{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["radius change","z vs H table","z = 0 table"],"read":"whole","date_system":"1900"}

{"sheet":"radius change","index":0,"n_rows":125,"n_cols":27,"rows_kept":125}
["HOW TO USE THIS SPREADSHEET:",{"$nulls":3},"INDEPENDENT VARIABLES HIGHLIGHTED"]
["1) enter z in G11, T in G12, density multiplier (=1) in G13, 1e12 in G14, and 1e-9 in G15.",{"$nulls":3},"MANUALLY ENTERED DEPENDENT VALUES IN RED "]
["2) copy D25 and paste its value into G17. (right click G17, 2nd from left in \"paste options\").",{"$nulls":4},"CONSTANTS","---------------------","units"]
["3) select E25:E125 and change the series value (in \"fill\") until you get near 1  in column  Z.",{"$nulls":4},"gravitational constant G",{"v":6.67408e-11,"d":"6.67408E-11"},"m^3kg^-1sec^-2",null,"H0",67.4,"Km/sec/Mpc"]
["4) find the row in Z just below 1, go over to column A, and paste its value into G15.",{"$nulls":4},"92/8 H/He mwt",{"v":0.0012475,"d":"1.24750E-03"},"kg^1mole^-1",{"v":0.0012475,"d":"1.24750E-03"},null,{"$f":"K4*1000","v":67400},"m/sec/Mpc"]
["5) repeat steps 3 and 4 until one of the cells in column Z is 1.00000000.",{"$nulls":4},"gas constant R",{"v":8.31446261815324,"d":"8.31446E+00"},"kg^1m^2sec^-2K^-1mole^-1",null,null,{"$f":"K5/I14","v":{"v":2.1840570317563187E-18,"d":"2.1841E-18"}},"sec-1"]
["6) You have found the endpoint! It's in column A.",{"$nulls":4},"Hubble constant",{"v":2.1840570317563187E-18,"d":"2.18406E-18"},"sec-1",{"$nulls":17},101050426.00057796]
[{"$nulls":5},"ΛCDM mean baryon density at z = 0",{"v":4.21e-28,"d":"4.21E-28"},"Kg/m^3",{"v":4.21e-28,"d":"4.21E-28"},{"$nulls":16},{"$f":"Z7/300000000","v":0.33683475333525986}]
[{"$nulls":5},"CDM multiplier",6.33]
[{"$nulls":5},"VARIABLES","----------------------"]
[{"$nulls":5},"cosmic redshift z",{"v":0,"d":"0.000"}]
[{"$nulls":5}," temperature",500,"K",{"v":9460730467457280,"d":"9.46073E+15"},"1 light year. m"]
[{"$nulls":5},"baryon density multiplier:",{"v":1,"d":"1.000"}]
[{"$nulls":5},"baryon density",{"$f":"$G$13*$G$8*(1+$G$11)^3","v":{"v":4.21e-28,"d":"4.210E-28"}},"Kg/m^3",{"v":3.086e+22,"d":"3.09E+22"},"1 megaparsec, m"]
[{"$nulls":5},"initial radius for log radial step:",{"v":1000000000000,"d":"1.0000E+12"},"m",{"v":6378100,"d":"6.3781E+06"},"Earth radius, m"]
[{"$nulls":5},"radial increment (r2-r1)/r1:",{"v":1e-09,"d":"1.00E-09"},null,{"$f":"(1.01)^(1/3)-1","v":3.3222835420891883E-3},"1% volume increment"]
[{"$nulls":5},"uncorrected initial radial velocity v(s0) (at r1<<rc)",{"v":0.14140261354531222,"d":"0.14140"},"m^1sec-1",{"$nulls":11},{"$f":"T25/S25","v":{"v":3.533166622853606e+18,"d":"3.53317E+18"}},{"$f":"(L25-U25)/L25","v":{"v":1.9999999949504856E-9,"d":"2.00000E-09"}}]
[{"$nulls":5},"correct initial radial velocity (vi)",{"$f":"SQRT(2*$G$6*$G$12/$G$5)","v":{"v":2581.6467408054136,"d":"2581.65"}},"m^1sec-1","Hg=vi/re:",{"$f":"G18/G20","v":{"v":1.2662621797283639E-18,"d":"1.2663E-18"}}]
[{"$nulls":5},"correction factor vi/v(s0)",{"$f":"G18/G17","v":{"v":18257.418841683073,"d":"1.83E+04"}},null,"Hg/HΛ:",{"$f":"J18/G7","v":{"v":0.579775235406785,"d":"5.7978E-01"}}]
[{"$nulls":5},"endpoint manually found by iteration:",{"v":2.0387932152875508E+21,"d":"2.0388E+21"},"m",{"$f":"G20/$I$14","v":{"v":0.0660658851356951,"d":"0.066"}},"megaparsecs"]
