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

2TheLense-Thirringe ect

whereGistheNewtoniangravitationalconstant,Sisthespinangularmomentumofthecentralbodywhichactsassourceofthegravitational eld,cisthespeedoflightinvacuum,a,eandiarethesemimajoraxis,theeccentricityandtheinclinationoftheorbitalplanetothecentralbody’sequator,respectively.Ingeneral,thegravitmagneticforcea ectsthein-planealong-trackandtheout-of-planecross-trackpartsoftheorbitofathetestparticle.Indeed,theshiftsalongtheradialR,along-trackTandcross-trackNdirectionscanbe,ingeneral,expressedintermsoftheKeplerianorbitalelementsas(Christodoulidisetal.1988)

R=, 2 T=a M+ ω+cosi +2 2 e2 1+2+(sini ),

(2)

whereMisthemeananomaly.TheLense-Thirringshiftsare,thus

RLT=0, TLT=a2( ωLT+cosi LT), N=asini .LT2LTTheLense-Thirringe ectconsistsoftinysecularprecessionsofthelongitudeoftheascendingnode andtheargumentofpericentreωofatestparticlefreelyorbitingacentralrotatingbody.Theyare(LenseandThirring1918;BarkerandO’Connell1974;So el1989;AshbyandAllison1993;Iorio2001) 2GS˙ LT=(1) ,c2a3(1 e2)3/2(3)

ForanearpolarsatellitelikeMGSonlytheout-of-planeshift NLTispresent.

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