Radio Science Techniques for Solar System Tests of General Relativity

A White Paper submitted to the Fundamental Physical Sciences Panel

of the 2009 Decadal Survey on Biological and Physical Sciences in Space

By:

Sami W. Asmar1 (contact: asmar@jpl.nasa.gov 818-354-6288) John W. Armstrong1

Neil Ashby2

Peter Bender2

Bruno Bertotti3

William M. Folkner1

Luciano Iess4

Andrea Milani5

Robert Preston1

Paolo Tortora6

Slava G. Turyshev1

James G. Williams1

Xiaoping Wu1

1: Jet Propulsion Laboratory, California Institute of Technology 2: University of Colorado 3: University of Pavia, Italy 4: University of Rome, Italy 5: University of Pisa, Italy 6: University of Bologna, Italy

Figure1:Anillustrationoftherelativistic

Summary ScientistsutilizeradiolinksbetweenspacecraftandEarthorbetweenspacecrafttoexaminechanges in thephase/frequency, amplitude, line‐width, andpolarization, aswell as round‐trip light timeof radio signals to investigategeophysicalphenomenaand for testsof fundamentalphysics including the theory of General Relativity. The BepiColombo Mercury Orbiter Radio‐science Experiment (MORE)teamwillcarryouthighprecisiontestsofrelativisticgravityinthemostdesirable“labora‐tory”inthesolarsystem,thegravitationalfieldoftheSun.Beingtheinnermostplanet,Mercuryisthe idealtestmassforprobinggeneralrelativity.Rangeandrange‐ratemeasurementsfromradiotrack‐inga spacecraft inorbitaroundMercury,with frequent superior solar conjunctions, provides abundant occasions to explore relativistic gravitational effects of thesun inaddition to thestructureof thesolarcorona. Figure 1 illustrates an example of the Radio Science investigations with BepiColombo. Figure 2 illustrates the MORE end‐to‐end instrumentation with two uplink radiosignals transmittedsimultaneously fromaground station and three coherent downlink signals are coherentlyreturnedbackbythespacecraft.

Background General relativity, Einstein’s theory of gravity, has passedeverytesttodate.Theincompatibilityofgeneral relativity and quantum mechanics, however, has led scientists toquestion therangesof theirvalidityandto believe that either one or both will ultimately fail. Furthermore, cosmological observations that the universe undergoes phases of accelerated expansion providecompelling motivationstoseekmoreaccurate bendingofaradiobeamtransmittedby lawsofgravity.Thetheoryofgeneralrelativitywilllikely theMercuryPlanetaryOrbiterandre­require a modification such as the inclusion of a scalar ceivedonEarth. terminthefieldequations.Deviationofthevaluesofthe parameterizedpost‐Newtonian (PPN)parameters from thoseexpected forgeneral relativityat the levelof10–7to10–5arepredicted,asdiscussedinDamourandNordtvedt(1993).Experimentalde‐tectionofviolationsofthetheorywouldhavesignificantimplicationsinphysicsandcosmology.Such experimentsrequiretechnologicaladvanceswhichhavebeenslowandoftenverycostly,withincre‐mentalimprovementstypicallymadeonthetimescaleofadecade.

AuniqueopportunityisavailableviatheEuropeanSpaceAgency’sMercuryPlanetaryOrbiter(MPO), one of two spacecraft comprising the multi‐national BepiColombo mission to Mercury; the second spacecraftisaJapaneseMercuryMagnetosphericOrbiter.ESAselectedtheMOREteamfortheMPO toinvestigaterelevantPPNparameters,solaroblateness,andpossibletimevariationofthegravita‐tionalconstant inadditiontoplanetarygeophysicalobjectives.Toreachorbit in2019,MPOisspe‐cificallydesigned forRadioScienceobservationswith flight instruments contributedby the Italian Space Agency. Compatible Radio Science ground instrumentation is proposed to be provided by NASAviatheDeepSpaceNetwork.

