Seconde \u2014 La gravitation universelle<\/title>\n<style>\n:root{\n --deep:#101828;\n --blue:#2563EB;\n --cyan:#0891B2;\n --teal:#14B8A6;\n --purple:#7C3AED;\n --pink:#DB2777;\n --orange:#F97316;\n --red:#B83227;\n --green:#0F766E;\n --amber:#F59E0B;\n --ink:#1F2937;\n --paper:#FFFFFF;\n --line:#D9E2EC;\n}\n*{box-sizing:border-box}\nhtml{scroll-behavior:smooth}\nbody{\n margin:0;\n font-family:Arial, Helvetica, sans-serif;\n background:\n radial-gradient(circle at top left, rgba(37,99,235,.12), transparent 28%),\n linear-gradient(180deg,#f8fbff,#eef4f8);\n color:var(--ink);\n line-height:1.65;\n}\nheader{\n background:\n radial-gradient(circle at 84% 18%, rgba(245,158,11,.30), transparent 25%),\n linear-gradient(135deg,#0f172a,#1d4ed8,#14b8a6);\n color:white;\n padding:54px 22px;\n text-align:center;\n}\nheader h1{margin:0;font-size:clamp(2.1rem,4vw,3.7rem)}\nheader p{font-size:1.15rem;margin:10px 0 0;opacity:.96}\n.container{max-width:1180px;margin:auto;padding:28px}\n.section{\n 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font-size:1.16rem;\n border-bottom:3px solid #111;\n padding:2px 4px;\n margin-top:8px;\n}\n.exercice{\n border-left:7px solid var(--pink);\n background:#fffdfb;\n border-radius:18px;\n padding:22px;\n margin:22px 0;\n}\n.methode{\n background:#fff8f2;\n border:2px dashed var(--orange);\n padding:18px;\n border-radius:16px;\n margin:16px 0;\n}\n.note{\n background:#f1f7ff;\n border-left:6px solid var(--blue);\n padding:16px;\n border-radius:14px;\n margin:16px 0;\n}\n.litteral{\n background:#f7fbff;\n border:2px solid var(--blue);\n border-left:8px solid var(--blue);\n border-radius:16px;\n padding:16px;\n margin:16px 0;\n}\n.litteral .start{color:var(--red);font-weight:900}\n.litteral .step{color:var(--deep);font-weight:800}\n.grid2{display:grid;grid-template-columns:repeat(auto-fit,minmax(320px,1fr));gap:22px;align-items:start}\n.grid3{display:grid;grid-template-columns:repeat(auto-fit,minmax(250px,1fr));gap:18px;align-items:start}\n.schema{\n background:#fbfdff;\n border:1px solid 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background:linear-gradient(135deg,var(--deep),var(--teal));\n color:white;\n border-radius:18px;\n padding:18px;\n font-size:1.3rem;\n font-weight:900;\n}\n.small{font-size:.92rem;color:#5b6770}\n@media print{button,.btns,.linkbtn{display:none}body{background:white}.section{box-shadow:none;break-inside:avoid}}\n<\/style>\n<\/head>\n<body>\n\n<header>\n<h1>La gravitation universelle<\/h1>\n<p>Seconde physique-chimie \u2022 Attraction gravitationnelle \u2022 Force entre deux corps \u2022 Champ de pesanteur \u2022 Terre \u2022 Lune \u2022 Altitude<\/p>\n<\/header>\n\n<div class=\"container\">\n\n<div class=\"btns\">\n<button onclick=\"playAudioSummary()\">\ud83d\udd0a \u00c9couter