["r1","r1/re","vs'","vs","log Δri/r1","r1","Δri","V1","M","Mcdm","P1","T1","U1"," ρ1","r2","V2","P2","U2","U2-U1","E","T2"," ρ2","Ek = E + U1 - U2","ΔPe","X'=Ur/Ek","X=ΔU/E","vs"]
["step radius","fraction of endpoint","corrected sphere radial velocity ","uncorrected sphere radial velocity ","log radial step","step radius","increment in meters","starting volume","thermodynamic mass","CDM adjusted mass","starting pressure","starting temperature","potential before reversible expansion","starting gas density","radius after reversible expansion"," volume after reversible expansion","internal pressure after reversible expansion","potential  after reversible expansion","energy lost  to gravity","energy released by expansion of the gas","temperature after reversible expansion","gas density after reversible expansion","radial kinetic energy after reversible expansion","expansion pressure","cutoff ratio","gravity ratio","uncorrected sphere radial velocity "]
[" (from column F)",null,null," (from column AA)"]
["m",null,null,"m^1sec^-1",null,"m","m","m^3","kg","kg","kg^1m^sec^-2 ","K","kg^1m^2sec^-2","kg^1m^-3","m","m^3","kg^1m^1sec^-2","kg^1m^2sec^-2","kg^1m^2sec^-2","kg^1m^2sec^-2","K","kg^1m^-3","kg-m^2sec^-2","kg^1m^1sec^-2",null,null,"M^1sec^-1"]
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[{"v":1000230285020.8247,"d":"1.00023E+12"},{"v":4.905991826541136e-10,"d":"4.90599E-10"},{"v":2581.6467408054136,"d":"2581.65"},{"$f":"$AA125","v":{"v":0.14140261354531222,"d":"0.141403"}},{"v":9.9999999999999991E-5,"d":"0.0001000"},{"v":1000230285020.8247,"d":"1.00023E+12"},{"v":1000.2302850208248,"d":"1.0002303E+03"},{"v":4.191684718165762e+36,"d":"4.1917E+36"},{"v":1764699266.3477857,"d":"1.76470E+09"},{"$f":"$I125*$G$9","v":{"v":11170546355.981483,"d":"1.11705E+10"}},{"v":1.4029614277525103E-21,"d":"1.40296E-21"},{"v":500,"d":"500.00"},{"v":-4.9956440772349255E-3,"d":"-4.99564E-03"},{"v":4.21e-28,"d":"4.21000E-28"},{"v":1000230286021.0549,"d":"1.0002303E+12"},{"v":4.191684730740815e+36,"d":"4.19168E+36"},{"v":1.4029614207377035E-21,"d":"1.40296E-21"},{"v":-0.004995644072239282,"d":"-4.99564E-03"},{"v":4.995643655691939e-12,"d":"4.99564E-12"},{"v":17642315.43169988,"d":"1.76423E+07"},{"v":499.999999,"d":"499.99999900"},{"v":4.209999987370001e-28,"d":"4.21000E-28"},{"v":17642315.43169988,"d":"1.76423E+07"},{"v":4.208884151595503e-30,"d":"4.20888E-30"},{"v":2.8316258571795623E-19,"d":"2.83163E-19"},{"v":2.8316258571795623E-19,"d":"2.83163E-19"},{"v":0.14140261354531222,"d":"1.41403E-01"}]

{"sheet":"z vs H table","index":1,"n_rows":141,"n_cols":13,"rows_kept":141}
[]
["cosmic redshift z","1/a","gas H = vi/re","gas  H/H0:","ΛCDM H:","ΛCDM H/H0:","gas/ΛCDM:","gas  H/H0 corrected for entropy","gas/ΛCDM corrected for entropy",null,null,"POLYNOMIAL CURVE FIT, HIGH Z"]
[0,1,1.3734537367608374E-18,0.6288543370391609,2.1830630596267425E-18,0.999544896440375,{"v":0.6291406611935749,"d":"0.629140661"},{"$f":"D3/($M$6+$M$7*B3+$M$8*B3^2)","v":0.5552546541698881},{"$f":"H3/F3","v":0.5555074675957892},null,null,"z = 19 to 999"]
[0.1,{"$f":"1+A4","v":1.1},1.5845407584261704E-18,0.7255033798966116,2.291782328536845e-18,1.0493234815823003,0.6914010718626133,{"$f":"D4/($M$6+$M$7*B4+$M$8*B4^2)","v":0.640601265027726},{"$f":"H4/F4","v":0.6104897834381328},null,null,"y = C(0) + C(1)*x + C(2)*x^2 + ..."]
