decay of debris in geostationary transfer orbit

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Page 1: Decay of debris in geostationary transfer orbit

Adv. Space Res. VoL II. No. 6,pp. (6)161 —(6)166, 1991 0273—I 177/91 $0.00 + .50Printed inGreatBrnain.Mi rightsrescrve~ Copyright C 1991 COSPAR

DECAY OF DEBRIS IN GEOSTATIONARYTRANSFERORBIT

GuyJaninEuropeanSpaceOperationsCentre,Robert-Bosch-Slrasse5, 6100Darmstadt,FR.G.

ABSTRACT

Thispaper reports on somecurrent djfJIculties encounteredin theprediction of the re-entry ofobjectson highlyeccentricorbits. Concernedhereareuncontrolledobjectsusuallycalleddebris.After recalling the importanceoffollowing the orbital evolutionof spacedebris, the particularcaseof debrison GeostazionaryTransferOrbits is treated. A ithough third bodyperturbationisthe mainperturbationin this typeoforbit, it will be shownhow the atmosphericdrag, acting atperigee,may considerablychangethe evolutionof the orbit. Theprediction ofre-entry dateofa debrison a high eccentricityorbit is usually rather accurate. For GTOhowever,the effectofthe dragat perigeemay rendertheprediction totally uncertain. This is illustratedin an exampletakenfrom the recentre-entryof thefirst Ariane launchpayload.

1. SPAcEDEBRIS

It is convenientto cover under the nameof space debris thoseobjectsgravitatingin spacehavingno defmedfunction, like deadsatellites,upper rocket stages,residualof disintegratedsatellitesor rocket stages,releasedadapters,appendagesand instrumentcovers,paint flakes,etc. The characteristicsof spacedebrisare:I their orbit canbe determinedonly by activemeans(radar)or opticalobservation(visual

observation,photographiccameraor CCD sensor);

2. shape,massandattitudeare poorlyor evennot atall known.

This implies that considerablemeanshaveto be used for tracking spacedebrisandstill manyobjects escapecataloguing. This is particularly true for small objects of size less thanacentimetre,whichpopulationcan only be speculated.

The debrispopulation is evolving: dueto collision betweendebris,newdebrisof smaller sizearecreated,while atmosphericfriction burns low altitudedebris.

It hasbeenshown(Ref. /1./) that, dueto the largenumberof debrisin space,the probabilityof collision of adebriswith an activesatellite is no morevanishinglysmall. This is particularlytrue for largeobjectsin orbit like aSpaceStationandobjectsconfinedin aparticularorbit likethe geostationaryring. Aiso, the re-entryof debrisinto the Earthatmospheremay causeahazardto the humanpopulation,particularlywhen largeobjects,like 10-20 tons surveillancesatellites or spacelaboratories(Skylab), are concerned. Some of thesesatellitesmay evencontaina nuclearreactor,which increasesthere-entryhazard.

This meansthat the investigationof the orbital behaviourof spacedebris is now aproblemnf im.,cwtnn,-e~ T’iis.~+,, ~ ~ ~+ ~,..l,,,, .~ ~ f,~,.4~ 4f~~

Page 2: Decay of debris in geostationary transfer orbit

(6)162 G. Janin

2. ORBITS OF SPACEDEBRIS

It is convenientto classifydebrisorbits in threecategories:

I. Low EarthOrbits (LEO)2. Highly EccentricEarthOrbits (}IEO)3. GeosynchronousEarthOrbit (GEO)

Orbital behaviourof debris in LEO andGEO havereceivedmostattentionup to now. ForLEO, wherethe dominatingperturbingforceis the atmosphericdrag, ratherelaboratemodelsof the air densityare available. Still hazardousis the predictionof the solar activity whichstrongly influencestheupper atmospheredensity.

The behaviourof objectsin the geostationaryring is well knownandperfectlypredictable. Inorderto preventcrowding in the geostationaryring, a re-orbitingprocedureis recommendedfor satellitesatthe endof their operationallife, consistingof raisingthe orbit by afew hundredkm. This shouldpreventcollisions with activesatelliteson the geostationaryring.

Spacedebrison HEO haveup to now receivedlittle attention. Although their numberisconsiderable(all launcher’supperstageon OeostationaryTransferOrbit (GTO) for instance),theseobjectsaregenerallythoughtto be harmless.

Other spacedebrisare orbiting aroundthe Sun or around othercelestial body of the solarsystemor alonginterstellartrajectories. They will not bediscussedhere.