le r\u00e9sum\u00e9 audio clair<\/button>\n<button class=\"stop\" onclick=\"stopAudioSummary()\">\u23f9 Arr\u00eater<\/button><br>\n<a class=\"linkbtn cyanbtn\" href=\"#fiche-bilan\">\ud83d\udccc Aller \u00e0 la fiche bilan<\/a>\n<a class=\"linkbtn pinkbtn\" href=\"#exercices\">\ud83d\ude80 Exercices contextualis\u00e9s<\/a>\n<a class=\"linkbtn greenbtn\" href=\"#type-bac\">\ud83c\udf93 Partie type bac \/ \u00e9valuation<\/a>\n<a class=\"linkbtn orangebtn\" href=\"#lune\">\ud83c\udf19 Terre \/ Lune<\/a>\n<\/div>\n\n<div id=\"audioText\" style=\"display:none;\">\nBienvenue dans le chapitre la gravitation universelle.\nC\u2019est la gravitation universelle qui r\u00e9git le mouvement des plan\u00e8tes et des \u00e9toiles de notre univers.\nC\u2019est Newton, au dix-septi\u00e8me si\u00e8cle, qui a \u00e9tabli la loi de la gravitation universelle.\nTout corps qui poss\u00e8de une masse exerce sur un autre corps qui poss\u00e8de lui aussi une masse une force attractive appel\u00e9e attraction gravitationnelle.\nLes deux forces gravitationnelles exerc\u00e9es entre deux corps ont la m\u00eame valeur, mais des sens oppos\u00e9s.\nLa valeur de la force gravitationnelle s\u2019\u00e9crit F \u00e9gale G fois m un fois m deux divis\u00e9 par d au carr\u00e9.\nG est la constante universelle de gravitation.\nLes masses doivent \u00eatre en kilogrammes et la distance entre les centres des objets doit \u00eatre en m\u00e8tres.\n\u00c0 la surface de la Terre, on peut simplifier l\u2019attraction gravitationnelle : la force exerc\u00e9e par la Terre sur un objet est son poids, P \u00e9gale m fois g.\nLe champ de pesanteur terrestre vaut environ 9,81 newtons par kilogramme.\nEn altitude, le champ gravitationnel diminue l\u00e9g\u00e8rement car la distance au centre de la Terre augmente.\nSur la Lune, le champ de pesanteur vaut environ 1,6 newton par kilogramme.\nOn se sent donc environ six fois plus l\u00e9ger sur la Lune.\nFin du r\u00e9sum\u00e9.\n<\/div>\n\n<section class=\"section\">\n<h2>Objectifs du chapitre<\/h2>\n<p>\nCe cours reprend les phrases du cahier comme base : gravitation universelle, force gravitationnelle,\nloi de Newton, repr\u00e9sentation des forces, gravitation \u00e0 la surface de la Terre,\nchamp gravitationnel, variation avec l\u2019altitude et comparaison Terre-Lune.\n<\/p>\n<div class=\"grid3\">\n<div class=\"card\"><h3>Comprendre<\/h3><p>La gravitation comme interaction attractive entre deux corps poss\u00e9dant une masse.<\/p><\/div>\n<div class=\"card\"><h3>Calculer<\/h3><p>Une force gravitationnelle, un champ g, un poids P.<\/p><\/div>\n<div class=\"card\"><h3>Repr\u00e9senter<\/h3><p>Des forces gravitationnelles avec une direction, un sens et une \u00e9chelle.