space Track - The Source for Space Surveillance Data, Responsibility of United States Strategic Command (USSTRATCOM) since 22 December, 2009, http://www.space-track.org 10. Xu Y.-L., Horstman M., Krisko P.H., Liou J.-C., Matney M., Stansbery E.G., Stokely C.L., Whitlock D., Modeling of LEO orbital debris populations for ORDEM2008, published by Elsevier Ltd. in Advances in Space Research Vol. 43, 2009, 769-782, doi:10.1016/j.asr.2008.11.023 11. Xu Y.-L. Statistical Inference in Modeling the Orbital Debris Environment Presented at the Internation Astronautical Congress in Valencia, Spain, Oct. 2-6, 2006, IAC-06- B6.2.03 12. Xu Y.-L., Stokely C., Matney M., Stansbery E., A Statistical Size Estimation Model For Haystack And HAX Radar Detections Presented at the 56th International Astronautical Congress in Fukuoka, Japan, 17-21 Oct. 2005 References 1. Barton David K., Brillinger David, El-Shaarawi A. H., McDaniel Patrick, Pollock Kenneth H., Tuley Michael T., Final Report of the Haystack Orbital Debris Data Review Panel, NASA, Lyndon B Johnson Space Center, Houston, Texas 77058-4406, Technical Memorandum 4809, February 1998 2. Database and Information System Characterising Objects in Space (DISCOS), Provided by European Space Operations Centre (ESOC), Darmstadt, Germany, http://mas15.esoc.esa.de:9000/ 14