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Cell[CellGroupData[{
Cell["Exercices sur la gravitation", "Title",
  CellMargins->{{1, 0}, {Inherited, Inherited}},
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Cell[TextData[{
  StyleBox["Mots cl\[EAcute]s: force de gravitation, \
acc\[EAcute]l\[EAcute]ration \[AGrave] la surface d'un astre.\n",
    FontSize->11],
  StyleBox["\n",
    FontFamily->"Verdana",
    FontSize->11],
  StyleBox["Pour la th\[EAcute]orie, voir l\[CloseCurlyQuote]ouvrage \
\[LeftGuillemet] M\[EAcute]canique \[RightGuillemet] de J.-A. Monard. \
\[CapitalEAcute]diteur : \ncentrale d\[CloseCurlyQuote]achats de la ville de \
Bienne, Rennweg 62, 2501 Bienne, 1977.\n",
    FontSize->11,
    FontWeight->"Bold"],
  StyleBox["\nExercice 1",
    FontFamily->"Verdana",
    FontSize->11,
    FontWeight->"Bold"],
  StyleBox["\n",
    FontFamily->"Verdana",
    FontSize->11],
  StyleBox["On a deux boules de plomb dont les diam\[EGrave]tres valent \
respectivement 2 et 16 cm. Il y a entre elles un espace vide de 1 cm. \
Calculez la force d'attraction exerc\[EAcute]e par une boule sur l'autre. \n",
    
    FontSize->11],
  StyleBox["Exercice 2",
    FontFamily->"Verdana",
    FontSize->11,
    FontWeight->"Bold"],
  StyleBox["\n",
    FontFamily->"Verdana",
    FontSize->11],
  StyleBox["Calculez les forces d'attraction exerc\[EAcute]es sur la terre \
par le soleil et par la lune.",
    FontSize->11],
  StyleBox["\n",
    FontFamily->"Verdana",
    FontSize->11],
  StyleBox["Exercice 3",
    FontFamily->"Verdana",
    FontSize->11,
    FontWeight->"Bold"],
  StyleBox["\n",
    FontFamily->"Verdana",
    FontSize->11],
  StyleBox["Calculez l'acc\[EAcute]l\[EAcute]ration d'un objet qui se trouve \
au milieu du segment terre-lune.\n",
    FontSize->11],
  StyleBox["Exercice 4",
    FontFamily->"Verdana",
    FontSize->11,
    FontWeight->"Bold"],
  StyleBox["\n",
    FontFamily->"Verdana",
    FontSize->11],
  StyleBox["O\[UGrave] un objet doit-il se trouver pour que les forces de ",
    FontSize->11],
  StyleBox["g",
    FontSize->11,
    FontVariations->{"Underline"->True}],
  StyleBox["ravitation qu'il subit de la part de la terre et de la lune se \
compensent exactement ?",
    FontSize->11],
  StyleBox["\n",
    FontFamily->"Times New Roman",
    FontSize->11],
  StyleBox["Exercice 5",
    FontFamily->"Verdana",
    FontSize->11,
    FontWeight->"Bold"],
  StyleBox["\n",
    FontFamily->"Verdana",
    FontSize->11],
  StyleBox["D\[EAcute]terminez l'acc\[EAcute]l\[EAcute]ration de la pesanteur \
\[AGrave] la surface de la lune\n",
    FontSize->11],
  StyleBox["Exercice 6",
    FontFamily->"Verdana",
    FontSize->11,
    FontWeight->"Bold"],
  StyleBox["\n",
    FontFamily->"Verdana",
    FontSize->11],
  StyleBox["La plan\[EGrave]te Jupiter a un rayon de 71'800 km et une masse \
volumique moyenne de 1140 kg/",
    FontSize->11],
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  StyleBox[". Calculez l'acc\[EAcute]l\[EAcute]ration d'un objet qui tombe en \
chute libre \[AGrave] la surface de cette plan\[EGrave]te.",
    FontSize->11],
  StyleBox["\n",
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    FontSize->11],
  StyleBox["Exercice 7",
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    FontSize->11,
    FontWeight->"Bold"],
  StyleBox["\n",
    FontFamily->"Verdana",
    FontSize->11],
  StyleBox["On imagine une petite plan\[EGrave]te constitu\[EAcute]e par une \
boule de 100 m de rayon faite d'une mati\[EGrave]re dont la masse volumique \
est de 4 kg/d",
    FontSize->11],
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    FontFamily->"Arial",
    FontSize->11,
    FontVariations->{"CompatibilityType"->0}],
  StyleBox[" .\na) Quel serait le poids d'un habitant de cette \
plan\[EGrave]te, si sa masse \[EAcute]tait de 60 kg ?\nb) Quel temps mettrait \
un objet pour tomber d'une hauteur de 5 m, sa vitesse initiale \[EAcute]tant \
nulle ?\n",
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  StyleBox["Exercice 8",
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    FontSize->11],
  StyleBox["D\[EAcute]terminez le poids qu'a sur la lune une personne qui sur \
la terre p\[EGrave]se 672 N.\nb) Si un objet est lanc\[EAcute] vers le haut \
\[AGrave] une vitesse de 2 m/s depuis la surface de la lune, quelle hauteur \
atteint-il ? Et combien de temps apr\[EGrave]s son d\[EAcute]part est-il de \
retour sur le sol ?",
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    FontSize->11],
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    FontSize->11,
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    FontSize->11],
  StyleBox["Calculez le temps de r\[EAcute]volution d'un satellite qui d\
\[EAcute]crit une trajectoire circulaire de 384'000 km de rayon autour de la \
terre. Exprimez le r\[EAcute]sultat en jours et en heures.\n",
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  StyleBox["Exercice 10",
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    FontSize->11,
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  StyleBox["\nCalculez le temps de r\[EAcute]volution d'un satellite qui d\
\[EAcute]crit une trajectoire circulaire tr\[EGrave]s pr\[EGrave]s d'un astre \
de rayon ",
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  StyleBox[" et de masse volumique \[Rho]",
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  StyleBox["Qu'est-ce que le r\[EAcute]sultat a de remarquable ?\n",
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  StyleBox["Exercice 11",
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    FontSize->11,
    FontWeight->"Bold"],
  StyleBox["\nCalculez le temps de r\[EAcute]volution et la vitesse d'un \
satellite d\[EAcute]crivant une trajectoire circulaire autour de la lune, \
\[AGrave] une altitude de 100 km au-dessus de sa surface.\n",
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  StyleBox["Exercice 12\n",
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  StyleBox["La trajectoire de la terre autour du soleil est \[AGrave] peu pr\
\[EGrave]s un cercle de 149'500'000 km de rayon. Sachant que la terre met une \
ann\[EAcute]e pour effectuer une r\[EAcute]volution, calculez la masse du \
soleil.",
    FontSize->11]
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Si on consid\[EGrave]re que les distances donn\[EAcute]es dans la \
table sont celles entre les surfaces des astres\
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        dTL \[Rule] 3.84404*10^8, rL \[Rule] 1.738*10^6, 
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        mL \[Rule] 7.35*10^22, mT \[Rule] 5.9742*10^24, 
        dTL \[Rule] 3.84404*10^8, rL \[Rule] 1.738*10^6, 
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Si on consid\[EGrave]re que les distances donn\[EAcute]es dans la \
table sont celles entre les surfaces des astres\
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    \(sol =. \), "\[IndentingNewLine]", 
    \(\(sol = 
        Solve[G \((mT/\((dTL - x)\)^2 - mL/x^2)\) \[Equal] 0, 
          x];\)\), "\[IndentingNewLine]", 
    \(sol /. {G \[Rule] 6.6732*10^\(-11\), mL \[Rule] 7.35*10^22, 
        mT \[Rule] 5.9742*10^24, dTL \[Rule] 3.84404*10^8}\)}], "Input"],