<\/p><\/div>\n<\/div>\n<\/section>\n\n<section class=\"section\">\n<h2>\ud83d\udd34 M\u00e9thode obligatoire pour les exercices<\/h2>\n<p>\nOn part toujours de la <span class=\"red\">formule du cours<\/span>, puis on fait le\n<span class=\"blue\">travail litt\u00e9ral<\/span>, et seulement ensuite l\u2019application num\u00e9rique.\n<\/p>\n<div class=\"litteral\">\n<p class=\"start\">Exemple : isoler une masse \u00e0 partir du poids<\/p>\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">P = m \u00d7 g<\/div>\n<p class=\"step\">On veut isoler m. On divise par g :<\/p>\n<div class=\"formule bluebox\">m = P \/ g<\/div>\n<p class=\"red\">Ensuite seulement, on remplace par les valeurs num\u00e9riques.<\/p>\n<\/div>\n<\/section>\n\n<section class=\"section\">\n<h2>I. Force gravitationnelle<\/h2>\n\n<p>\nC\u2019est la gravitation universelle qui r\u00e9git le mouvement des plan\u00e8tes et \u00e9toiles de notre univers.\n<\/p>\n<p class=\"red\">\nC\u2019est Newton au XVII\u1d49 si\u00e8cle qui a \u00e9tabli la loi de la gravitation universelle.\n<\/p>\n<p class=\"red\">\nTout corps qui poss\u00e8de une masse exerce sur un autre corps qui poss\u00e8de lui aussi une masse\nune force attractive appel\u00e9e attraction gravitationnelle.\n<\/p>\n\n<div class=\"schema\">\n<svg width=\"820\" height=\"370\" viewBox=\"0 0 820 370\">\n<rect x=\"50\" y=\"45\" width=\"720\" height=\"250\" rx=\"22\" fill=\"#fbfdff\" stroke=\"#D9E2EC\"\/>\n<circle cx=\"230\" cy=\"165\" r=\"60\" fill=\"#dbeafe\" stroke=\"#2563EB\" stroke-width=\"4\"\/>\n<text x=\"205\" y=\"100\" font-size=\"18\" fill=\"#2563EB\" font-weight=\"900\">m\u2081<\/text>\n<circle cx=\"590\" cy=\"165\" r=\"70\" fill=\"#fef3c7\" stroke=\"#F59E0B\" stroke-width=\"4\"\/>\n<text x=\"570\" y=\"85\" font-size=\"18\" fill=\"#F97316\" font-weight=\"900\">m\u2082<\/text>\n<circle cx=\"230\" cy=\"165\" r=\"5\" fill=\"#111827\"\/>\n<circle cx=\"590\" cy=\"165\" r=\"5\" fill=\"#111827\"\/>\n<line x1=\"230\" y1=\"165\" x2=\"590\" y2=\"165\" stroke=\"#0F766E\" stroke-width=\"4\"\/>\n<polygon points=\"590,165 568,153 568,177\" fill=\"#0F766E\"\/>\n<polygon points=\"230,165 252,153 252,177\" fill=\"#0F766E\"\/>\n<text x=\"372\" y=\"190\" fill=\"#0F766E\" font-size=\"18\" font-weight=\"900\">d = G\u2081G\u2082<\/text>\n<line x1=\"230\" y1=\"135\" x2=\"325\" y2=\"135\" stroke=\"#B83227\" stroke-width=\"5\"\/>\n<polygon points=\"325,135 303,123 303,147\" fill=\"#B83227\"\/>\n<text x=\"260\" y=\"125\" fill=\"#B83227\" font-size=\"17\" font-weight=\"900\">F\u2082\/\u2081<\/text>\n<line x1=\"590\" y1=\"135\" x2=\"495\" y2=\"135\" stroke=\"#7C3AED\" stroke-width=\"5\"\/>\n<polygon points=\"495,135 517,123 517,147\" fill=\"#7C3AED\"\/>\n<text x=\"525\" y=\"125\" fill=\"#7C3AED\" font-size=\"17\" font-weight=\"900\">F\u2081\/\u2082<\/text>\n<text x=\"150\" y=\"325\" fill=\"#B83227\" font-size=\"17\" font-weight=\"900\">Forces attractives, m\u00eame valeur, sens oppos\u00e9s.