Table Of ContentSpace Debris – Models and Risk Analysis
Heiner Klinkrad
Space Debris
Models and Risk Analysis
Published inassociationwith
PPrraaxxiiss PPuubblliisshhiinngg
Chichester, UK
Dr. Heiner Klinkrad
European Space Agency
Darmstadt
Germany
Coverimageshowsacomputer-generatedsnapshotoftheobservablepopulationofspaceobjects
in 1997, basedon orbitinformation provided byNASA.
SPRINGER–PRAXIS BOOKS IN ASTRONAUTICAL ENGINEERING
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Table of Contents
Prolog ix
1 Introduction 1
1.1 HistoryoftheEvolvingSpaceDebrisResearch . . . . . . . . . . . . 1
1.2 GuidanceforReadingthisBook . . . . . . . . . . . . . . . . . . . . . 4
1.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 TheCurrentSpaceDebrisEnvironmentanditsSources 5
2.1 LaunchHistoryandtheResultingOrbitalEnvironment . . . . . . . 5
2.2 HistoricOn-OrbitBreak-UpEvents . . . . . . . . . . . . . . . . . . . 18
2.3 Non-FragmentationDebrisSources . . . . . . . . . . . . . . . . . . . 23
2.4 Ground-BasedRadarandOpticalMeasurements . . . . . . . . . . . 27
2.5 In-SituMeasurementsandRetrievedSurfaces. . . . . . . . . . . . . 47
2.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3 ModelingoftheCurrentSpaceDebrisEnvironment 59
3.1 OrbitPropagationMethodsforLargePopulations . . . . . . . . . . 59
3.2 VolumeDiscretizationandCell-PassageEvents . . . . . . . . . . . . 61
3.3 TheTrackableSpaceObjectPopulation. . . . . . . . . . . . . . . . . 66
3.4 ModelingExplosionandCollisionFragments . . . . . . . . . . . . . 67
3.5 ModelingSolidRocketMotorSlagandDust . . . . . . . . . . . . . 76
3.6 ModelingSodium–PotassiumCoolantDroplets. . . . . . . . . . . . 83
3.7 ModelingWestfordNeedleClusters . . . . . . . . . . . . . . . . . . 86
3.8 ModelingSurfaceDegradationandImpactEjecta . . . . . . . . . . 87
3.9 HistoricEvolutionandSpatialDistributionofDebris . . . . . . . . 91
3.10 ComparisonofMeasurementsandModeledData . . . . . . . . . . 104
3.11 AlternativeSpaceDebrisEnvironmentModels . . . . . . . . . . . . 111
3.12 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
vi TableofContents
4 ModelingofCollisionFluxfortheCurrentSpaceDebrisEnvironment 115
4.1 DeterminationofCollisionFlux . . . . . . . . . . . . . . . . . . . . . 115
4.2 AnalysisofCollisionGeometries . . . . . . . . . . . . . . . . . . . . 119
4.3 CollisionFluxAssessmentforTypicalTargetOrbits . . . . . . . . . 122
4.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5 ModelingoftheFutureSpaceDebrisEnvironment 143
5.1 OrbitPropagationMethodsforLong-TermPredictions . . . . . . . 143
5.2 ConceptsofaLong-TermDebrisEnvironmentProjection . . . . . . 144
5.3 ModelingFutureLaunchTrafficandReleaseEvents . . . . . . . . . 145
5.4 DeploymentsofConstellationsandNano-Satellites . . . . . . . . . 148
5.5 DefinitionofaBusiness-as-UsualForecastScenario . . . . . . . . . 151
5.6 VariationsofaBusiness-as-UsualForecastScenario . . . . . . . . . 159
5.7 AlternativeDebrisEnvironmentProjectionModels . . . . . . . . . 161
5.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
6 EffectsofDebrisMitigationMeasuresonEnvironmentProjections 165
6.1 SpaceDebrisMitigationOptions . . . . . . . . . . . . . . . . . . . . 165
6.2 ExplosionPreventionbyEnd-of-LifePassivation . . . . . . . . . . . 168
6.3 Post-MissionDisposalfromLow-EarthOrbits . . . . . . . . . . . . 170
6.4 Post-MissionDisposalfromGeo-SynchronousOrbits . . . . . . . . 183