3. DEBRIS ON HIGHLY ECCENTRICORBIT’S

To be consistentwith precedingstudies(/2.!), an orbit is consideredas highly eccentricwhenits eccentricityis largerthan 0.7. Objectsin GTO (e= 0.73)enterthereforein this category.Most other satelliteson highly eccentricorbits are scientific sateffites,whoseeccentricitycanreachandevenexceed0.9. Their decayhavealreadybeendiscussedin a former paper(Ref./2./).

Third-bodyPerturbation

The dominatingperturbationin highly eccentricorbits is the third-bodyperturbationfrom theSun and the Moon. From the sole study of this perturbationonecan predict the generalbehaviourof objectsin HEO. Thisbehaviouris characterisedby:

1. little or no effect on the semi-majoraxis;

2. astrongfluctuationof the eccentricity:a long periodic (quasisecular)fluctuationduetothe perturbationof the Sun superposedby a short periodic fluctuationof smallamplitudeby the Moonperturbation;

3. a smallvariation of the angularelements.

The fluctuation in eccentricity translatesinto an increase(positiveor negative)of the perigeeheightanda correspondingdecreaseof the apogeeheight.

An approximatedexpressionof the rateof changefor theorbital elementscanbe obtainedbyexpandingthe disturbingforce in power of the ratio of the orbital radius vector over thethird-body radiusvector in the Lagrangeplanetaryequations. The long-termbehaviourcanbe estimatedby consideringonly the first ordertermsandby averagingthe equationsover onerevolutionof the satellitewhile keepingthe positionof the third-bodyfixed. By asecondav-eraging,this time over one revolutionof the third-bodysupposedto be on acircular orbit ofradiusr1, the following result is obtainedfor the variationof the perigeeradiusôr~(Ref. /3./):

~5r~=~

Page 3: Decay of debris in geostationary transfer orbit

Decayof Debrisin GTO (6)163

perigeeis located. When the perigeeis in the first or third quadrantits height decreasesandmaylead to orbitaldecay.

Due to the rotation of the argumentof perigee inducedby ‘the oblatenesperturbation,theoverall behaviourof theperigeeheightduringa long period cannotbe simplypredicted.

If atacertaintime the perigeefalls belowthe Earthsurface,the satellitedecays. As third-bodyperturbationsareof periodic nature,the occurrenceof suchan event is mostlikely. Its timescaleis usually of a few yearsbut canreachhundredsor eventhousandsof years. However,onecan generallysaythat spacedebrisin highly eccentricorbitsare not alongterm problem.

As debrison HEO aremostlyupperstagerockets,thereforeratherlarge objectswith massiveparts (propulsionunit), it is of interestto be able to exactly predicttime andlocationof theirre-entrypoint. If third-body perturbationwould be the only perturbation,this predictioncould be madeas accurateas needed,providinggood observationsof the objectsareavailable.Unfortunately,whenthe perigeereachesthe Earthatmosphere,drag effectsenterinto consid-erationsandintroduceuncertaintiesin the re-entryprediction.

3. THE EFFECTOF ATMOSPHERICDRAG FOR THE RE-ENTRY PREDICTIONOF OBJECTSON HIGHLY ECCENTRICORBITS

When, due to the luni-solar perturbations,the perigeeheight decreasesand reachesthe at-mosphere,thedragperturbationbeginsto play its role: to decreasetheorbitalenergy,thereforethe semi-majoraxis. The perigeeheight itself is not affectedbut the apogeeheightdecreases.This introducestwo changesin the orbital behaviour:

1. the luni-solareffect is reduced;2. the rotationof the argumentof perigeeis reduced.

Changenumber I dampsthe perigeeheight motion. If for instancethe perigeeheightwastofurtherdecreaseby aspecific distance,it will actuallydecreaseby asmallerdistance.This mayparadoxicallyincreasethe lifetime of the satellite. I lere is an exampleof drag perturbationhelping to postponethe decayof a satellite

Changenumber 2 maymodify completely the orbital behaviour. As the third-bodypertur-bationis dependentin theargumentof perigee,achangein its ratemayafteratimereversetheperigeechangedirection.

In conclusion,to add drag perturbationto third-body perturbationmakes orbital evolutionpredictionhazardous,evenmorehazardousthanin the caseof anear-Earthsatellite.

