First independent lunar gravity field solution in the framework of project GRAZIL. Wirnsberger H., Klinger B., Krauss S., and Mayer-Gürr, T. European Geoscience Union 2017, Vienna. Krauss, S., Klinger, B., Baur, O., Mayer-Guerr, T. 2015. Development of the lunar gravity field model GrazLGM300a. Oesterr. Zeitschr. Verm. Geoinf., ISSN 1605-1653, 103, 156-161, 2015. This file contains coefficients and related data for the Graz Lunar gravity field LGM420a, 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 N6 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 DE421 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 GrazLGM420a gravity_constant 4.9027995295e+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 -9.087057900393e-05 0.000000000000e+00 1.630745184612e-08 0.000000000000e+00 gfc 2 1 -3.384584059708e-09 2.287745583182e-09 3.883303651181e-09 3.865745588623e-09 gfc 2 2 3.466939162913e-05 -3.738190493796e-09 3.717897280193e-09 3.639222703747e-09 gfc 3 0 -3.196265468125e-06 0.000000000000e+00 2.860676856662e-09 0.000000000000e+00 gfc 3 1 2.636700400770e-05 5.455063026093e-06 3.760874856020e-10 3.763047515913e-10 gfc 3 2 1.417119913739e-05 4.878092991818e-06 3.045228640543e-10 2.818555325716e-10 gfc 3 3 1.227524570792e-05 -1.774755594203e-06 4.656097653732e-10 4.829289276591e-10 gfc 4 0 3.234764528647e-06 0.000000000000e+00 2.617877254716e-10 0.000000000000e+00 gfc 4 1 -6.013615578576e-06 1.664296712566e-06 1.085080863834e-10 9.823515578862e-11 gfc 4 2 -7.116327891561e-06 -6.777108377129e-06 7.733209230409e-11 7.543088219618e-11 gfc 4 3 -1.349811201917e-06 -1.344474431558e-05 9.353084903981e-11 9.624353957398e-11 gfc 4 4 -6.007469457334e-06 3.926148945153e-06 2.712589424527e-10 2.410326731253e-10 gfc 5 0 -2.237902057438e-07 0.000000000000e+00 7.684171428487e-12 0.000000000000e+00 gfc 5 1 -1.011611836272e-06 -4.118908819056e-06 7.970757137879e-12 7.226814566752e-12 gfc 5 2 4.399515856654e-06 1.057155653138e-06 8.462132604893e-12 1.345196692236e-11 gfc 5 3 4.661871756133e-07 8.698911478652e-06 1.565927271368e-11 1.359631096152e-11 gfc 5 4 2.754077093102e-06 6.744305586047e-08 7.688418082473e-11 6.630275689752e-11 gfc 5 5 3.111172630981e-06 -2.754186651486e-06 3.273774122107e-10 3.245498758546e-10 gfc 6 0 3.818439832446e-06 0.000000000000e+00 5.312988907395e-12 0.000000000000e+00 gfc 6 1 1.528254778723e-06 -2.599603127210e-06 1.048346579149e-11 3.580589060184e-12 gfc 6 2 -4.397299826377e-06 -2.167692816748e-06 8.342185918550e-12 4.625867981165e-12 gfc 6 3 -3.317520882793e-06 -3.427420357198e-06 9.506414963296e-12 7.138988904885e-12 gfc 6 4 3.411924682075e-07 -4.058132176153e-06 4.224878908928e-11 3.246597474792e-11 gfc 6 5 1.454288736755e-06 -1.034158875684e-05 6.376977960116e-11 6.310332370438e-11 gfc 6 6 -4.684205075634e-06 7.229892406552e-06 1.659722798808e-10 1.615516694945e-10 gfc 7 0 5.593411866480e-06 0.000000000000e+00 1.298094580865e-11 0.000000000000e+00 gfc 7 1 7.471658898830e-06 -1.197396673087e-07 1.151961161237e-11 9.573413548027e-12 gfc 7 2 -6.501521667304e-07 2.411119484746e-06 