<\/text>\n<\/svg>\n<\/div>\n\n<div class=\"formule\">F\u2081\/\u2082 = F\u2082\/\u2081<\/div>\n\n<h3>Loi de la gravitation universelle<\/h3>\n<div class=\"formule\">F\u2081\/\u2082 = G \u00d7 m\u2081 \u00d7 m\u2082 \/ d\u00b2<\/div>\n\n<ul>\n<li><span class=\"red\">G<\/span> : constante universelle de la gravitation ;<\/li>\n<li><span class=\"red\">G = 6,67 \u00d7 10\u207b\u00b9\u00b9 N\u00b7m\u00b2\u00b7kg\u207b\u00b2<\/span> ;<\/li>\n<li><span class=\"red\">m\u2081<\/span> : masse de l\u2019objet 1 en kg ;<\/li>\n<li><span class=\"red\">m\u2082<\/span> : masse de l\u2019objet 2 en kg ;<\/li>\n<li><span class=\"red\">d<\/span> : distance entre les deux objets, de centre \u00e0 centre, en m.<\/li>\n<\/ul>\n\n<div class=\"note\">\n<p class=\"red\">Attention unit\u00e9s :<\/p>\n<p>Les masses doivent \u00eatre en <span class=\"red\">kg<\/span>.<\/p>\n<p>La distance doit \u00eatre en <span class=\"red\">m<\/span>, m\u00eame si elle est souvent donn\u00e9e en km.<\/p>\n<\/div>\n\n<div class=\"exercice\">\n<h3>Exercice type \u2014 Force exerc\u00e9e par la Terre sur la Lune<\/h3>\n<p>\nCalculer et repr\u00e9senter la force qu\u2019exerce la Terre sur la Lune.\n<\/p>\n<p>Donn\u00e9es : m<sub>T<\/sub> = 5,98 \u00d7 10\u00b2\u2074 kg ; m<sub>L<\/sub> = 7,2 \u00d7 10\u00b2\u00b2 kg ; d<sub>T\/L<\/sub> = 3,84 \u00d7 10\u2075 km.<\/p>\n<p>\u00c9chelle : 1 cm \u2194 1 \u00d7 10\u00b2\u2070 N.<\/p>\n\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">F = G \u00d7 m\u2081 \u00d7 m\u2082 \/ d\u00b2<\/div>\n<p class=\"step\">Pour Terre-Lune :<\/p>\n<div class=\"formule bluebox\">F<sub>T\/L<\/sub> = G \u00d7 m<sub>T<\/sub> \u00d7 m<sub>L<\/sub> \/ d\u00b2<\/div>\n<\/div>\n\n<p class=\"red\">Conversion :<\/p>\n<p>d = 3,84 \u00d7 10\u2075 km = 3,84 \u00d7 10\u2078 m<\/p>\n\n<p>Application num\u00e9rique :<\/p>\n<p>F<sub>T\/L<\/sub> = (6,67 \u00d7 10\u207b\u00b9\u00b9 \u00d7 5,98 \u00d7 10\u00b2\u2074 \u00d7 7,2 \u00d7 10\u00b2\u00b2) \/ (3,84 \u00d7 10\u2078)\u00b2<\/p>\n<p class=\"resultat\">F<sub>T\/L<\/sub> \u2248 1,95 \u00d7 10\u00b2\u2070 N<\/p>\n<p>Avec l\u2019\u00e9chelle propos\u00e9e, cela correspond \u00e0 environ 1,95 cm.<\/p>\n\n<div class=\"schema\">\n<svg width=\"760\" height=\"250\" viewBox=\"0 0 760 250\">\n<circle cx=\"180\" cy=\"125\" r=\"55\" fill=\"#dbeafe\" stroke=\"#2563EB\" stroke-width=\"4\"\/>\n<text x=\"150\" y=\"195\" font-size=\"16\" font-weight=\"900\">Terre<\/text>\n<circle cx=\"570\" cy=\"125\" r=\"38\" fill=\"#f1f5f9\" stroke=\"#64748b\" stroke-width=\"4\"\/>\n<text x=\"545\" y=\"195\" font-size=\"16\" font-weight=\"900\">Lune<\/text>\n<line x1=\"570\" y1=\"125\" x2=\"430\" y2=\"125\" stroke=\"#B83227\" stroke-width=\"6\"\/>\n<polygon