First independent Graz Lunar Gravity Field Model derived from GRAIL. Wirnsberger H., Krauss S., and Mayer-Gürr, T. submitted to Icarus 2018_244. This file contains coefficients and related data for the Graz Lunar gravity field LGM420b, a model resolved up to degree and order 420. It is based on inter-satellite Ka-band ranging observations collected by the GRAIL mission during the primary mission phase (March 1 to May 29, 2012). Concerning the GRAIL spacecraft position and velocity Release P8 orbits (AAS/SRI) are used. Some details describing this model are: The spherical harmonic coefficients are fully normalized. The reference radius = 1738.0 km The planetary ephemeris is DE430 and defines the lunar body-fixed coordinate system. SGM150j up to degree and order 150 was introduced as a priori gravity field model. Love numbers used: k2=0.02408, k21=0.02414, k22=0.02394, k3=0.0089. No gravity field regularization is applied. begin_of_head =================================== product_type gravity_field body moon modelname GrazLGM420b gravity_constant 4.9028000707e+12 radius 1.7380000000e+06 tide_system tide_free max_degree 420 norm fully_normalized errors formal key L M C S sigma C sigma S end_of_head ================================================================================ gfc 0 0 1.000000000000e+00 0.000000000000e+00 0.000000000000e+00 0.000000000000e+00 gfc 1 0 0.000000000000e+00 0.000000000000e+00 0.000000000000e+00 0.000000000000e+00 gfc 1 1 0.000000000000e+00 0.000000000000e+00 0.000000000000e+00 0.000000000000e+00 gfc 2 0 -9.086168594185e-05 0.000000000000e+00 9.469899476877e-09 0.000000000000e+00 gfc 2 1 -2.547621530556e-09 7.777894419222e-10 1.479978353379e-09 1.471564811945e-09 gfc 2 2 3.467272674041e-05 -8.360425480790e-11 1.522707418605e-09 1.446337309900e-09 gfc 3 0 -3.196810839130e-06 0.000000000000e+00 2.337628497327e-09 0.000000000000e+00 gfc 3 1 2.636713697337e-05 5.454864492005e-06 2.419470328394e-10 2.425350434676e-10 gfc 3 2 1.417117925104e-05 4.878065260323e-06 1.940706140335e-10 1.822150954991e-10 gfc 3 3 1.227513408695e-05 -1.774709271478e-06 2.960504740678e-10 3.117049660506e-10 gfc 4 0 3.234790628142e-06 0.000000000000e+00 2.347430243838e-10 0.000000000000e+00 gfc 4 1 -6.013619703435e-06 1.664237237373e-06 9.689869181976e-11 8.707887732305e-11 gfc 4 2 -7.116357976751e-06 -6.777120136201e-06 6.799794101251e-11 6.708608049939e-11 gfc 4 3 -1.349807072717e-06 -1.344468509204e-05 8.288386421088e-11 8.550658190392e-11 gfc 4 4 -6.007371857414e-06 3.926110519263e-06 2.499796696843e-10 2.208718030655e-10 gfc 5 0 -2.238056982673e-07 0.000000000000e+00 7.449053610989e-12 0.000000000000e+00 gfc 5 1 -1.011601148751e-06 -4.118919889302e-06 7.441745572210e-12 6.813059559380e-12 gfc 5 2 4.399524096764e-06 1.057182790410e-06 7.996399895885e-12 1.312163450467e-11 gfc 5 3 4.661734764186e-07 8.698894880695e-06 1.499152804180e-11 1.275323395628e-11 gfc 5 4 2.754042372260e-06 6.743056261422e-08 6.770186760388e-11 6.010640665502e-11 gfc 5 5 3.111066102842e-06 -2.754320348497e-06 2.073315294435e-10 2.089723580344e-10 gfc 6 0 3.818432918982e-06 0.000000000000e+00 5.139781217353e-12 0.000000000000e+00 gfc 6 1 1.528231924189e-06 -2.599609968135e-06 1.044991249669e-11 3.430391671992e-12 gfc 6 2 -4.397324806627e-06 -2.167696968633e-06 8.219854537270e-12 4.495858934830e-12 gfc 6 3 -3.317522854423e-06 -3.427421546996e-06 9.365800615704e-12 6.940152074817e-12 gfc 6 4 3.411868213914e-07 -4.058128399886e-06 4.082549230672e-11 3.159430439616e-11 gfc 6 5 1.454312053480e-06 -1.034161633663e-05 5.568460990518e-11 5.480813477988e-11 gfc 6 6 -4.684271959487e-06 7.229847386576e-06 1.449584723962e-10 1.405209267010e-10 gfc 7 0 5.593436572668e-06 0.000000000000e+00 1.286009399207e-11 0.000000000000e+00 gfc 7 1 7.471652366687e-06 -1.197553410029e-07 1.126931374024e-11 9.571374164843e-12 gfc 7 2 -6.501636025045e-07 2.411094121355e-06 8.793596468636e-12 9.964680525696e-12 gfc 7 3 5.994340892796e-07 2.357331620608e-06 5.346869457816e-12 4.573468113314e-12 gfc 7 4 -8.437597875140e-07 7.564518875510e-07 2.106092145744e-11 1.905870528985e-11 gfc 7 5 -2.067547701982e-07 1.069362091062e-06 3.439626777367e-11 3.459196548093e-11 gfc 7 6 -1.065364208014e-06 1.100395029151e-06 3.678032053301e-11 3.473512926638e-11 gfc 7 7 -1.820089736069e-06 -1.600020449157e-06 1.666871368106e-10 1.632604521266e-10 gfc 8 0 2.346838978587e-06 0.000000000000e+00 3.474345848301e-12 0.000000000000e+00 gfc 8 1 4.184762330044e-09 1.098027059185e-06 3.340813607301e-12 8.929346262677e-12 gfc 8 2 3.009317640380e-06 1.930569232597e-06 4.931432622383e-12 4.103785139057e-12 gfc 8 3 -1.889039142781e-06 9.544530334112e-07 3.550238225451e-12 9.261015308650e-12 gfc 8 4 3.408708119170e-06 -5.282608157413e-07 1.609113205354e-11 1.394777562363e-11 gfc 8 5 -1.248104516676e-06 2.918584098402e-06 1.595933150971e-11 1.446881533983e-11 gfc 8 6 -1.660462362502e-06 -2.114709908620e-06 3.361570866503e-11 3.125954755428e-11 gfc 8 7 -1.509685394413e-06 3.268872535350e-06 4.094201052861e-11 3.933816274723e-11 gfc 8 8 -2.485373230054e-06 2.116427788975e-06 9.841484608193e-11 9.796094372586e-11 gfc 9 0 -3.530895373792e-06 0.000000000000e+00 4.714668051937e-12 0.000000000000e+00 gfc 9 1 1.866997708035e-06 8.104853688522e-08 1.073616962002e-11 5.274185458155e-12 gfc 9 2 1.927801656078e-06 -1.387555132442e-06 6.899285843986e-12 3.786454560469e-12 gfc 9 3 -1.992438024893e-06 2.201758322743e-06 7.862764157727e-12 3.648048526998e-12 gfc 9 4 -1.884468814969e-06 -1.425830383412e-06 9.976832309821e-12 1.303753426547e-11 gfc 9 5 -1.562496443561e-06 -3.524661241546e-06 1.398963535871e-11 1.316755248799e-11 gfc 9 6 -2.127274145044e-06 -3.002644712477e-06 1.899179431647e-11 1.869827312298e-11 gfc 9 7 -3.914731601421e-06 -1.068052771887e-07 4.483274969356e-11 4.474397257892e-11 gfc 9 8 -1.311955043011e-06 -2.203442834474e-06 2.436835814227e-11 2.481332432189e-11 gfc 9 9 -9.384805860324e-07 2.488066971505e-06 1.321391309475e-10 1.318228898302e-10 gfc 10 0 -1.069302295678e-06 0.000000000000e+00 3.333626575238e-12 0.000000000000e+00 gfc 10 1 8.416057316898e-07 -9.540696994610e-07 3.839963861424e-12 2.384451950683e-12 gfc 10 2 3.572441372824e-07 -2.651147184268e-07 1.982623593469e-12 3.743153552556e-12 gfc 10 3 4.841855032758e-07 6.688503363749e-07 6.889884308999e-12 6.080725013604e-12 gfc 10 4 -3.572977311456e-06 1.578895932903e-06 8.409808059733e-12 8.620410200682e-12 gfc 10 5 6.997030818351e-07 -3.145720014285e-07 8.076884863344e-12 9.605211441848e-12 gfc 10 6 -1.273332053514e-07 -2.095316385398e-06 1.767904975410e-11 1.500830778961e-11 gfc 10 7 -3.998665713116e-06 -9.107424333843e-07 1.743923639840e-11 2.044823040760e-11 gfc 10 8 -3.559391582440e-06 2.848876259420e-06 2.856932788752e-11 3.069157564493e-11 gfc 10 9 -4.753055875823e-06 -5.159948874641e-08 3.066671041645e-11 3.413126049342e-11 gfc 10 10 9.478145846290e-07 -1.719467837542e-06 7.342531166357e-11 7.374788758131e-11 gfc 11 0 -8.852059884739e-07 0.000000000000e+00 2.159375540646e-12 0.000000000000e+00 gfc 11 1 -1.946152902727e-08 6.142428615757e-07 