8.820057132944e-12 9.989008708524e-12 gfc 7 3 5.994289290741e-07 2.357326955742e-06 5.431177314832e-12 4.819513270067e-12 gfc 7 4 -8.437503248210e-07 7.564571113139e-07 2.374021441673e-11 2.094011134233e-11 gfc 7 5 -2.067404770859e-07 1.069377902488e-06 5.348039742108e-11 5.301774151680e-11 gfc 7 6 -1.065326716265e-06 1.100391521664e-06 4.045205819864e-11 3.755153507960e-11 gfc 7 7 -1.820168738040e-06 -1.599972288190e-06 2.590624346808e-10 2.527146073116e-10 gfc 8 0 2.346829793994e-06 0.000000000000e+00 3.703616279370e-12 0.000000000000e+00 gfc 8 1 4.178400718806e-09 1.098049355738e-06 3.433239637530e-12 8.937358079848e-12 gfc 8 2 3.009316299448e-06 1.930555906776e-06 5.140101017868e-12 4.217207777932e-12 gfc 8 3 -1.889042476588e-06 9.544898005248e-07 3.684948913960e-12 9.289990245301e-12 gfc 8 4 3.408684909253e-06 -5.282901011295e-07 1.672871787073e-11 1.423234532042e-11 gfc 8 5 -1.248068456556e-06 2.918612457357e-06 1.775626681905e-11 1.655059733947e-11 gfc 8 6 -1.660487659974e-06 -2.114706021910e-06 3.602386595149e-11 3.371166761608e-11 gfc 8 7 -1.509647198724e-06 3.268865036631e-06 4.954856508201e-11 4.751148761659e-11 gfc 8 8 -2.485380398095e-06 2.116566496126e-06 1.242598315286e-10 1.236671261581e-10 gfc 9 0 -3.530902158881e-06 0.000000000000e+00 4.987743269940e-12 0.000000000000e+00 gfc 9 1 1.866983851306e-06 8.103598250957e-08 1.080992311871e-11 5.291940843843e-12 gfc 9 2 1.927798208772e-06 -1.387564736981e-06 6.960589777921e-12 3.881614364377e-12 gfc 9 3 -1.992407340686e-06 2.201762613352e-06 7.944149774582e-12 3.843547726176e-12 gfc 9 4 -1.884461474004e-06 -1.425824880615e-06 1.117736209247e-11 1.363421944732e-11 gfc 9 5 -1.562487596917e-06 -3.524657936293e-06 1.912139428219e-11 1.838980695773e-11 gfc 9 6 -2.127256015461e-06 -3.002665369640e-06 2.050034658110e-11 1.980773638034e-11 gfc 9 7 -3.914734846852e-06 -1.067890675933e-07 6.946907197862e-11 6.834124636321e-11 gfc 9 8 -1.311975041645e-06 -2.203457580140e-06 2.642056193270e-11 2.681644870670e-11 gfc 9 9 -9.385603821063e-07 2.488206002263e-06 1.992409286027e-10 1.991220715617e-10 gfc 10 0 -1.069298073591e-06 0.000000000000e+00 3.396444929143e-12 0.000000000000e+00 gfc 10 1 8.416000958608e-07 -9.540756462691e-07 3.921844175941e-12 2.464214660150e-12 gfc 10 2 3.572463044359e-07 -2.651132570709e-07 2.129370182008e-12 3.791648522228e-12 gfc 10 3 4.841923065482e-07 6.688269909022e-07 6.919847769842e-12 6.105703374723e-12 gfc 10 4 -3.572974703223e-06 1.578915422275e-06 8.842619815383e-12 8.783364739270e-12 gfc 10 5 6.996941543315e-07 -3.145776840647e-07 8.668580906824e-12 1.007620834816e-11 gfc 10 6 -1.273265775307e-07 -2.095327044998e-06 1.839369025113e-11 1.570715857667e-11 gfc 10 7 -3.998657671760e-06 -9.107426200674e-07 2.098779939979e-11 2.325020061993e-11 gfc 10 8 -3.559365209950e-06 2.848891148967e-06 3.362130291107e-11 3.549538680488e-11 gfc 10 9 -4.753004318944e-06 -5.158609313483e-08 3.983879852275e-11 4.286154561749e-11 gfc 10 10 9.475446825395e-07 -1.719420287533e-06 1.041839879791e-10 1.045190626466e-10 gfc 11 0 -8.852101251959e-07 