Theparticular caseofthe GTO

A typical perigeeheight history of an objecton GTO submittedonly to third-bodyperturba-tion is shown on Fig. 1. The amplitudeof the perigeeheight oscillation is relatively small:±50km averagewith some peaksof 75 km. I)ue to the low initial perigeeheight of thelauncher’sdelivery orbit, this meansthat theperigeeheightis practicallyall the time insidetheEarthatmosphere.Thedragperturbationis thereforeactive at everyrevolution.

It is well known that theestimationof the dragperturbationis adelicatematterbecauseof theuncertaintiesattachedto the knowledgeof the atmosphericdensityandthe importanceof thesatellite’scrosssectionalarea,poorly known for uncontrolledobjects. But in thecaseof GTO,an additional difficulty appears:the irregularities in the perigeeheight motion. Decaypredic-tion are thereforeextremelyuncertain,as it will be illustratedin the following example.

4. THE CASE OF THE RE-ENTRY OF CAPSULEARIANE TECHNOLOGIQUE 1

A NumericalToolfor GTO DecayEstimation

Page 4: Decay of debris in geostationary transfer orbit

(6)164 G.Janin

debris,excludingthe resultof the explosionof an Arianethird-stageon anear-Earthorbit, arelocatedon the GTO. Object 1979-104A (CAT-I, CapsuleAriane Technologique1, payloadof the first Arianelaunch)belongedto them. CAT-l is composedof a 217 kg technologicalcapsuleanda 1385 kg ballast. The meancrosssectionalareais about 1.5 squaremeter. Thisobjecthas thereforearelatively low ballistic coefficient.

This payloadwas launchedon December24, 1979. Its perigeeheighthistory, underthe soleinfluenceof the luni-solar perturbations,is shownin Fig. I.

This history hasbeenestimatedusingasemi-analyticmethod:the StroboscopicMethod(Ref./ 4./). As long as the perigeeis aboveseveralhundredof km from the Earth surface,suchamethodallows to predictthe orbitalbehaviourwith very good accuracy(seediscussionin Ref./2./). But whentheperigeeheightreachesthe densepart of the atmosphere,amore accuratemethodhasto beused.

In orderto eliminatepossibleuncertaintiesdueto the useof methodbasedon analyticalap-proximations,a precise numericalintegrationschemewas set up with the help of the toolUSOC(Unified Systemfor Orbit Computation,see Ref. /5./). The orbit computationwasdivided in two phases.The following numericalcomponentswerechosen:

• PhaseI, propagationunderluni-solaranddragperturbation:

1. as high accuracyis neededfor relatively shortterm orbit propagation(afew hundredof revolutions),aformulation in termsof orbital elementsis not necessaryanddif-ferentialequationsin Cartesiancoordinateswere taken. However,as theorbit is ec-centric,atransformationof theindependentvariablein oneof the classicalanomaliesis needed.Amongthe four anomaliesofferedin celestialmechanics(mean,eccentric,elliptic andtrue anomaly),the true anomalygives the highestdensityof integrationstepsaroundperigee. In orderto havea goodestimationof thetime, atime elementwas added. Suchaformulationis discussedin Ref. /6.!.

2. As manyrevolutionshaveto be integrated,an efficient 8th ordermultistepintegratoris chosenwith acorresponding8th order Runge-Kuttamethodas a starter.

3. The air densitymodel is a Jacchia-Lineberrymodel,dependingon themeananddaily10.7 cm solar activity flux and geomagneticindex. This densitymodeloffers highaccuracywhile keepingcomputationoverheadat a reasonablelevel. The solarac-tivity parametersare takenout of a tableof actualor predictedvalues.

4. For the potentialof the Earth,only the .12 termis taken,the highertermsdo not playa significant role for orbital decaystudies.

• Phase2, the final revolutionswith vanishingthird-body perturbationand heavyatmo-sphericdrag:

1. As theorbit is still eccentric,the sameformulation as in Phase1 is chosen,howeverwithoutthe timeelement.

2. As the atmosphericdragperturbationcan havean extremelyhigh magnitude,largerthanthe centralbody attraction,the fixed stepsize integrationhasto be substitutedby a more flexible integrationwith adaptive stepsize regulation:a Runge-Kutta-Fehlberg7/8 methodhasbeenchosen.