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Scientific Goals and Objectives MORE’sscientificgoalsaretocarryouthighprecisiondynamictestsofrelativisticgravityinanideal laboratoryaswellascharacterizethestructureofthesolarwindinandoutofthesolarecliptic.The conventional framework fordiscussing solar system tests is the post‐Newtonianparameterization. Generalrelativitypredictsdefinitevaluesoftheparametersbutalternatetheoriesofgravitypredict deviations fromthesevalues.Nearlyeverymetric theoryofgravitycan fit into thegeneralized10‐parameter PPN framework except for possible cosmological effects on the gravitational constant (Ashbyetal.,2007).Ofthe10parameters,4areconsideredforimprovementbyMOREtechniques, namelythePPNparametersγ,β,η,andα1.Inaddition,thesolaroblatenesswillbedeterminedwith muchimprovedaccuracy,useful informationwillbeobtainedonthepossiblerateofchangeof the gravitationalconstant,andpropertiesofthesolarcoronawillbemonitoredaccurately.Thustheob‐jectivesoftheMOREinvestigationare: Determineγ toanaccuracyof2×10–6: InthePPNformalismaccordingtoShapiro(1967),Will(1971,1993)andothers,γ isameasureof howmuchspacecurvatureisproducedbyaunitrestmass.Thetheoryofgeneralrelativity,whereγ =1,predicts that a rayof light grazing theSun isdeflectedby1.75arcsecanddelayed in timeby roughly200microseconds.Deflectionanddelayexperimentsplaceconstraintsonγ.Thebestaccu‐racy measured to date for this parameter is 2.3×10–5 from the Cassini experiment (Bertotti et al., 2003).MOREwillachieveanaccuracyforγof2×10–6,animprovementofoneorderofmagnitude. Determineβ toanaccuracyof~3×10–5: Inthesameformalism,β=1forgeneralrelativityandisameasureofthenonlinearityinthesuper‐positionlawforgravity.MOREwillachieveanaccuracyforβof~3×10–5orbetter,whichissignifi‐cantlybetterthanthebestcurrentaccuracyof1.2×10–4(Williamsetal.,2004)whichwasderivedby determiningηandusingtheCassinivalueforγintheη=4β‐γ‐3parameterrelationship. Determineη toanaccuracyofatleast4.4×10–4: Ifgravityisdescribedbyametrictheory,thePPNparameterηisalinearcombinationoftheparame‐tersγandβandequals4β‐γ‐3intheNordtvedtrelationship.Itaddressesthedifferencebetweenra‐dial and transverse stress of gravity and bears on possible strong equivalence principle violation. MOREwillachieveanaccuracyforηof4.4×10–4(Ashbyetal.,2007)topossibly2×10–5(Milanietal., 2002), comparable with or an improvement over the current accuracy of 5×10–4 (Williams et al., 2004). Determineα1toanaccuracyof7.8×10–6: AccordingtoWill(2006),whiletheparametersγandβareusedtodescribe“classical”testsofgen‐eralrelativityandare,insomesense,themostimportant,theyaretheonlynon‐zeroparametersin generalrelativityandscalar‐tensorgravity.Theparametersα1,α2,andα3measurewhetherornot thetheorypredictspost‐Newtonianpreferred‐frameeffects.TheMOREsimulationsbyMilanietal. (2002)achieveadeterminationforthePPNpreferred‐frameparameterα1toanaccuracyof7.8×10–6, asignificantimprovementofthepresentaccuracyof~10–4(Will,2006). Determinethesolaroblatenesstoanaccuracyof4.8×10–9: MeasurementoftherelativisticPPNparameter(suchasβ) is inextricablyconnectedwiththesolar quadrupole moment J2, which contributes, just as the relativistic corrections do, to the advance of Mercury’sperihelion.However,forsolarstudies,itisreasonabletoalsoconsidertheaccuracywith