6.5 De-OrbitofGTOUpperStages . . . . . . . . . . . . . . . . . . . . . 190
6.6 DefinitionofProtectedRegions . . . . . . . . . . . . . . . . . . . . . 192
6.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
7 HypervelocityImpactDamageAssessmentandProtectionTechniques 199
7.1 HypervelocityAcceleratorsandHydrocodeSimulations . . . . . . 199
7.2 EffectsofHypervelocityImpacts . . . . . . . . . . . . . . . . . . . . 203
7.3 Single-WallDamageEquations . . . . . . . . . . . . . . . . . . . . . 205
7.4 Multiple-WallDamageEquations . . . . . . . . . . . . . . . . . . . . 208
7.5 HVIShieldDesignsandImplementations . . . . . . . . . . . . . . . 212
7.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
8 OperationalCollisionAvoidancewithRegardtoCatalogObjects 215
8.1 OrbitPredictionandAssociatedUncertainties . . . . . . . . . . . . 215
8.2 DeterminationofNear-MissConjunctionEvents . . . . . . . . . . . 219
8.3 CollisionRiskEstimateforNear-MissConjunctions . . . . . . . . . 222
8.4 StatisticalForecastofAvoidanceManeuverFrequency. . . . . . . . 226
8.5 CollisionAvoidanceforOperationalSatellites. . . . . . . . . . . . . 233
8.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
9 Re-EntryPredictionandOn-GroundRiskEstimation 241
9.1 HistoryofHazardousRe-EntryEvents . . . . . . . . . . . . . . . . . 241
9.2 Long-andMedium-TermRe-EntryPredictions . . . . . . . . . . . . 244
9.3 Short-TermRe-EntryPredictions . . . . . . . . . . . . . . . . . . . . 249
9.4 PredictionofBreak-UpandSurvivalofEntryObjects . . . . . . . . 256
TableofContents vii
9.5 EstimationofOn-GroundRiskDuetoRe-Entries . . . . . . . . . . . 266
9.6 Long-andShort-TermRe-EntryRiskManagement . . . . . . . . . . 272
9.7 HazardousRe-EntryMaterials . . . . . . . . . . . . . . . . . . . . . 285
9.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
10 ModelingoftheTerrestrialMeteoroidEnvironment 289
10.1 TheDivine–StaubachMeteoroidModel . . . . . . . . . . . . . . . . 289
10.2 MeteoroidFluxAssessmentforTypicalTargetOrbits . . . . . . . . 294
10.3 ModelingMeteoroidStreamEvents . . . . . . . . . . . . . . . . . . 296
10.4 Near-EarthObjectsandAssociatedRisks . . . . . . . . . . . . . . . 301
10.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
11 SpaceDebrisActivitiesinanInternationalContext 311
11.1 InternationalForumsforInformationExchange . . . . . . . . . . . 311
11.2 InternationalCooperationataTechnicalLevel . . . . . . . . . . . . 312
11.3 InternationalStandardsandPolicies . . . . . . . . . . . . . . . . . . 313
11.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
Epilog 315
A BasicsofOrbitMechanics 317
A.1 KeplerOrbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
A.2 PlanarOrbitTransferManeuvers . . . . . . . . . . . . . . . . . . . . 321
A.3 ShapeoftheEarthandtheGeodeticPosition . . . . . . . . . . . . . 322
A.4 MajorPerturbationsonEarthOrbits . . . . . . . . . . . . . . . . . . 322
A.5 ThePerturbedNewtonEquations. . . . . . . . . . . . . . . . . . . . 324
A.6 TheGaussPerturbationEquations . . . . . . . . . . . . . . . . . . . 325
A.7 TheLagrangePerturbationEquations . . . . . . . . . . . . . . . . . 326
A.8 IntegratingthePerturbationEquations . . . . . . . . . . . . . . . . . 326
A.9 ResultingPerturbationsonEarthOrbits . . . . . . . . . . . . . . . . 328
A.10References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
B TheAtmosphereoftheEarth 331
B.1 StructureofThermosphereModels . . . . . . . . . . . . . . . . . . . 331