points=\"430,125 452,113 452,137\" fill=\"#B83227\"\/>\n<text x=\"455\" y=\"110\" fill=\"#B83227\" font-size=\"18\" font-weight=\"900\">F<sub>T\/L<\/sub><\/text>\n<\/svg>\n<\/div>\n<\/div>\n<\/section>\n\n<section class=\"section\">\n<h2>II. Force gravitationnelle \u00e0 la surface de la Terre<\/h2>\n\n<p>\nAu niveau de la mer, on cherche la force gravitationnelle qu\u2019exerce la Terre sur un homme de masse m<sub>H<\/sub>.\n<\/p>\n\n<div class=\"schema\">\n<svg width=\"760\" height=\"420\" viewBox=\"0 0 760 420\">\n<rect x=\"55\" y=\"45\" width=\"650\" height=\"300\" rx=\"22\" fill=\"#fbfdff\" stroke=\"#D9E2EC\"\/>\n<circle cx=\"360\" cy=\"210\" r=\"120\" fill=\"#dbeafe\" stroke=\"#2563EB\" stroke-width=\"4\"\/>\n<circle cx=\"360\" cy=\"210\" r=\"5\" fill=\"#111827\"\/>\n<text x=\"348\" y=\"215\" font-size=\"17\" fill=\"#111827\" font-weight=\"900\">T<\/text>\n<circle cx=\"455\" cy=\"115\" r=\"12\" fill=\"#F97316\"\/>\n<line x1=\"360\" y1=\"210\" x2=\"455\" y2=\"115\" stroke=\"#0F766E\" stroke-width=\"4\"\/>\n<text x=\"405\" y=\"155\" fill=\"#0F766E\" font-size=\"16\" font-weight=\"900\">R<sub>T<\/sub><\/text>\n<line x1=\"455\" y1=\"115\" x2=\"415\" y2=\"155\" stroke=\"#B83227\" stroke-width=\"5\"\/>\n<polygon points=\"415,155 438,148 424,134\" fill=\"#B83227\"\/>\n<text x=\"460\" y=\"105\" fill=\"#B83227\" font-size=\"16\" font-weight=\"900\">F<sub>T\/H<\/sub><\/text>\n<text x=\"85\" y=\"375\" font-size=\"16\" fill=\"#0f172a\" font-weight=\"900\">\u00c0 la surface de la Terre, la distance au centre vaut R<sub>T<\/sub>.<\/text>\n<\/svg>\n<\/div>\n\n<p>\nLorsqu\u2019on est au niveau de la mer, <span class=\"red\">d = R<sub>T<\/sub><\/span>.\n<\/p>\n\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">F<sub>T\/H<\/sub> = G \u00d7 m<sub>T<\/sub> \u00d7 m<sub>H<\/sub> \/ d\u00b2<\/div>\n<p class=\"step\">\u00c0 la surface de la Terre, d = R<sub>T<\/sub> :<\/p>\n<div class=\"formule bluebox\">F<sub>T\/H<\/sub> = G \u00d7 m<sub>T<\/sub> \u00d7 m<sub>H<\/sub> \/ R<sub>T<\/sub>\u00b2<\/div>\n<p class=\"step\">On factorise la masse m<sub>H<\/sub> :<\/p>\n<div class=\"formule bluebox\">F<sub>T\/H<\/sub> = m<sub>H<\/sub> \u00d7 (G \u00d7 m<sub>T<\/sub> \/ R<sub>T<\/sub>\u00b2)<\/div>\n<\/div>\n\n<p>On d\u00e9finit alors le champ gravitationnel terrestre :<\/p>\n<div class=\"formule\">g<sub>T<\/sub> = G \u00d7 m<sub>T<\/sub> \/ R<sub>T<\/sub>\u00b2<\/div>\n\n<p class=\"red\">\ng<sub>T<\/sub> est le champ gravitationnel \u00e0 la surface de la Terre.\n<\/p>\n\n<p>\nOn pourra dans ce cas particulier simplifier l\u2019attraction gravitationnelle :\n<\/p>\n<div class=\"formule\">F<sub>T\/objet<\/sub> = P = m \u00d7 g<\/div>\n\n<div class=\"note\">\n<p class=\"red\">\u00c0 retenir :<\/p>\n<div class=\"formule bluebox\">g = 9,81 N\u00b7kg\u207b\u00b9<\/div>\n<p>N\u2019importe quel objet \u00e0 la surface de la Terre subit une force appel\u00e9e poids.