[0.2,{"$f":"1+A5","v":1.2},1.805454660159752e-18,0.8266517924707708,2.4157394890414407E-18,1.106078941124909,0.7473714232639181,0.7299232015767034,0.659919626382502,null,null,"Coefficients"]
[0.3,1.3,2.035770643395597e-18,0.9321050750027913,2.5544440565546356E-18,1.1695867000782798,0.7969525259994885,0.823048890774252,0.7037091741203673,null,null,"C(00) = ",1.13271306028]
[0.4,1.4,2.2751328483531598E-18,1.0417002922875152,2.7072598235845187E-18,1.2395554622524962,0.8403821563535023,0.9198346216648451,0.7420681443275958,null,null,"C(01) = ",{"v":-1.61864422221E-4,"d":"-1.619E-04"}]
[0.5,1.5,2.523197128100926e-18,1.1552798720058544,2.8734718174677577E-18,1.31565786776046,0.8781005307803886,1.020141410634367,0.7753850264817499,null,null,"C(02) = ",2.60303208745e-08]
[0.6,1.6,2.779674271598275e-18,1.2727113949780826,3.05233814189291e-18,1.3975542293592762,0.9106704900900846,1.1238524772933984,0.8041566142364585]
[0.7,1.7,3.044304632257822e-18,1.3938759785085517,3.2431266421438472E-18,1.48490932012699,0.9386943428904783,1.2308629879696589,0.8289145817095384,null,null,"Correlation coefficient is 0.999998108135"]
[0.8,1.8,3.316827431633157E-18,1.518654221664677,3.4451385014656504E-18,1.5774031773772994,0.9627559037821247,1.3410676453550627,0.8501743020353334,null,null,"Standard error about the line = 7.93563562163e-005"]
[0.9,1.9,3.597036702254496e-18,1.6469518194595512,3.657721688374184e-18,1.6747372596918,0.9834090750226921,1.4543833077380801,0.8684247629420562]
[1,2,3.884670388109659E-18,1.7786487860098528,3.880277129091038e-18,1.7766372730526623,1.00113220238464,1.5707041501453247,0.8840882570511998]
[1.1,2.1,4.179678271270903e-18,1.9137221283593482,4.112260021819392e-18,1.8828537726015795,1.016394451978667,1.6900099961025523,0.8975789945532675]
[1.2000000000000002,2.2,4.481757273329722e-18,2.052033077966695,4.353178136879708e-18,1.9931613843339433,1.0295368423728644,1.8121784249746298,0.9091980404688641]
[1.3,2.3,4.790778675219072e-18,2.193522699069148,4.602588415037074e-18,2.107357247597094,1.0408879185388733,1.9371575115471056,0.9192354612659729]
[1.4000000000000001,2.4000000000000004,5.106586061137733e-18,2.3381193745802737,4.860092746491671e-18,2.225259082444109,1.05071782114117,2.0648841282608053,0.9279297608765823]
[1.5,2.5,5.429055659241108e-18,2.48576643388992,5.125333493297918e-18,2.3467031395129636,1.0592590055535605,2.1953083439448724,0.935486175043209]
[1.6,2.6,5.7580320317887744E-18,2.636392707729994,5.3979890936300735E-18,2.4715421873801793,1.0666994563926726,2.328367419873753,0.9420706762613709]
[1.7000000000000002,2.7,6.093409996570658e-18,2.7899500370054975,5.6777699358798695E-18,2.599643623460724,1.073204808469644,2.4640189357792948,0.9478295076842566]
[1.8000000000000003,2.8000000000000003,6.4350343637839464E-18,2.9463673659699197,5.964414593684559E-18,2.73088775016477,1.0789046037473158,2.602200246883994,0.952877044004093]
[1.9000000000000001,2.9000000000000004,6.782833465991849e-18,3.1056118807197106,6.257686453103877e-18,2.865166230605128,1.0839203141326288,2.7428824800946368,0.9573205389606086]
[2,3,7.136686578435925e-18,3.267628305794253,6.557370727952913e-18,3.0023807220271053,1.0883457523628322,2.8860169222870855,0.9612428234413073]
[2.1,3.1,7.496469746998893e-18,3.4323598871273866,6.863271840025494e-18,3.142441676308409,1.0922588995063098,3.031553551602759,0.9647127501071345]
[2.2,3.2,7.862106684342421e-18,3.5997716955312633,7.175211131659469e-18,3.2852672926262794,1.0957317547984249,3.179461619919733,0.9677938921609134]