B.2 ImplementationsofThermosphereModels . . . . . . . . . . . . . . 334
B.3 SolarandGeomagneticActivities . . . . . . . . . . . . . . . . . . . . 336
B.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
C TheGravitationalPotentialoftheEarth 349
C.1 MathematicalFormulationoftheGeopotential . . . . . . . . . . . . 349
C.2 HarmonicCoefficientsoftheGeopotential. . . . . . . . . . . . . . . 350
C.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
viii TableofContents
D TheWorldPopulationViewedfromOrbit 355
D.1 ModeloftheWorldPopulationDensityDistribution . . . . . . . . . 355
D.2 SamplingtheWorldPopulationalongGroundTracks . . . . . . . . 356
D.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
E ColorSupplement 371
ListofSymbols 387
ListofAbbreviations 393
ListofTables 399
ListofFigures 401
Bibliography 407
Index 417
Prolog
Mostcolleagueswhoenterthesolemnhallsofspaceflightusethemainentrance,
following the footsteps of generations of famous predecessors in their endeavor
toconceiveandrealizenew,ground-breakingspacemissions. SinceIamdealing
with residues of space flight, sometimes disrespectfully denoted as space junk,
Iapproachedthesesolemnhallsfromthealleyway, throughthebackdoor. This
wasin1978,whenIgotinvolvedinthere-entryassessmentofthereactor-equipped
Cosmos 954 satellite after it spread its radioactive debris across Canada. At that
time almost 6,000 trackable objects were on orbit, with more than 90% thereof
spacedebris. Spacedebrisareuselessspaceobjectsincludingspentorbitalstages,
de-commissioned satellites, items released during nominal missions, and frag-
mentsfromdeliberateandunintentionalon-orbitexplosions,butalsoexoticrelicts
ofspaceactivities,suchasprotectivegloves,orascrewdriverlostbyanastronaut.
The space debris population has steadily increased since the early 1960s. By the
year2005morethan14,000spaceobjectsofdiameterslargerthan5to10cmcould
be tracked, of which no more than 5% were operational spacecraft. With these
numbersinmind,andwith20yearsofinvolvementinthefield,Ifeltthatitwas
time to write a book on space debris, which today represent the overwhelming
majorityofman-madeobjectsinEarthorbits.
Severalyearselapsedbetweenthefirstideasforthisbookanditscompletion.
Notjustthespacedebrisenvironmentitself,butalsotherelatedresearchactivities
undergo a highly dynamic evolution. As a consequence, a book on space debris
runstheriskofbecominginconsistentduringthewrite-upprocess, andobsolete
bythetimeofitspublication.Myintentionwastominimizethisriskbyproviding
a consistent snapshot of the space debris situation around the year 2002, and by
developinganddocumentingatheoreticalbasiswithahopefullybetterdurability
andlongevitythattheenvironmentitself.
This book was written by a single author. In many chapters, however, the
research contributions of several colleagues deserved more than a citation or ac-
knowledgment. Insuchcases,theyhavebeenlistedascontributingauthorsinthe
chapterheadings.
x Prolog
Thisisnotthefirstbookdealingwithspacedebris,norwillitbethelastone.
Therecouldhavebeenmanydifferentwaysofselectingthematerial, ofpresent-
ingit,andofcitingrelevantwork. Whatyouseehereisaverypersonal,probably
unintentionallybiasedpresentationandviewofthesubject,basedoninformation
whichIcollectedduring25yearsofworkfortheEuropeanSpaceAgency,with20
years thereof at the European Space Operations Center in Darmstadt, Germany.