0.000000000000e+00 2.311938081983e-12 0.000000000000e+00 gfc 11 1 -1.945658665327e-08 6.142452253590e-07 5.209240186239e-12 3.885109243251e-12 gfc 11 2 6.995139974986e-07 -1.968039313194e-06 3.455871936524e-12 2.263650831646e-12 gfc 11 3 4.084172062606e-07 7.362668055828e-07 3.668637611590e-12 7.545518530697e-12 gfc 11 4 -1.086796130534e-06 2.190854043808e-06 9.046022850272e-12 6.522734825194e-12 gfc 11 5 5.035206761775e-08 2.588030604664e-06 9.402121418910e-12 9.729867932537e-12 gfc 11 6 5.242971161163e-07 -1.367038816733e-06 1.149272133800e-11 1.325650545082e-11 gfc 11 7 -8.450891860347e-08 -2.841058018275e-06 2.979683825676e-11 2.802822717105e-11 gfc 11 8 -2.095249299839e-06 -3.829390511746e-07 1.521165734875e-11 1.664993582618e-11 gfc 11 9 -2.335002561341e-06 2.526492028113e-07 6.799518213827e-11 6.883839163101e-11 gfc 11 10 -4.680573588343e-06 -1.735789315128e-07 1.991896973374e-11 2.605608422818e-11 gfc 11 11 -2.888866687807e-06 -1.746287492290e-06 1.523490369163e-10 1.506853254373e-10 gfc 12 0 -2.012266616063e-06 0.000000000000e+00 5.438134851133e-12 0.000000000000e+00 gfc 12 1 -7.068802047955e-07 1.647781827415e-06 6.445431733511e-12 6.782919213783e-12 gfc 12 2 -1.051997346435e-07 1.507813604600e-06 5.737576963139e-12 1.122184539232e-11 gfc 12 3 8.556881154174e-07 -4.058952835574e-06 5.450526070044e-12 5.594145395993e-12 gfc 12 4 8.130181043999e-07 -3.446149867179e-07 7.878728497317e-12 1.035250775939e-11 gfc 12 5 2.085412200025e-10 8.936411356826e-07 4.156930883292e-12 5.290274285350e-12 gfc 12 6 1.089056386058e-06 5.452338785247e-07 1.022368600311e-11 1.012984871126e-11 gfc 12 7 2.139992575996e-06 -9.675659510673e-07 1.117472151143e-11 1.224749951895e-11 gfc 12 8 3.985649292728e-07 -2.206536559440e-06 1.718689729417e-11 1.576810598848e-11 gfc 12 9 -1.345107285683e-06 1.094985487446e-06 2.259054792252e-11 2.259769773492e-11 gfc 12 10 -3.075593449269e-06 -1.273938850982e-06 3.271746915427e-11 3.475643775590e-11 gfc 12 11 -9.817514017972e-07 -3.284396044597e-07 3.443069134710e-11 3.388686896616e-11 gfc 12 12 3.025678074425e-07 1.246878564798e-06 9.354370292828e-11 9.233607856345e-11 gfc 13 0 2.564838616452e-07 0.000000000000e+00 4.346665147605e-12 0.000000000000e+00 gfc 13 1 1.354458263280e-06 -7.667346718198e-08 8.338916954553e-12 6.631700315246e-12 gfc 13 2 -3.425233390587e-06 3.839743233840e-07 6.084349524986e-12 4.568740488013e-12 gfc 13 3 -4.333422424974e-07 -1.456316071046e-06 9.048807895347e-12 6.403842825905e-12 gfc 13 4 7.772581154829e-07 -5.819399601020e-07 4.333575849698e-12 7.212040169625e-12 gfc 13 5 -1.186338331023e-06 1.021347117827e-06 5.304259462190e-12 6.281312144386e-12 gfc 13 6 -2.768534674051e-08 1.384206504613e-06 8.214785686422e-12 7.921047958924e-12 gfc 13 7 -1.621179040718e-07 -6.726550195864e-07 1.445750254043e-11 1.486494442926e-11 gfc 13 8 -2.922672603909e-07 -1.210531386410e-06 9.959917629589e-12 9.752882139857e-12 gfc 13 9 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7.527052429168e-12 7.151607517888e-12 gfc 14 7 -5.154378488480e-07 1.161510096855e-06 