Evidence of the gravitomagnetic field of Mars

1、evidence of the gravitomagnetic field of mars according to general relativity, the gravitomagnetic lense-thirring force of mars would secularly shift the orbital plane of the mars global surveyor (mgs) spacecraft by an amount of 1.5 m, on average, in the cross-track direction over 5 years. the deter

2、mi 6 2 n ju 1 2 1 v2 9 6 6 / c q - r :gv i x r aevidenceofthegravitomagnetic eldofmarslorenzoioriovialeunitadiitalia68,70125bari,italytel./fax00390805443144e-mail:lorenzo.ioriolibero.itabstractaccordingtogeneralrelativity,thegravitomagneticlense-thirringforceofmarswouldsecularlyshifttheorbitalplaneo

3、fthemarsglobalsurveyor(mgs)spacecraftbyanamountof1.5m,onaverage,inthecross-trackdirectionover5years.thedeterminedcross-trackpost- tresidualsofmgs,builtupbyneglectingjustthegravitomagneticforceinthedynamicalforcemodelsandwithout ttinganyempiri-calcross-trackaccelerationwhichcouldremovetherelativistic

4、signal,amountto1.6m,onaverage,overa5-yearstimeintervalspanningfrom10february2000to14january2021.thediscrepancywiththepredictionsofgeneralrelativityis6%.keywords:generalrelativity;lense-thirringe ect;marsgravity eld;marsglobalsurveyor;out-of-planepartoftheorbit1introductioninthiscommunicationwepropos

5、etoexplaincertainmeasuredfeaturesof thepathofthemartianorbitermarsglobalsurveyor(mgs)(konoplivetal.2021),whoseorbitalparametersarequotedintable1,withtheactionofthegeneralrelativisticgravitomagneticforceonthespacecraft.ifcon rmedbysubsequent,dedicatedanalysesitwouldbe,ingeneral,the rsttestofgeneralre

6、lativityinthegravitational eldofasolarsystembodyotherthanthesunandtheearthand,inparticular,the rstindependenttestofthelense-thirringe ectwithrespecttothoseconductedsofarwiththelageossatellitesintheearthsgravitational eld(iorioandmorea2021,ciufoliniandpavlis2021,iorio2021). 1 according to general rel

7、ativity, the gravitomagnetic lense-thirring force of mars would secularly shift the orbital plane of the mars global surveyor (mgs) spacecraft by an amount of 1.5 m, on average, in the cross-track direction over 5 years. the determi 2thelense-thirringe ect wheregisthenewtoniangravitationalconstant,s

8、isthespinangularmomentumofthecentralbodywhichactsassourceofthegravitational eld,cisthespeedoflightinvacuum,a,eandiarethesemimajoraxis,theeccentricityandtheinclinationoftheorbitalplanetothecentralbodysequator,respectively.ingeneral,thegravitmagneticforcea ectsthein-planealong-trackandtheout-of-planec

9、ross-trackpartsoftheorbitofathetestparticle.indeed,theshiftsalongtheradialr,along-tracktandcross-trackndirectionscanbe,ingeneral,expressedintermsofthekeplerianorbitalelementsas(christodoulidisetal.1988) r=, 2 t=a m+ +cosi +2 2 e2 1+2+(sini ), (2) wheremisthemeananomaly.thelense-thirringshiftsare,thu

10、s rlt=0, tlt=a2( lt+cosi lt), n=asini .lt2ltthelense-thirringe ectconsistsoftinysecularprecessionsofthelongitudeoftheascendingnode andtheargumentofpericentreofatestparticlefreelyorbitingacentralrotatingbody.theyare(lenseandthirring1918;barkerandoconnell1974;so el1989;ashbyandallison1993;iorio2021) 2

11、gs lt=(1) ,c2a3(1 e2)3/2(3) foranearpolarsatellitelikemgsonlytheout-of-planeshift nltispresent. 2 according to general relativity, the gravitomagnetic lense-thirring force of mars would secularly shift the orbital plane of the mars global surveyor (mgs) spacecraft by an amount of 1.5 m, on average,

12、in the cross-track direction over 5 years. the determi table1:orbitalparametersofmgsanditslense-thirringprecession.altisisthesemimajoraxis,iistheinclination,andeistheeccentricity. thegravitomagneticnodeprecessionand nlt istheaverageout-of-planegravitomagneticshiftover veyears. 33.8(masyr 1)3792.42(k