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whichJ2canbedeterminedifgeneralrelativityisassumedtobecorrect.TheexpectedaccuracyforJ2 willprovideinformationaboutthedifferentialrotationofthesolarcoreandwillberelevanttobetter understandingofthestructureofthedeepinterioroftheSun.MOREwilldeterminethesolaroblate‐nessinadynamicalmeasurementtoanaccuracyof4.8×10–9,muchmoreaccuratethanthepresent estimateof4×10–8(Milanietal.,2002). Testanytimevariationofthegravitational“constant,”G,toanaccuracyof3×10–13peryear: Alternatetheoriesofgravityincludecosmologicallyevolvingscalarfieldsthatleadtotimevariability offundamentalphysicalconstantssuchasthegravitationalconstant,G.Lunarlaserrangingexperi‐mentshaveplacedlimitsonvariationof G /G =(4±9)×10–13peryear(Williamsetal.,2004),making theuncertainty9×10–13. Before this resultwasobtained, Will (1993) summarized recent classical testsofpost‐Newtoniangravityandtheimprovedobservationalconstraintsontimevariationofthe gravitational constant first by ranging measurements to the Viking spacecraft at Mars, lunar laser rangingmeasurements,andpulsar timingdataandquotesasuggestionbyBenderetal., (1989)of thepossibilityofreachinganaccuracyoftheorderof10–14peryearforaMercuryorbiterwithrang‐ingaccuracyoftheorderof20cm.MOREwillimproveontheconstraintsfordetectingavariationof thisfundamental“constant”toanaccuracyof3×10–13peryearfromoneyearofmeasurements,and willprovideanindependentcheckofthelunarlaserrangingresult;after2years,theaccuracywould improveto1×10–13peryear. Characterizethesolarcorona: During therelativityobservations, theEarth‐spacecraft line‐of‐sightnecessarilypassesclose to the Sun.Astheradiobeamspropagatethroughthesolarcorona,informationaboutthenear‐Sunplasma isimposedontheradiosignals.Theseradio‐wavepropagationeffectsarenoisefortheMORErelativ‐ityobservationsandwillbeestimatedandlargelyremovedusingthesophisticatedMOREradiosys‐tem(spacecraftandDSNcomponents).Toimplementtherequiredcalibration,however,theplasma effectswillbeknownwithexcellent accuracy.Thispresentsanopportunity touse the radio‐wave scintillations for science: the radio measurements contain near‐sun plasma information on spatial andtemporalscalesthatcannotbemeasuredbyothertechniques.

Comparison with Other Experiments Dedicatedmissions to study relativisticgravityhavebeenproposed in thepast (e.g.,Benderetal., 1989)butrecentsimulations(Milanietal.,2002,Ashbyetal.,2007) indicatedthatprecisionradio trackingofaspacecraftinsertedinacircularorbitaroundMercurycouldleadtoanimprovementin thedeterminationofmanyPPNparameters.Testingrelativisticgravitywasrecognizedasacrucial scientificobjectiveofBepiColomboattheinceptionoftheproject,althoughitisprimarilyaplanetary mission. The Ka‐band Transponder and accelerometer instruments will allow the MORE team to carryoutmanyclassicaltestsofrelativityinthebestdynamicsolarsystemconditions.Testinggen‐eralrelativity,however,shouldnotbeviewedasaracebetweenmissions.Eachexperimentalresult, with important implications inphysicsandcosmology,would requireconfirmationbyothermis‐sionsandthesciencecommunitybenefitsfrommultipleinvestigationsinthisfield. Cassini Launched in1997, theCassinimissiontoSaturnhada longcruiseperiodduringwhicharelativity experimentwascarriedoutduringthesolarconjunctionperiodof2002.RadiosciencedataatX‐and Ka‐bands were acquired at the DSN’s station equipped for precision measurements at Ka‐ and X‐bands forapproximatelyonemonthcenteredonthesolarconjunctionwheretheminimumimpact parameterwas1.6solarradii,andnooccultationbytheSun.Theexperimentwascarriedoutusing

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containing four veryprecise gyroscopes, sought precessionofagyroscope’sspinaxisasthe

measurementcanbecastintermsofPPNparameters. isexpectedtodetermineγwithsubstantiallybetter

Doppler (range‐rate)observations, amethod that hadnot beenuseduntil Cassini for suchexperi‐ments because of the overwhelming noise contribution of the solar corona. Cassini overcame this limitationbyaugmentingthestandardX‐bandlinkwithahighfrequencyKa‐bandlink,providinga multi‐frequencylinksystemthatcalibratedandremovedtheeffectofthesolarcorona.Thiscapabil‐itywasenabledonCassinibyaKa‐bandTranslatorpayloadprovidedbyASI(differentdesignfrom the MORE Ka‐band TransponderalsoprovidedbyASI). Theexperiment determined, in agreement withgeneralrelativity(Bertottietal.,2003),theparameterγ=1+(2.1±2.3)×10–5. GravityProbeBGravityProbeB (GPB),apolarorbitingspacecraftdirectmeasurementofthegeodeticandframe‐draggingspacecraftorbitsthespinningEarth.TheGPBThefinalresultsarenotyetavailable,butMOREaccuracy. MESSENGER The MESSENGER mission’s published science objectives (Solomon et al., 2001) do not include determinationofPPNparametersor J2of theSun. MESSENGER is equipped with only one radio link (X‐band) so precision measurements would be severely degraded by the un‐calibrated noise on Doppler and range from the solar corona. The absence of an accelerometer further limits the necessary precision calibration of non‐gravitationalforcesactingonthespacecraft. LunarLaserRangingWilliamsetal.(2004)reportedanalysisoflaser rangestotheMoonthatprovideincreasingly stringentlimitsonanyviolationoftheEquivalence Principleandalsoenableveryaccuratetestsof relativisticgravity.Theyreportavalueforthe StrongEquivalencePrincipleviolationparameterη of(4.4±4.5)×10–4.Williamsetal.(2004)also Figure2:MOREend­to­endinstrumentation:

reportedthesearchforatimevariationinthe twouplinkfrequencies(X­bandandKa­band) aretransmittedsimultaneouslyfromaground gravitationalconstantresultsin G /G =(4±9)× stationandthreecoherentdownlinksignals