Itwasthisenvironment,andtheprofessionalandpersonallinksandinformation
exchangewithESAcolleagues,andwithcolleaguesoftheEuropeanandinterna-
tionalspacedebriscommunity,whichmadethisbookpossible.Aboveall,Iwould
like to acknowledge the role of Walter Flury, who has led ESA’s space debris ac-
tivities since the mid 1980s. His dedication and enthusiasm helped to advance
spacedebrisresearchinESAandwithinEurope,andithelpedtodevelopaEuro-
peanspacedebrisexpertisewhichtodayhasreachedaninternationallyrecognized
level.
ThecontentofthebookislargelyfocusedonEuropeanactivities,inparticular
onthosewhichwereperformedunderthelead,orwiththeparticipationofESA.
Theviewsexpressedinthistext, however, arethoseoftheauthor, andtheymay
notnecessarilyreflectthoseofESA.Inconsistentorerroneousinformationwhich
maybecontainedinthistextarethesoleresponsibilityoftheauthor.
Thetopicswhichareaddressedinthisbookfollowtheoutlineofagraduate
course on Space Debris which I have given in a curriculum for aeronautical en-
gineers since 2001. I have tried to keep the volume and technical detail of the
presented material at a level which allows this text book to be used for teaching
purposes at graduate level. Worked problems, which would have been helpful
for teaching applications, are not yet contained in this text. They are, however,
foreseenforalaterrelease.
IwouldliketothankthepublishingstaffatPraxisandSpringerfortheiren-
durance, and for their constructive comments and guidance during the prepara-
tion of the manuscript, and during the final typesetting of this book. The type-
setting was done in LATEX, by means of an expert-designed LATEX class-file which
was provided by Clare Martin, one of the contributing authors. Apart from the
contributingauthorsIwouldalsoliketoacknowledgesupport,contributions, or
editorialcommentsfromLudgerLeushacke,ThomasSchildknecht,FrankScha¨fer,
MichaelOswald,SebastianStabroth,GerhardDrolshagen,MichelLambert,Mar-
kusLandgraf,CristinaHerna´ndez,I´n˜igoMascaraque,SantiagoLlorente,Dorothea
Danesy,andTomMohr. TherearemanymoreindividualstowhomIamgrateful,
and who may not recognize themselves in the previous acknowledgments. My
apologiestoallofyou.
Finally, and most of all, I would like to thank my wife Angelika for her pa-
tienceandforhercontinuoussupport.
HeinerKlinkrad
Seeheim-Jugenheim,July2005
1
Introduction
H.Klinkrad
Weseemtoexistinahazardoustime,driftn’alongherethroughspace;
nobodyknowsjustwhenwebegun,orhowfarwe’vegoneintherace.
BenjaminFranklin
1.1 HISTORYOFTHEEVOLVINGSPACEDEBRISRESEARCH
On June 29, 1961, the US Transit-4A satellite was launched from Kennedy Space
CenteronaThor-Ablestarrocket. Thespacecraftwasdeployedintoanorbitalti-
◦
tude between 881 km and 998 km, with an orbit inclination of 66.8 . Transit-4A
wascatalogedbytheFirstAerospaceControlSquadronoftheUSAirForceasthe
116th space object since the launch of Sputnik-1 on October 4, 1957. At 06:08:10
UTC on June 29, 77 minutes after the injection and separation of Transit-4A and
two additional payloads, the Ablestar upper stage exploded, distributing its dry
mass of 625 kg across at least 298 trackable fragments, of which nearly 200 were
stillonorbit40yearslater. Thisfirston-orbitbreak-upeventinspacehistoryin-
creasedtheobservablenumberofman-madespaceobjectsinstantaneouslybyat
leastafactor3.5(PortreeandLoftus,1993). Sincethisdatespacedebrishasbeen
the largest contributor to the observable space object population, with on-orbit
explosionsasitslargestsinglesource.
Thetermsspacedebrisandorbitaldebrisareoftenusedassynonyms, withthe
following definition, as adopted by the Inter-Agency Space Debris Coordination
Committee (IADC): ”Space debris are all man made objects including fragments
and elements thereof, in Earth orbit or re-entering the atmosphere, that are non
functional” (anon., 2002a). According to this definition, 46.5% of the cataloged
space objects prior the Ablestar explosion had already been space debris, for in-