<\/p>\n<\/div>\n\n<div class=\"exercice\">\n<h3>Exercice type \u2014 Poids d\u2019une personne au niveau de la mer<\/h3>\n<p>\nCalculer la force gravitationnelle exerc\u00e9e par la Terre sur une personne de masse <span class=\"red\">m = 70 kg<\/span>.\n<\/p>\n\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">P = m \u00d7 g<\/div>\n<p class=\"step\">On cherche P : la formule est d\u00e9j\u00e0 sous la bonne forme.<\/p>\n<div class=\"formule bluebox\">P = m \u00d7 g<\/div>\n<\/div>\n\n<p>Application num\u00e9rique :<\/p>\n<p>P = 70 \u00d7 9,81<\/p>\n<p class=\"resultat\">P \u2248 687 N<\/p>\n<\/div>\n<\/section>\n\n<section class=\"section\">\n<h2>III. Force gravitationnelle en altitude<\/h2>\n\n<p>\nEn altitude, la distance entre l\u2019objet et le centre de la Terre augmente.\n<\/p>\n<p>\nOn n\u2019a plus d = R<sub>T<\/sub>, mais :\n<\/p>\n<div class=\"formule bluebox\">d = R<sub>T<\/sub> + h<\/div>\n\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">F = G \u00d7 m<sub>T<\/sub> \u00d7 m \/ d\u00b2<\/div>\n<p class=\"step\">En altitude, d = R<sub>T<\/sub> + h :<\/p>\n<div class=\"formule bluebox\">F = G \u00d7 m<sub>T<\/sub> \u00d7 m \/ (R<sub>T<\/sub> + h)\u00b2<\/div>\n<p class=\"step\">On d\u00e9finit le champ gravitationnel \u00e0 l\u2019altitude h :<\/p>\n<div class=\"formule bluebox\">g(h) = G \u00d7 m<sub>T<\/sub> \/ (R<sub>T<\/sub> + h)\u00b2<\/div>\n<\/div>\n\n<p class=\"red\">\ng : le champ gravitationnel de la Terre varie avec l\u2019altitude h.\n<\/p>\n\n<div class=\"exercice\">\n<h3>Exercice type \u2014 Calculer g \u00e0 10 000 m<\/h3>\n<p>\nDonn\u00e9es : R<sub>T<\/sub> = 6378 km ; m<sub>T<\/sub> = 5,98 \u00d7 10\u00b2\u2074 kg ; G = 6,67 \u00d7 10\u207b\u00b9\u00b9 N\u00b7m\u00b2\u00b7kg\u207b\u00b2.\nCalculer g(h = 10 000 m).\n<\/p>\n\n<p class=\"red\">Conversions :<\/p>\n<p>R<sub>T<\/sub> = 6378 km = 6378 \u00d7 10\u00b3 m.<\/p>\n\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">g(h) = G \u00d7 m<sub>T<\/sub> \/ (R<sub>T<\/sub> + h)\u00b2<\/div>\n<p class=\"step\">On cherche g(h) : la formule est d\u00e9j\u00e0 sous la bonne forme.<\/p>\n<div class=\"formule bluebox\">g(h) = G \u00d7 m<sub>T<\/sub> \/ (R<sub>T<\/sub> + h)\u00b2<\/div>\n<\/div>\n\n<p>Application num\u00e9rique :<\/p>\n<p>g(h) = (6,67 \u00d7 10\u207b\u00b9\u00b9 \u00d7 5,98 \u00d7 10\u00b2\u2074) \/ (6378 \u00d7 10\u00b3 + 10 000)\u00b2<\/p>\n<p class=\"resultat\">g(h = 10 000 m) \u2248 9,77 N\u00b7kg\u207b\u00b9<\/p>\n<p>\nM\u00eame \u00e0 10 km d\u2019altitude, g a tr\u00e8s peu diminu\u00e9 par rapport \u00e0 9,81 N\u00b7kg\u207b\u00b9.