10–13peryear.Furthermeasurementswith arecoherentlyreturnedbackbythespacecraft.improvedaccuracyinthenext5to10yearsappear likelytoimprovetheaccuraciesbyfactorsofroughly3to5. Gaia Tobelaunchedin2011,Gaiawillchartathree‐dimensionalmapofourgalaxyandprovideunprece‐dentedpositionalandradialvelocitymeasurementswiththeaccuraciesneededtoproduceastereo‐scopicandkinematiccensusofaboutonebillionstars.Additionalscientificproductsincludeanum‐berofstringentnewtestsofgeneralrelativityandcosmology.Gaiaisexpectedtoprovideaprecision of γ of1×10–6 (Mignard2009), an improvement approaching twoorders‐of‐magnitudebetter than thecurrentbestestimate(Bertottietal.,2003).Gaia,however,willnotaddresstheotherMOREsci‐enceobjectives.

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Conclusion and Goals

TheBepiColomboMercuryOrbiterRadio‐scienceExperimentteamwillcarryouthighprecisiontests ofrelativisticgravity in themostdesirable laboratory in thesolarsystem, thegravitational fieldof theSun.General relativitypredictsdefinitevaluesof thePPNparametersbutalternate theoriesof gravity predict deviations from these values. Of the 10 parameters, 4 are considered for improve‐mentbyMOREtechniques,namelythePPNparametersγ,β,η,andα1.Inaddition,thesolaroblate‐nesswillbedeterminedwithmuch improvedaccuracy,useful informationwillbeobtainedon the possiblerateofchangeofthegravitationalconstant,andpropertiesofthesolarcoronawillbemoni‐toredaccurately.TestingrelativisticgravitywasrecognizedasacrucialscientificobjectiveofBepiCo‐lombo; the Ka‐band Transponder and accelerometer instruments enable many tests of relativity. Testinggeneralrelativityshouldnotbeviewedasaracebetweenmissionssinceexperimentalresult, withimportantimplicationsinphysicsandcosmology,wouldrequireconfirmationbyothermissions and the science community benefits from multiple investigations in this field. With BepiColombo, comparableaccuracieswouldbeachievedwithquitedifferenttypesofmeasurementsforγ,β,η,and G /G ,andtheaccuracyforJ2oftheSunwouldbeimprovedbyasubstantialfactor. Thegoalofthiswhitepaperisinformthecommunityoftheplannedexperimentsandseekcontinued supporttoenablethem.TheteamintendstoseekNASAsupportforparticipationintheseimportant investigations with the range and range‐rate radio tracking with the instrumentation of the Deep SpaceNetwork.AproposedadvancedranginginstrumentfordualX‐andKa‐bandwidebandcoher‐entlinksandexpandedKa‐banduplinkcapabilitythroughoutthenetworkwouldincreasethesensi‐tivityandexperimentcoverage. Acknowledgements:ThisworkwascarriedoutinpartattheJetPropulsionLaboratory,CaliforniaInstituteof Technology,undercontractwiththeNationalAeronauticsandSpaceAdministration. References • Ashby,N.,P.Bender,andJ.Wahr,“FuturegravitationalphysicstestsfromrangingtotheBepiColomboMer‐

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Nature,425,374,2003. • Damour,T.andK.Nordtvedt,“GeneralRelativityasaCosmologicalAttractorofTensor‐ScalarTheories,”

PhysicalReviewLetters,70,no.15,1993. • Mignard,F.,IAUSymposium261,VirginiaBeach,VA,USA,April2009 • Milani,A.,D.Vokrouhlicky,D.Villani,C.Bonanno,andA.Rossi,“TestinggeneralrelativitywiththeBepiCo‐

lomboradioscienceexperiment,”PhysicalReviewD,66,2002. • Shapiro,I.I.,Science157,806−808,1967. • Solomon,S.C.,etal.,“TheMESSENGERmissiontoMercury:Scientificobjectivesandimplementations,”

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