5.175111245622e-12 3.860452697999e-12 gfc 11 2 6.995270494029e-07 -1.968041856857e-06 3.389153789061e-12 2.036585944835e-12 gfc 11 3 4.084102460780e-07 7.362842104605e-07 3.616463334907e-12 7.530730914173e-12 gfc 11 4 -1.086791453462e-06 2.190854519960e-06 8.549464357516e-12 6.079909597550e-12 gfc 11 5 5.034998551196e-08 2.588020987835e-06 7.623466673144e-12 7.999019351697e-12 gfc 11 6 5.242958422677e-07 -1.367050379495e-06 1.062755100567e-11 1.273448365149e-11 gfc 11 7 -8.449776869291e-08 -2.841055047215e-06 2.032129424822e-11 1.834062483580e-11 gfc 11 8 -2.095268687092e-06 -3.829316365417e-07 1.420334709563e-11 1.581385214309e-11 gfc 11 9 -2.334976994397e-06 2.526127446557e-07 4.483024527179e-11 4.603607485557e-11 gfc 11 10 -4.680576757843e-06 -1.735988863047e-07 1.783359685059e-11 2.459393570017e-11 gfc 11 11 -2.888830382387e-06 -1.746345183967e-06 1.038974979536e-10 1.020279051035e-10 gfc 12 0 -2.012256143652e-06 0.000000000000e+00 5.335859679669e-12 0.000000000000e+00 gfc 12 1 -7.068620100936e-07 1.647806698272e-06 6.415241847601e-12 6.741673891121e-12 gfc 12 2 -1.052121427068e-07 1.507793037370e-06 5.736349117964e-12 1.120349181910e-11 gfc 12 3 8.557103613511e-07 -4.058963888278e-06 5.419791726599e-12 5.199679133086e-12 gfc 12 4 8.129969285895e-07 -3.445998448740e-07 7.764344585472e-12 1.031818712442e-11 gfc 12 5 2.061266915859e-10 8.936303922029e-07 3.835475887905e-12 5.027750649471e-12 gfc 12 6 1.089061526248e-06 5.452215374221e-07 9.839301572724e-12 9.847002747671e-12 gfc 12 7 2.139988283845e-06 -9.675711352514e-07 9.457301737120e-12 1.094910086876e-11 gfc 12 8 3.985681394777e-07 -2.206539824126e-06 1.576957800017e-11 1.409461585396e-11 gfc 12 9 -1.345174403210e-06 1.094998419354e-06 1.797157942784e-11 1.778549314359e-11 gfc 12 10 -3.075509372512e-06 -1.273976754714e-06 2.430459995633e-11 2.694157617466e-11 gfc 12 11 -9.817952449412e-07 -3.284418710540e-07 2.422154865967e-11 2.437938514224e-11 gfc 12 12 3.026783400314e-07 1.246971834617e-06 5.862785590826e-11 5.759462014104e-11 gfc 13 0 2.564905671867e-07 0.000000000000e+00 4.317110205607e-12 0.000000000000e+00 gfc 13 1 1.354447502301e-06 -7.664907348287e-08 8.300958943438e-12 6.637421392157e-12 gfc 13 2 -3.425254189930e-06 3.839564489581e-07 5.800694180411e-12 4.534809626534e-12 gfc 13 3 -4.333237485467e-07 -1.456304210327e-06 9.044813942933e-12 6.344270593757e-12 gfc 13 4 7.772518025769e-07 -5.819171458449e-07 4.014696568874e-12 7.059585022888e-12 gfc 13 5 -1.186342964866e-06 1.021343848974e-06 4.441178555178e-12 5.615223337626e-12 gfc 13 6 -2.769164909253e-08 1.384211172435e-06 7.676013026236e-12 7.511772136355e-12 gfc 13 7 -1.621070302985e-07 -6.726643573248e-07 9.543874175320e-12 1.038196683579e-11 gfc 13 8 -2.922618798806e-07 -1.210524887337e-06 9.399480224690e-12 9.194718819855e-12 gfc 13 9 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7.326844225145e-12 6.929747570378e-12 gfc 14 7 -5.154257643536e-07 1.161503178203e-06 7.588772694722e-12 5.841074072836e-12 gfc 14 8 3.061465821037e-07 4.414511756181e-07 8.422914204131e-12 9.868942805660e-12 gfc 14 9 8.052265575640e-08 -1.638051552914e-06 1.103133587072e-11 9.655415484888e-12 gfc 14 10 -7.782242773510e-07 5.930299046995e-07 1.251667438545e-11 1.416520082638e-11 gfc 14 11 -1.928500444473e-06 1.937217979600e-06 1.690632478555e-11 1.715492398957e-11 gfc 14 12 -1.448562715758e-06 -5.394707917472e-07 2.188965725380e-11 2.272280768987e-11 gfc 14 13 -3.214058816574e-07 -1.017729340819e-06 1.900224523940e-11 1.930135568118e-11 gfc 14 14 -6.134447025869e-07 