[2.3000000000000003,3.3000000000000003,8.233514794716921e-18,3.7698259134267684,7.493024874860352e-18,3.4307826059078708,1.0988238971874986,3.3297078261743582,0.9705388561899959]
[2.4000000000000004,3.4000000000000004,8.610593211664677e-18,3.942476357744391,7.816562541465462e-18,3.5789186948015455,1.101583102033282,3.482251478449001,0.9729898260910606]
[2.5,3.5,8.993234516403355E-18,4.117673845344326,8.145685300987488E-18,3.729611993894271,1.1040488533620518,3.637049232600041,0.9751816646220133]
[2.6,3.6,9.381410108188335e-18,4.295405280989496,8.480264715833176e-18,3.882803696299879,1.1062638281411976,3.794089618094268,0.9771520568268358]
[2.7,3.7,9.775002755991777e-18,4.475616988871012,8.8201816069574E-18,4.038439234283462,1.1082541371122347,3.9533253188015807,0.9789240569080933]
[2.8000000000000003,3.8000000000000003,1.0173949232063317E-17,4.658280019309703,9.165325066346737e-18,4.196467827113654,1.110047833373641,4.114730856856077,0.9805224360998388]
[2.9000000000000004,3.9000000000000004,1.0578180883559362E-17,4.843362938674212,9.515591595849266e-18,4.356842086764219,1.11166823176539,4.278278558785725,0.9819677816147697]
[3,4,1.0987638123128492E-17,5.030838464091176,9.870884354693955e-18,4.519517673380645,1.1131361414343266,4.443944416065301,0.9832784684612564]
[3.1,4.1,1.1402245641014496E-17,5.220672113971919,1.0231112500546203E-17,4.684452993573529,1.1144678196438336,4.611698059783247,0.9844688517762711]
[3.2,4.2,1.182192173021928E-17,5.412826477664199,1.0596190611130373E-17,4.851608935600643,1.1156765826580528,4.781506531852565,0.9855506895385419]
[3.3000000000000003,4.300000000000001,1.2246649254527077E-17,5.6072937091202615,1.0966038175336893E-17,5.020948636363451,1.1167797392927497,4.953362989035497,0.986539267333174]
[3.4000000000000004,4.4,1.2676315556598246E-17,5.8040222266561114,1.1340579144350253E-17,5.1924372758849975,1.117783791748717,5.12722195202314,0.9874403251504387]
[3.5,4.5,1.31109065315464E-17,6.003005572159079,1.1719741534716124E-17,5.366041895568837,1.1187027028462513,5.303077801236779,0.9882661940481583]
[3.6,4.6,1.3550360058158209E-17,6.204215302592913,1.2103457076442652E-17,5.541731237077452,1.119544603874517,5.4809054949293605,0.9890240541184798]
[3.7,4.7,1.3994613175929697E-17,6.407622590640808,1.2491660900230262E-17,5.7194755991262,1.1203164485254102,5.660679650433527,0.9897200455402492]
[3.8000000000000003,4.800000000000001,1.4443626947893028E-17,6.613209608486334,1.2884291258773187E-17,5.899246709877457,1.1210261129464965,5.842384601043252,0.990361123778906]
[3.9000000000000004,4.9,1.4897325728119007E-17,6.820941720619475,1.3281289277796018E-17,6.081017612949334,1.12167767876457,6.025989830324368,0.9909508924118579]
[4,5,1.535568821554099e-17,7.030809174059273,1.3682598733099692E-17,6.264762565333183,1.1222786339844868,6.211486802984053,0.9914959646445441]
[4.1,5.1,1.5818658884262578E-17,7.242786545524379,1.4088165850411006E-17,6.450456945751983,1.122833096389271,6.398853138848288,0.9919999765384561]
[4.199999999999999,5.199999999999999,1.6286191939624882E-17,7.456852867311927,1.44979391252709e-17,6.638077172193769,1.1233453112819969,6.588070392928027,0.9924666770258088]
[4.3,5.3,1.675822798975829e-17,7.672980946052535,1.4911869160573065E-17,6.827600627526481,1.123818067963404,6.779114618770191,0.992898528868134]
[4.3999999999999995,5.3999999999999995,1.723475106923764e-17,7.891163471760735,1.532990851968482e-17,7.019005592247382,1.1242566155634164,6.971979435862771,0.9933001682693412]
[4.5,5.5,1.771569781106594E-17,8.111371431001409,1.5752011593355895E-17,7.212271183545444,1.1246625680835785,7.16663928767739,0.9936730199535256]
