{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "EQ := m*(f/2+C^2/r^2)-K*m/r = -K*m/ 2/alpha; #Conservation de l'\351nergie" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#EQG/,&*&%\"mG\"\"\",&%\"fG#F)\"\"#*&*$)%\"CGF-\"\"\"F2*$)%\"r G\"\"#F2!\"\"F)F)F)*&*&%\"KGF)F(F2F2F5F7!\"\",$*&*&F:F2F(F2F2%&alphaGF 7#F;F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "f := unapply(solv e(EQ,f),r);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"rG6\"6$%)op eratorG%&arrowGF(,$*&,(*&)%\"CG\"\"#\"\"\"%&alphaG\"\"\"F2*(%\"KGF59$F 5F4F3!\"#*&F7F3)F8F2F3F5F3*&)F8\"\"#F3F4\"\"\"!\"\"!\"\"F(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "solutions := solve(f(r)=0,r) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*solutionsG6$,$*&,&*&%\"KG\"\" \"%&alphaGF+\"\"#*$-%%sqrtG6#,&*&)F*F-\"\"\")F,F-F5F+*(F*F5)%\"CGF-F5F ,F5!\"#F5F-F5F*!\"\"#F+F-,$*&,&F)F-F.F:F5F*F;F<" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 58 "r0 := solutions[2];\nr1 := solutions[1]; #V \351rifiez l'ordre!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#r0G,$*&,&*&% \"KG\"\"\"%&alphaGF*\"\"#*$-%%sqrtG6#,&*&)F)F,\"\"\")F+F,F4F**(F)F4)% \"CGF,F4F+F4!\"#F4F9F4F)!\"\"#F*F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#r1G,$*&,&*&%\"KG\"\"\"%&alphaGF*\"\"#*$-%%sqrtG6#,&*&)F)F,\"\"\")F+ F,F4F**(F)F4)%\"CGF,F4F+F4!\"#F4F,F4F)!\"\"#F*F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "q := simplify(expand(2*r0*r1/(r0+r1)));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG,$*&*$)%\"CG\"\"#\"\"\"F+%\"KG! \"\"F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "epsilon := simpli fy(expand((r1-r0)/(r1+r0)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(eps ilonG*&*$-%%sqrtG6#,$*(%\"KG\"\"\"%&alphaGF-,&*&F,\"\"\"F.F1!\"\"*$)% \"CG\"\"#F-F6F1F2F-F-*&F.\"\"\"F,\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "rr := theta -> q/(1 + epsilon*cos(theta));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#rrGR6#%&thetaG6\"6$%)operatorG%&arr owGF(*&%\"qG\"\"\",&\"\"\"F0*&%(epsilonGF0-%$cosG6#9$F0F0!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "simplify(rr(0)-r0);\nsimp lify(rr(Pi)-r1); #Simples v\351rifications\na := simplify((r0+r1)/2); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG%&alphaG " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 118 "T := 70.0; e := 0.90; \+ #La com\350te \351tudi\351e\na := solve(T^2/alpha^3 = 1.0,alpha)[3]; # Attention \340 l'ordre des solutions..." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"TG$\"$+(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"eG$\"#! *!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG$\"+_#*\\)p\"!\")" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "alpha := a; K := evalf(4*Pi ^2*a^3/T^2); #Kepler\nC := solve(epsilon=e,C)[2]; #Attention \340 l'or dre des solutions..." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alphaG$\"+_ #*\\)p\"!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"KG$\"+g<%y%R!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG$\"+eJJ\")z!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "evalf(r0); #r min en UA\nevalf(r1); #on la perdra de vue" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+e#*\\)p\" !\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+x&[rA$!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "t := unapply(int(1/sqrt(f(r)),r),r) : #Surtout ne pas faire afficher t(r)!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "tau := t(10.0) - t(r0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$tauG$\"*1'3%H$!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "tau * 365.25*24*3600.; #en unit\351s SI" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+-X`R5!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 161 "with(plots):\nComete := plot([rr(theta),theta,theta=0..2*Pi],co ords=polar):\nTerre := plot([1,theta,theta=0..2*Pi],coords=polar,color =blue):\ndisplay(Comete,Terre);" }}{PARA 13 "" 1 "" {GLPLOT2D 666 342 342 {PLOTDATA 2 "6%-%'CURVESG6$7eo7$$\"1Pi#[D*\\)p\"!#:\"\"!7$$\"1'oaT D\"4!p\"F*$\"1$y\"f4`DHB!#;7$$\"1l+4]7))o;F*$\"1Xq3ysJqVF17$$\"1#Rz^uZ )G;F*$\"1Kdp!>$)zp'F17$$\"1Swb4^))p:F*$\"1g:%=k%z$4*F17$$\"1'yJU:-0\\ \"F*$\"1x2([j*4b6F*7$$\"1*z&[4i(eR\"F*$\"1XNkHqL\"R\"F*7$$\"1$4V;=qIF \"F*$\"1Rsx7/lY;F*7$$\"1(=\\!*3iW6\"F*$\"1PBib-xC>F*7$$\"1'R\\D=;S<*F1 $\"1[eUh+N>AF*7$$\"1*4zJ**40k'F1$\"1CJiB@FWDF*7$$\"1ldfy6=sQF1$\"11k!#=$\"1)e>&)>$))GKF*7$$!1IEF\"pa9,&F1$\"1\">2Y[z Qk$F*7$$!1:)**z[:47\"F*$\"1\"p$Q!*Q(\\3%F*7$$!1^uL/FtV=F*$\"1nE$y&)H`_ %F*7$$!1D97P#H#zHF*$\"1)H%*fdbB5&F*7$$!1B&4@F>+F%F*$\"1Lj&f)[3NcF*7$$! 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