ࡱ> VU Fɀ\puser Ba= =R8V@"1Arial1Arial1Arial1Arial1Arial1 Arial1 Arial1Arial1Arial1@Arial1Arial1Arial1Arial1 Arial1Arial1 Arial1Symbol1Arial1Arial1Arial1 Arial1Arial1Arial "R$ "#,##0_);\("R$ "#,##0\)% "R$ "#,##0_);[Red]\("R$ "#,##0\)&!"R$ "#,##0.00_);\("R$ "#,##0.00\)+&"R$ "#,##0.00_);[Red]\("R$ "#,##0.00\)=*8_("R$ "* #,##0_);_("R$ "* \(#,##0\);_("R$ "* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)E,@_("R$ "* #,##0.00_);_("R$ "* \(#,##0.00\);_("R$ "* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_)"R$"#,##0_);\("R$"#,##0\)#"R$"#,##0_);[Red]\("R$"#,##0\)$"R$"#,##0.00_);\("R$"#,##0.00\))$"R$"#,##0.00_);[Red]\("R$"#,##0.00\):5_("R$"* #,##0_);_("R$"* \(#,##0\);_("R$"* "-"_);_(@_)B=_("R$"* #,##0.00_);_("R$"* \(#,##0.00\);_("R$"* "-"??_);_(@_) 0.0000 0.000000000000.000000000000 0.00000E+000.0000000000000000.000000000000000E+00 0.000000.0000000000000000E+000.0000000000000E+000.000000000E+00 0.000000000 0.000000 0.0000000 0.0E+00 0.0000E+00 0.000E+00 0.00000000 0.0000000000 0.000 0.000000E+00                   + ) # #X #X          !  !                       "  #8@ @  "  #  #X #X  8@  8  8 <    (   <  x  8 x <  8   #8  < <  ( < < <  8  8@  8  x <  <  8 <  8  8@@  8@  8 @ ` #Plan177-CUniversoOktabela do tempo do Universo.xlsTABELAPLAN138PLAN13PLAN12PLAN11PLAN10PLAN9PLAN8PLAN7PLAN6PLAN5PLAN4PLAN3PLAN2PLAN1YYYYYYYYYY Y Y Y Y Y  ;* Diferenas): ; ;;&&;22;>>;JJ;VV;bb;nn;zz;T_ZcAng AAng EAng Msoma1Ang Lsoma2Ang Bsoma3Velocidade de expanso da TerraIdade do UniversoVelocidade da Luz/Distncia da Terra, hoje, ao centro do Universo?Tempo gasto pelo fton e pelo raio de luz para alcanar a TerraConstante de Hubbleunidade de velocidadegraus csoma4fmHz Redshift f'lKm/s/Mpcc ABbaSoma 1Soma 2Soma 3Soma 4T Ang O !Planilha do Universo verdadeiro [ 1 ][ 2 ] [ 3 ][ 4 ][ 5 ] [ 6 ][ 7 ][ 8 ][ 9 ][ 10 ][ 11 ][ 12 ][ 13 ][ 14 ][ 15 ][ 16 ][ 17 ][ 18 ][ 19 ][ 20 ][ 21 ][ 22 ][ 23 ][ 24 ][ 25 ][ 26 ][ 27 ][ 28] [ 29 ][ 30 ][ 31 ][ 32 ][ 33 ][ 34 ][ 35 ][ 36 ][ 37 ][ 38 ][ 39 ][ 40 ][ 41 ]f'1Raio do Universo Visvelbilhes de anos luzVt  VpT2T1b1a1c2c1[ 42 ]c1a c1b HoV1V2Vac4Rvoutra maneira de calcular f '@Outra maneira de calcular c1, considerando o observador na Terra bilhes de anosFrequncia da luz na emissoXX2X1 =X/c*Comprimento da onda da luz amarela ( Sol )"Velocidade de expanso da galxia @ngulo que a velocidade da Terra faz com a velocidade da galxia1Distncia da galxia, hoje, ao centro do Universo.Distncia entre a Terra e a galxia atualmente2Idade do Universo na ocasio da emisso dos ftons8ngulo que o raio de luz faz com a trajetria da galxiaIDistncia da galxia ao centro do Universo na poca da emisso dos ftons<Distncia percorrida pelo fton na sua trajetria verdadeira@Distncia de Terra ao centro do Universo na idade T1 do Universo34 2Distncia percorrida pela Terra depois da idade T11/Distncia entra a galxia e a Terra na idade T1.