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Cell[CellGroupData[{

Cell[BoxData[
    \(\(G*mJ/rJ^2 /. {mJ \[Rule] 4/3*\[Pi]*rJ^3*rhoJ}\) /. {G \[Rule] 
          6.6732*10^\(-11\), rJ \[Rule] 7.18*10^7, 
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Cell[BoxData[
    \(\(G*M*m/r^2 /. {M \[Rule] 4/3*\[Pi]*r^3*rho}\) /. {G \[Rule] 
          6.6732*10^\(-11\), r \[Rule] 100, rho \[Rule] 4000, 
        m \[Rule] 60}\)], "Input"],

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Cell[BoxData[
    \(Sqrt[\(2  h*
            r^2/\((G*M)\) /. {M \[Rule] 4/3*\[Pi]*r^3*rho}\) /. {G \[Rule] 
            6.6732*10^\(-11\), r \[Rule] 100, rho \[Rule] 4000, 
          h \[Rule] 5}]\)], "Input"],

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        mL \[Rule] 7.35*10^22, rL \[Rule] 1.738*10^6, p \[Rule] 672, 
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Cell["\<\
Le temps de mont\[EAcute]e est \[EAcute]gal au temps de descente. \
L'objet est de retour apr\[EGrave]s :\
\>", "Text",
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          T] /. {G \[Rule] 6.6732*10^\(-11\), mT \[Rule] 5.9742*10^24, 
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Cell[BoxData[{
    \(IntegerPart[
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Cell["\<\
On admet que le rayon de l'orbite est \[EAcute]gal \[AGrave] celui \
de l'astre.\
\>", "Text",
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Cell["La p\[EAcute]riode de r\[EAcute]volution ne d\[EAcute]pend pas du rayon \
de l'astre", "Text",
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            v \[Rule] 2  \[Pi] \((rL + h)\)/T\) /. {G \[Rule] 
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