\n<\/p>\n<\/div>\n<\/section>\n\n<section class=\"section\" id=\"lune\">\n<h2>IV. Force gravitationnelle sur la Lune<\/h2>\n\n<p>\nComparons la pesanteur sur Terre et sur la Lune.\n<\/p>\n<p class=\"red\">\nPesanteur : c\u2019est le fait de subir l\u2019attraction gravitationnelle de la Terre ou de la Lune.\n<\/p>\n\n<div class=\"schema\">\n<svg width=\"780\" height=\"380\" viewBox=\"0 0 780 380\">\n<rect x=\"55\" y=\"45\" width=\"660\" height=\"270\" rx=\"22\" fill=\"#fbfdff\" stroke=\"#D9E2EC\"\/>\n<circle cx=\"240\" cy=\"180\" r=\"105\" fill=\"#e5e7eb\" stroke=\"#64748b\" stroke-width=\"4\"\/>\n<circle cx=\"240\" cy=\"180\" r=\"5\" fill=\"#111827\"\/>\n<line x1=\"240\" y1=\"180\" x2=\"315\" y2=\"105\" stroke=\"#0F766E\" stroke-width=\"4\"\/>\n<circle cx=\"315\" cy=\"105\" r=\"10\" fill=\"#F97316\"\/>\n<text x=\"170\" y=\"305\" font-size=\"18\" fill=\"#111827\" font-weight=\"900\">Lune<\/text>\n<text x=\"280\" y=\"145\" fill=\"#0F766E\" font-size=\"16\" font-weight=\"900\">R<sub>Lune<\/sub><\/text>\n<text x=\"430\" y=\"115\" font-size=\"17\" fill=\"#B83227\" font-weight=\"900\">g<sub>Lune<\/sub> = G \u00d7 m<sub>Lune<\/sub> \/ R<sub>Lune<\/sub>\u00b2<\/text>\n<\/svg>\n<\/div>\n\n<div class=\"formule\">g<sub>Lune<\/sub> = G \u00d7 m<sub>Lune<\/sub> \/ R<sub>Lune<\/sub>\u00b2<\/div>\n\n<p>Donn\u00e9es du cahier :<\/p>\n<ul>\n<li>m<sub>Lune<\/sub> = 7,35 \u00d7 10\u00b2\u00b2 kg ;<\/li>\n<li>R<sub>Lune<\/sub> = 1738 km ;<\/li>\n<li>G = 6,67 \u00d7 10\u207b\u00b9\u00b9 USI.<\/li>\n<\/ul>\n\n<p class=\"red\">Conversion :<\/p>\n<p>R<sub>Lune<\/sub> = 1738 km = 1738 \u00d7 10\u00b3 m.<\/p>\n\n<p>Application num\u00e9rique :<\/p>\n<p>g<sub>Lune<\/sub> = (6,67 \u00d7 10\u207b\u00b9\u00b9 \u00d7 7,35 \u00d7 10\u00b2\u00b2) \/ (1738 \u00d7 10\u00b3)\u00b2<\/p>\n<p class=\"resultat\">g<sub>Lune<\/sub> \u2248 1,6 N\u00b7kg\u207b\u00b9<\/p>\n\n<p>Or, sur Terre :<\/p>\n<div class=\"formule bluebox\">g<sub>Terre<\/sub> = 9,8 N\u00b7kg\u207b\u00b9<\/div>\n\n<div class=\"formule\">g<sub>Terre<\/sub> \u2248 6 \u00d7 g<sub>Lune<\/sub><\/div>\n<p class=\"red\">\nOn se sent donc 6 fois plus l\u00e9ger sur la Lune.\n<\/p>\n\n<div class=\"exercice\">\n<h3>Exercice type \u2014 Poids sur Terre et sur la Lune<\/h3>\n<p>\nUn astronaute a une masse de <span class=\"red\">m = 80 kg<\/span>.\nComparer son poids sur Terre et sur la Lune.\n<\/p>\n\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">P = m \u00d7 g<\/div>\n<p class=\"step\">On l\u2019applique une fois avec g<sub>Terre<\/sub>, puis une fois avec g<sub>Lune<\/sub>.<\/p>\n<div class=\"formule bluebox\">P<sub>Terre<\/sub> = m \u00d7 g<sub>Terre<\/sub><\/div>\n<div class=\"formule bluebox\">P<sub>Lune<\/sub> = m \u00d7 g<sub>Lune<\/sub><\/div>\n<\/div>\n\n<p>P<sub>Terre<\/sub> = 80 \u00d7 9,81 = 785 N.<\/p>\n<p>P<sub>Lune<\/sub> = 80 \u00d7 1,6 = 128 N.