$Velocidade do Fton na trajetria X2#2Velocidade de um fton para um observador na Terra@Velocidade de afastamento entre a galxia e a Terra devido a Vp >? CVelocidade de afastamento da Terra em relao a galxia devido a VtB3Velocidade de afastamento entre a galxia e a TerraVelocidade da raio de luz = Vt * T=Vp * T=T - T2 = raiz (A2 + B2 - 2*A*B*cosO)   = Vt * T1 = T1 * Vp  = T2 * Vp $ = ( A2 + X22 - b2 ) / ( 2 * A * X2 )   !"$ = ( b2 + X22 - A2 ) / ( 2 * b * X2 )   !" = V1 + V2ang B1ang E1 = Ang B - Ang A= c - Va" = ang E + ang M + ( 180 - ang L )= f * ( 1- Va / c )   = 3 * 108 * c1 /   "= ( B2 + X2 - A2 ) / ( 2 * B * X )  "= ( A2 + X2 - B2 ) / ( 2 * A * X )  = ang O + ang M + ang B1&= raiz ( A2 + b2 - 2 *A * b * cos O )  = ang O + ang L + ang A%= raiz( a2 + b2 - 2 * a * b * cos O )   = X2 / T2  = X1 / T2  = 180 - ang B= ang L - ang M = Vp * cos M = Vt * cos B = ang A + ang B1 + ang E1* = raiz (c22 + Vp2 + 2 * c2 * Vp * cos L )    >Distncia percorrida pela galxia depois da emisso dos ftons6ngulo que o raio de luz faz com a trajetria da Terra/ngulo formado por X2 com a trajetria da Terra 2ngulo formado por X2 com a trajetria da galxia  Suplemento do ngulo Bngulo da 1 Aberrao/ngulo de Aberrao do fton ao chegar na Terra;Outra maneira de calcular c1,considerando o tringulo P1L1L 78 9: %Frequncia da luz ao chegar na terra * = raiz ( c22 + Vt2 -2 * c2 * Vt * cos A )    ) = ( 300000 * 0,00326 * ( V1 + V2 ) ) / X !*= raiz ( (1+Va / c ) / ( 1-Va / c ) ) - 1  = T2 * Vt= T * c D(#oL84| X1I E H  H" Fɀ  t(Ub{  dMbP?_*+%,&[Vj?'\.?(M&d2?)i4F?M6HP DeskJet 695CXC 4d,,A4DINU"4$H$$$$" A,,jZ?jZ?U} /} (} m} I} } m'} v} wItww@wXw;w;wXwwwwwXwX wX wX wX wX wXwXwwwXwXwww;wwwwwXwwwwwwwX T&UUUUV 5' 6 7~ 8? 9:2++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++v 5( 6 7$~ ;h@ <f:2****************************************************************************************************************v 5) 6g =Ra.C >:3""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""v 5* 6l ?@d%ؠ> <A4!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!v 5+ 6 7S~ ;T@ 9:2****************************************************************************************************************v 5, 6m 7T~ BV@ 9C2----------------------------------------------------------------------------------------------------------------v 5- 6n 7%DaDt>@ <A2................................................................................................................v 5. 6 7!EQ%@  DD >R S~2$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$v 5/ 6o 7! E)\(@  DD >R S 2$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$v 50 6p 7hH EbKU@ 2DD DD DAVAA >R S 2$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$v 51 6 7U! EbKU@  D D <f Sk 2$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$v 52 6q 7V! E2j w@ DD  <f S 2$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$v 53 6r 7K F!yu"EO@5D D DD D AcAW < S 2 v 54 6 7KFU@5DD D DD AcAW < S2 v 55 6 7'Ff@ FDD D < S2 v 56 6s 7!F6tDŽ@ D D >R S2 v 57 6 =W!FX$@ D D >R S3 v 58 6t 7iHE]Mn@2DDDDDAVAA >R S2$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$v 59 6 7KF>j@@5DDDDDAcAW < S2 v 5: 6 7KF:]OG]@5DDDDDAcAW < S2 v 5; 6! 