8.241747208706e-12 6.648405419917e-12 gfc 14 8 3.061498822126e-07 4.414573250182e-07 9.105340232557e-12 1.046446757751e-11 gfc 14 9 8.052519815748e-08 -1.638058542373e-06 1.349021061714e-11 1.261454613977e-11 gfc 14 10 -7.782414159811e-07 5.930215324510e-07 1.557807592766e-11 1.703735960203e-11 gfc 14 11 -1.928449478540e-06 1.937232595087e-06 2.291420363043e-11 2.268403897593e-11 gfc 14 12 -1.448621011650e-06 -5.394887659309e-07 3.334959662108e-11 3.362692645233e-11 gfc 14 13 -3.214235772632e-07 -1.017694050177e-06 2.869246782789e-11 2.905201449837e-11 gfc 14 14 -6.134665480506e-07 1.070998910308e-06 8.587904288833e-11 8.482684463028e-11 gfc 15 0 -2.280919108375e-07 0.000000000000e+00 3.188538723009e-12 0.000000000000e+00 gfc 15 1 -7.975298914340e-07 3.536152036734e-07 2.432094608005e-12 2.361606593848e-12 gfc 15 2 -5.401537516724e-08 7.446502295564e-07 2.149175537310e-12 5.929658704413e-12 gfc 15 3 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1.552154171099e-11 1.576873812035e-11 gfc 15 15 5.483491859443e-07 7.779956397353e-07 9.136158462447e-11 9.078947125393e-11 gfc 16 0 5.568468117758e-07 0.000000000000e+00 3.231204784033e-12 0.000000000000e+00 gfc 16 1 1.155899614872e-07 8.252581983947e-07 2.027435268824e-12 5.913622012982e-12 gfc 16 2 1.455226746313e-06 7.656241822275e-09 4.031052738469e-12 1.748362176942e-12 gfc 16 3 -1.942776946164e-07 5.233410638465e-07 2.584709350480e-12 5.636828155689e-12 gfc 16 4 6.859478274088e-07 3.124353857796e-07 3.484212074584e-12 4.272151287708e-12 gfc 16 5 7.634225639981e-07 -6.484785493972e-07 2.628736608913e-12 4.884305543153e-12 gfc 16 6 7.298048204337e-07 -7.280792743827e-07 6.087444924015e-12 4.454725413572e-12 gfc 16 7 -2.807036218072e-07 -5.803963138523e-07 4.486885183579e-12 4.802069832525e-12 gfc 16 8 2.371992633948e-08 3.200885677464e-07 7.056320513630e-12 6.748817268954e-12 gfc 16 9 -7.806670336284e-07 -8.233699564696e-07 8.293386740183e-12 8.501433250882e-12 gfc 16 10 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109 2.564867730204e-08 2.291600859395e-08 1.051848993348e-11 1.052151917450e-11 gfc 128 110 -2.134321532857e-08 5.029554190558e-09 1.513096092145e-11 1.536903077966e-11 gfc 128 111 1.597470513072e-08 7.748860203799e-09 1.114944343468e-11 1.117993964580e-11 gfc 128 112 -1.943510846191e-08 1.668901633026e-08 1.602839575631e-11 1.614750541227e-11 gfc 128 113 -1.123412801250e-08 1.682116464227e-08 1.203621067072e-11 1.229625073178e-11 gfc 128 114 2.232479202782e-08 -9.461309918871e-09 1.702068461219e-11 1.676043148849e-11 gfc 128 115 7.492514060954e-09 -2.342750544286e-08 1.341904876697e-11 1.353474572047e-11 gfc 128 116 -1.218951477495e-08 3.291903844874e-08 1.795973938691e-11 1.778263936983e-11 gfc 128 117 -7.723972690423e-09 -8.524793147523e-09 1.482300454640e-11 1.475039807700e-11 gfc 128 118 6.131651380852e-09 7.650585733544e-09 1.938385617095e-11 1.920840522336e-11 gfc 128 119 1.323928725501e-08 -1.983321338727e-08 1.594433475196e-11 1.575656621791e-11 gfc 128 120 -2.385299256642e-08 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