13、m)92.86(deg)0.00851.5(m) itcomesfroms=mr2(2/t),wherethepolarmomentis=c/mr2=0.3654(konoplivetal2021)andthesiderealrotationperiodist=1.02595675d(seidelmann1992).2theformulasofeq. (1)holdinaframewhosereferenceplaneisthecentralbodysequator.thisisjustthecasebecausethemarsequatoristiltedonlyby1.7degtothee

14、arthsequator,whichisthereferenceplaneoftheframeusedintheanalysisof(konoplivetal.2021).indeed,theobliquityofmarsandtheearthamountto25.2degand23.5degrespectively.1 3 according to general relativity, the gravitomagnetic lense-thirring force of mars would secularly shift the orbital plane of the mars gl

15、obal surveyor (mgs) spacecraft by an amount of 1.5 m, on average, in the cross-track direction over 5 years. the determi figure1:orbitoverlapdi erences(10february2000-14january2021)fortheout-of-planedirection(dataprovidedbya.konopliv,2021).theaverageamountsto1.6m:theaveragelense-thirringout-of-plane

16、shift,overthesametimespan,is1.5m. 4 according to general relativity, the gravitomagnetic lense-thirring force of mars would secularly shift the orbital plane of the mars global surveyor (mgs) spacecraft by an amount of 1.5 m, on average, in the cross-track direction over 5 years. the determi shifted

17、by3mbythegravitomagnetic eldofmars,aquantitywhichfallswithinthereachedorbitaccuracy.theaveragedlense-thirringshiftover veyearsisthus1.5m. tocorroboratethisinterpretationofthedata,itisimportanttonotethatinthesuiteofdynamicalforcemodelsusedtoreducethegatheredobserva-tionsgeneralrelativityis,infact,pre

18、sent,butonlywiththegravitoelectricschwarzschildpart:thegravitomagneticlense-thirringpartisnotincluded,sothatitisfullyaccountedforbytheshowedresiduals.moreover,noem-piricalout-of-planeaccelerationswere ttedinthedatareductionprocess;thiswasdoneonlyforthealong-trackcomponentofmgsorbittoaccountforothern

19、on-gravitationalforceslikethermal,solarradiationpressureanddragmismodelling.thus,itisunlikelythattheout-of-planelense-thirringsignalwasremovedfromthedataintheleast-squareprocedure.moreover,iftherelativisticsignaturewasremovedsothatthedeterminedout-of-planeresidualswereonly(ormainly)duetoothercausesl

20、ikemismodellingorun-modellinginthenon-gravitationalforces,itisdi culttounderstandwhythealong-trackresiduals(middlepaneloffigure3of(konoplivetal.2021)havealmostthesamemagnitude,sincethealong-trackcomponentofthemgsorbitismuchmorea ectedbythenon-gravitationalaccelerations(e.g.theatmosphericdrag)thanthe

21、out-of-planeone. 4conclusions inthiscommunicationweshowedthatthegeneralrelativisticgravitomag-neticlense-thirringe ectcanaccommodate94%ofthe1.6maverageerrorinthedeterminedout-of-planeorbitresidualsofthemartianorbitermgs.thecollectionandtheprocessingofmoredatafrommgs,odysseyandtherecentlylaunchedmros

22、pacecraftwillbeoftheutmostimportanceincorroboratingsuchtest.forexample,thedopplertrackingdatafromthemarsexplorationrover(mer)toodysseywillimprovethedetermina-tionofjusttheout-of-planeportionoftheodysseyorbit.anindependentcheckwhichcould,andshould,bedoneistoproduceaparticularsolutioninwhichitisalsoin

23、troducedaparameterwhichexplicitlyaccountsforthelense-thirringe ectandsolveforit. acknowledgments igratefullythanka.konopliv,nasajetpropulsionlaboratory(jpl),forhavingkindlyprovidedmewiththeentiremgsdataset.iamalso 5 according to general relativity, the gravitomagnetic lense-thirring force of mars would secularly shift the orbital plane of the mars global surveyor (mgs) spacecraft by an amount of 1.5 m, on average, in the cross-track direction over 5 years. the determi gratefultoh.lichteneggerforhiskindhospitalityatoa