7'Ff@DDD < S2 v 5< 6u 7!F!Mgx@ DD  >R S2 v 5= 6v =X!F#֑D@ D D >R S3 v 5> 6w 7jHENE> @2DDDDDAVAA >R S2$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$v 5? 6x 7Y!E XX? DD  9 S2 v 5@ 6y 7Z!E 4?) DD  9 S2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%v 5A 6 7FUZKXW@  D < S2 v 5B 6 7!FqA)lJ@" DD  < S2 v 5C 6z 7_'E=?DD AVA 9 S2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%v 5D 6{ 7`'E,p7?DDAVA 9 S2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%v 5E 6| 7a!EB䍖?' DD 9 S2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%vDu,l"4488448WW~WW]WW~]WW~WWUW]] w!w"wX#w$w%w&w;'w(w)w*wX+w,@,w,@-w,@.w,@/w,@0w,@1w,@2w,@3w,@4w,@5w,@6w,@7w,@8w,@9w,@:w,@;w,@<w,@=w,@>w,@?w,@ 5F 6" 7 ' Ff@#DDD < A 2 v !5G !6} !7bH!E?2DDDDDAVAA !9 !A!2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%v "5H "6 "7!"FqA)lJ@& DD "< "A"2 v #5I #6 #7\H#E 4?!2DDDDDAVAA #9 #A#2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%v $5J $6e $7]!$E 4? DD $< $G$2,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,v %5K %6 %7^=%HUQ@$'OAQ,j?DDD  %< %A%2&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&v &5L &6# &=,&Ff@D"D D &< &A&3 v '5M '6 '=@'IM1?(*DDDDA'< 'S'3''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''v (5N (6 (=-(JHMCB%DDD (> (G(3!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!v )5O )6d )=P,)J\CB ADD )> )K)3!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!v *L[ *MQ *Nc!*Offffff+@ DD *PR *Q*3 v+1+($((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((v,#)################################################################################################################v -$- $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$v.) ))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))v /$/$ v0$  v1$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$v2$ v3 v4 v5 v6 v7 v8 0 v9 v: v; v< v= v> v? vD &l]~W~WsbrcbW@w,@Aw,@Bw,@Cw,@Dw,@Ew,@Fw,@Gw,@Hw,@Iw,@Jw,@Kw,@Lw,@Mw,@Nw,@Ow,@Pw,@Qw,@Rw,@Sw,@Tw,@Uw,@Vw,@Ww,@Xw,@Yw,@Zw,@[w,@\w,@]w,@^w,@_w,@@ @ vA A vB B BtvC C Ctv D Dtv E Etv F Ftv G Gtv H Htv I Itv J Jtv K Ktv L Ltv M Mtv N Ntv O Otv P Ptv Q Qtv R Rtv S Stv T Ttv U Utv V Vtv W Wtv X Xtv Y Ytv Z Ztv [ [tv \ \tv ] ]tv ^ ^tv _ _tvDl((`w,@aw,@bw,@cw,@dw,@ew,@fw,@gw,@hw,@iw,@jw,@kw,@lw,@mw,@nw,@ow,@pw,@qw,@rw,@sw,@ ` `tv a atv b btv c ctv d dtv e etv f ftv g gtv h htv i itv j jtv k ktv l ltv m mtv n ntv o otv p ptv q qtv r rtv s stv,|>@,,, 7 Oh+'0HPhx Geraldo Caciqueuserdo Microsoft Excel@4~X@bOI@՜.+,0 PXh px SistopA Plan1Plan1!Area_de_impressao  PlanilhasIntervalos nomeados  !"#$%&'()*+,-./0123456789:;<=>?@ABCDFGHIJKLNOPQRSTRoot Entry F#nWorkbookgSummaryInformation(EDocumentSummaryInformation8M