1.071109885369e-06 4.760963270825e-11 4.825413287819e-11 gfc 15 0 -2.280929443139e-07 0.000000000000e+00 3.166078427101e-12 0.000000000000e+00 gfc 15 1 -7.975236381507e-07 3.536209291726e-07 2.320863717608e-12 2.330841351675e-12 gfc 15 2 -5.402203029620e-08 7.446636249220e-07 1.955058583188e-12 5.912794263583e-12 gfc 15 3 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1.302355994439e-11 1.341701010034e-11 gfc 15 15 5.483053465433e-07 7.779264997660e-07 6.308211591062e-11 6.233468205491e-11 gfc 16 0 5.568582950090e-07 0.000000000000e+00 3.208596352994e-12 0.000000000000e+00 gfc 16 1 1.155928738296e-07 8.252397540632e-07 1.997891799385e-12 5.899699904149e-12 gfc 16 2 1.455238394002e-06 7.657774299634e-09 3.922244413394e-12 1.719370223507e-12 gfc 16 3 -1.942794224706e-07 5.233244647512e-07 2.543809762413e-12 5.631874380488e-12 gfc 16 4 6.859512739626e-07 3.124276681986e-07 3.405733418390e-12 4.184742377227e-12 gfc 16 5 7.634226109979e-07 -6.484929077416e-07 2.479563969856e-12 4.833377936581e-12 gfc 16 6 7.297935936266e-07 -7.280784361107e-07 5.943012844000e-12 4.273178057000e-12 gfc 16 7 -2.807076706714e-07 -5.804002497024e-07 4.037747192731e-12 4.414224924941e-12 gfc 16 8 2.370368020705e-08 3.200952308034e-07 6.735803170077e-12 6.392849076879e-12 gfc 16 9 -7.806676176641e-07 -8.233777828543e-07 6.695970878954e-12 6.810286096785e-12 gfc 16 10 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109 2.564350425282e-08 2.291894204130e-08 9.206015457259e-12 9.260895329978e-12 gfc 128 110 -2.135089881540e-08 5.040081424991e-09 1.196660617454e-11 1.212280932186e-11 gfc 128 111 1.597035120963e-08 7.754046757211e-09 9.769054782391e-12 9.854443846676e-12 gfc 128 112 -1.944336960761e-08 1.669595690649e-08 1.261735066675e-11 1.263325487745e-11 gfc 128 113 -1.124031764770e-08 1.682052564461e-08 1.065835790460e-11 1.087675225731e-11 gfc 128 114 2.231916228315e-08 -9.459547108285e-09 1.302318956463e-11 1.306310388951e-11 gfc 128 115 7.493420230185e-09 -2.343411735541e-08 1.202267814156e-11 1.205822969831e-11 gfc 128 116 -1.218835680432e-08 3.291831838211e-08 1.354405863494e-11 1.351735715104e-11 gfc 128 117 -7.729046604231e-09 -8.532274272344e-09 1.331155171660e-11 1.331149383737e-11 gfc 128 118 6.138379511773e-09 7.649365096915e-09 1.452421200524e-11 1.432355670101e-11 gfc 128 119 1.324088850919e-08 -1.983356960912e-08 1.440229222915e-11 1.425555108274e-11 gfc 128 120 -2.384333362908e-08 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129 14 3.150069818761e-08 6.926012539963e-09 1.122041959914e-12 8.281348540461e-13 gfc 129 15 -9.979536387911e-09 -1.178957642397e-08 2.065749284786e-12 1.253831248243e-12 gfc 129 16 -5.902904808493e-08 -3.156366630767e-08 1.181233079960e-12 1.205147717917e-12 gfc 129 17 -2.563318566796e-08 -1.749463515813e-08 1.181334339845e-12 2.214284434506e-12 gfc 129 18 -2.427253452399e-08 2.343091074708e-08 1.455653500278e-12 1.075635953263e-12 gfc 129 19 5.032453672930e-09 -2.620566774523e-08 1.196958671791e-12 1.350655895038e-12 gfc 129 20 4.431424354887e-09 -1.443523107656e-08 1.230463955933e-12 1.145737633878e-12 gfc 129 21 -6.047058341032e-10 -4.784607546151e-09 1.365111371055e-12 1.138892379138e-12 gfc 129 22 -1.302845673685e-08 -1.967216180841e-08 1.201138579318e-12 1.149326029625e-12 gfc 129 23 2.831518684562e-09 -1.364227394441e-08 1.332572619493e-12 1.340878292512e-12 gfc 129 24 -7.734094332322e-09 -4.338673253460e-09 1.331998445093e-12 1.268544333744e-12 gfc 129 25 -1.937949119809e-08 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