[4.6,5.6,1.8201055943755922E-17,8.333599205108424,1.6178134478855272E-17,7.407377299962517,1.1250404654223018,7.363089286494556,0.994021093880531]
[4.699999999999999,5.699999999999999,1.8690724531932156E-17,8.557800579457364,1.660823486997655E-17,7.604304571030807,1.1253889819272858,7.5612886755431745,0.9943432177017864]
[4.8,5.8,1.918476708872009e-17,8.784004634390238,1.7042271956725046E-17,7.803034311343248,1.1257165205106117,7.761263223924122,0.9946468148476031]
[4.8999999999999995,5.8999999999999995,1.9683037672268164E-17,9.012144548459876,1.7480206333647935E-17,8.003548478581235,1.126018611941666,7.962953965267041,0.9949279355997116]
[5,6,2.0185565379811256E-17,9.242233644228122,1.7921999915896563E-17,8.20582963508261,1.1263009415543488,8.16637274451327,0.9951916025162588]
[5.1,6.1,2.0692328380593226E-17,9.47426192618853,1.8367615862220632E-17,8.409860912583513,1.126565828456494,8.371510803300248,0.9954398640260647]
[5.199999999999999,6.199999999999999,2.1203240390038072E-17,9.70818988778301,1.8817018504189368E-17,8.615625979811334,1.1268119009032935,8.578333306258129,0.9956715073703766]
[5.3,6.3,2.1718277340956564E-17,9.94400650952403,1.9270173281017708E-17,8.823109012644013,1.1270411025494198,8.786830588076757,0.9958882493103887]
[5.3999999999999995,6.3999999999999995,2.223743392167905e-17,10.18170935939192,1.972704667944767e-17,9.032294666583903,1.1272561110146704,8.99700057114903,0.9960924552688203]
[5.5,6.5,2.2760655257564048E-17,10.421273312291195,2.0187606178197558E-17,9.243168051323096,1.1274568691628908,9.208821124871056,0.9962840742198641]
[5.6,6.6,2.3287885385231034E-17,10.66267274463249,2.0651820196546604E-17,9.4557147072022,1.1276432374287877,9.4222696768674,0.9964629822947888]
[5.699999999999999,6.699999999999999,2.3819185120527457E-17,10.905935501772662,2.1119658046670234E-17,9.669920583386402,1.127820586294144,9.63737090297551,0.9966339247432069]
[5.8,6.8,2.4354428905331102E-17,11.151004095230235,2.1591089889383198E-17,9.885772017601862,1.1279851563818784,9.854074071446451,0.9967935790852781]
[5.8999999999999995,6.8999999999999995,2.4893620184432805E-17,11.397880102249205,2.206608669298453E-17,10.103255717292324,1.1281393266866495,10.072380644395505,0.9969440471704606]
[6,7,2.5436705413847508E-17,11.646539006993088,2.2544620194930462E-17,10.322358742070536,1.1282827208403083,10.292269025063284,0.997084996001484]
[6.1,7.1,2.5983756873068246E-17,11.897013903603652,2.302666286609013E-17,10.543068487352247,1.1284204326165228,10.513768527218067,0.9972209266999139]
[6.199999999999999,7.199999999999999,2.6534640337773796E-17,12.149243335663195,2.351218787736375e-17,10.76537266907189,1.1285483288996638,10.736824907776404,0.9973481864332014]
[6.3,7.3,2.7089370605141708E-17,12.403234078259246,2.4001169068465348E-17,10.989259309389327,1.1286687964184998,10.961444220620281,0.9974688841180332]
[6.3999999999999995,7.3999999999999995,2.764790137766405e-17,12.65896493345271,2.4493580918691723E-17,11.214716723306033,1.1287815150199283,11.18760779826371,0.9975827365317229]
[6.5,7.5,2.821017116991527e-17,12.916407749311356,2.4989398519516673E-17,11.441733506116982,1.1288855611263786,{"$f":"D68/($M$6+$M$7*B68+$M$8*B68^2)","v":11.41529082633564},{"$f":"H68/F68","v":0.9976889271396502}]
[6.6,{"$f":"1+A69","v":7.6},2.877629027709766e-17,13.175613025982697,2.5488597548865174E-17,11.670298521631741,1.1289868036846484,11.644538001341719,0.9977926425581768]
[6.699999999999999,7.699999999999999,2.9346071516958256E-17,13.436495059544983,2.599115424693588E-17,11.90040089110447,1.1290791951041532,11.875273644171635,0.9978885377759318]
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