3. An air densitymodelextendedtowardthe Earthsurfaceuntil altitude zeroby an ex-ponentialmodel is neededfor this phase.

TheRe-entryofCAT-I

The tool describedhereaboveallowsefficient, fast andprecisenumericalintegrationof orbits.It was appliedto the caseof CAT-i. As initial value,NASA 2-lineelementsweretaken. Thetransformationof 2-line into osculatingelements,neededfor the numericalintegration,wasperformedby usingprogramSDP4. This programis recommendedby the US SpaceCom-mand - producingthe 2-line elements,which aredoubly averagedmodified Brouwerelements- for handlinghighly eccentricorbits.

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DecayofDebrisin GTO (6)165

Actual re-entryoccurredon November27, 1989. The resultof the May 1989 run was totallyerroneous.

The run wasagainperformedrecently,with the measuredvaluesof the solaractivity parame-ters(seeFig. 2 and3 respectivelyfor the perigeeandapogeehistory). This time re-entrywascalculatedto be on April 10, 1990. This showsthat the solar activity was underestimatedinthe May 1989 computation,but still a largediscrepancysubsisted. Therewas no way to ex-plain it, until the validity of the 2-line elementsthemselveswasput underscrutiny.

TheAccuracyof2-line Elementsfor GTOOrbits

Indeed,by decreasingthe perigeeheight of the initial osculatingelementsresultingfrom the89-04-042-line elementsby 8 km, the actual re-entrypatterncould be approximatelyre-produced(seeFig. 4 and 5 illustrating the correspondingperigeeandapogeehistory).

The inaccuracyof the 2-line elementsis in fact not so surprisingfor suchanorbit. The epochcorrespondsto true anomaly 1110 when the satellite is at an altitude of 13000km. This isprobablythelast contactpoint of a seriesof radarobservationsdedicatedto thistarget. Radarobservations,quite accuratefor near-Earthorbits, areapparentlyno more so reliableat suchdistances. 2-line elementsfor this type of orbit havethereforeto beusedwith precaution.

The only outlook for improvingthe situationis to haveaccessto the raw radardata in orderto extractthe maximumamountof informationfrom the observations.The analysisof thesignal signaturewould alsogive someclue on the satellite’sattitude.

6. CONCLUSION

Orbit computationof debrisdecayon GTO aresubjectedto numerousuncertainties:

• theperigeeheightis oscillatingwith an irregularamplitu(leof ±50kin average.• the drag,operatingat perigee,is subjectedto an uncertaintydueto the inaccurateknow-

ledgeof the atmosphericdensity.• the cross-sectionalareaof the debris, which is usually an elongatedcylinder, is poorly

knowndueto theabsenceof observationon the attitudemotion.• the only regular sourceof informationon orbital debriselementsare the NASA 2-line

elements.They arefound to be of insufficient accuracy.

This rendersthe decayprediction of GTO debris hazardous,even if state-of-the-artorbitpropagationmethodsareused.

5. REFERENCES

I. Space Debris, A Reportfrom the ESA SpaceDebris Working Group, ESA SP-llO9(1988).

2. G. Janin& E. A. Roth, Decayof a Highly EccentricSatellite, C’el Mech. 14 pp. 141-149(1976).

3. E. A. Roth, Evolution of the TransferOrbit to theSynchronousFleight and PreliminaryLaunchWindow Studyfor the PassengerSatelliteof the Ariane Vehicle, ESOCInternalNote 156, ESA/ESOC(1974).

4. E. A. Roth, MissionAnalysisfor TerrestrialSatelliteand PlanetaryOrbiters,with SpecialEmphasison Highly EccentricOrbits: 1. The MathematicalBackground,ESAJour.Vol1(1977).

5. G. Janin& M. Bello-Mora, A Flexible Tool for the Calculationof Orbits in the SolarSystem,Ad;’. SpaceRes.Vol. 10, No. 3-4, pp. (3)327-(3)330(1990).

6. 0. Janin & V. R. Bond, A GeneralTime Element for Orbit Integrationin Cartesian

Page 6: Decay of debris in geostationary transfer orbit

(6)166 0. Janin

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FIG. 1. CAT-I perigeeheighthistory

undertheinfluenceof third.bodyperturbation

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FIG. 2. CAT-I perigeeheighthistoryprediction FIG. 3. CAT-I apogeeheight historypredictionbasedon 89-04.042-lineelements basedon 89-04.042-lineelements

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FIG. 4. CAT-i last8 monthsactualperigeeheight history FIG. 5. CAT-I last 8 months actualapogeeheighthistory