<\/p>\n<p class=\"resultat\">L\u2019astronaute a la m\u00eame masse, mais son poids est environ 6 fois plus faible sur la Lune.<\/p>\n<\/div>\n<\/section>\n\n<section class=\"section\" id=\"exercices\">\n<h2>V. Exercices contextualis\u00e9s<\/h2>\n\n<div class=\"exercice\">\n<h3>1. Satellite autour de Wallis et Futuna<\/h3>\n<p>\nUn petit satellite de masse <span class=\"red\">m = 250 kg<\/span> est \u00e0 une altitude de\n<span class=\"red\">h = 500 km<\/span>.\nOn donne R<sub>T<\/sub> = 6378 km, m<sub>T<\/sub> = 5,98 \u00d7 10\u00b2\u2074 kg et G = 6,67 \u00d7 10\u207b\u00b9\u00b9.\nCalculer le champ gravitationnel \u00e0 cette altitude puis la force gravitationnelle exerc\u00e9e sur le satellite.\n<\/p>\n\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">g(h) = G \u00d7 m<sub>T<\/sub> \/ (R<sub>T<\/sub> + h)\u00b2<\/div>\n<p class=\"step\">On calcule d\u2019abord g(h), puis on utilise :<\/p>\n<div class=\"formule bluebox\">F = m \u00d7 g(h)<\/div>\n<\/div>\n\n<p class=\"red\">Conversions :<\/p>\n<p>R<sub>T<\/sub> = 6378 \u00d7 10\u00b3 m ; h = 500 \u00d7 10\u00b3 m.<\/p>\n<p>g(h) = (6,67 \u00d7 10\u207b\u00b9\u00b9 \u00d7 5,98 \u00d7 10\u00b2\u2074) \/ (6378 \u00d7 10\u00b3 + 500 \u00d7 10\u00b3)\u00b2<\/p>\n<p>g(h) \u2248 8,43 N\u00b7kg\u207b\u00b9<\/p>\n<p>F = 250 \u00d7 8,43<\/p>\n<p class=\"resultat\">F \u2248 2,11 \u00d7 10\u00b3 N<\/p>\n<\/div>\n\n<div class=\"exercice\">\n<h3>2. Va\u2019a et poids d\u2019une rameuse<\/h3>\n<p>\nUne rameuse a une masse de <span class=\"red\">m = 62 kg<\/span>.\nCalculer son poids sur Terre.\n<\/p>\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">P = m \u00d7 g<\/div>\n<p class=\"step\">On cherche P : la formule est d\u00e9j\u00e0 sous la bonne forme.<\/p>\n<div class=\"formule bluebox\">P = m \u00d7 g<\/div>\n<\/div>\n<p>P = 62 \u00d7 9,81<\/p>\n<p class=\"resultat\">P \u2248 608 N<\/p>\n<\/div>\n\n<div class=\"exercice\">\n<h3>3. Mission lunaire<\/h3>\n<p>\nUn objet p\u00e8se <span class=\"red\">120 N<\/span> sur la Lune.\nOn donne g<sub>Lune<\/sub> = 1,6 N\u00b7kg\u207b\u00b9.\nCalculer sa masse.\n<\/p>\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">P = m \u00d7 g<\/div>\n<p class=\"step\">On veut isoler m. On divise par g :<\/p>\n<div class=\"formule bluebox\">m = P \/ g<\/div>\n<\/div>\n<p>m = 120 \/ 1,6<\/p>\n<p class=\"resultat\">m = 75 kg<\/p>\n<\/div>\n<\/section>\n\n<section class=\"section\" id=\"type-bac\">\n<h2>VI. Partie type bac \/ \u00e9valuation \u2014 niveau seconde<\/h2>\n\n<div class=\"exercice\">\n<h3>Situation 1 \u2014 Une sonde autour de la Lune<\/h3>\n<p>\nUne sonde de masse m = 500 kg se trouve \u00e0 la surface de la Lune.\nOn donne m<sub>Lune<\/sub> = 7,35 \u00d7 10\u00b2\u00b2 kg, R<sub>Lune<\/sub> = 1738 km et G = 6,67 \u00d7 10\u207b\u00b9\u00b9.\n<\/p>\n<ol>\n<li>Calculer g<sub>Lune<\/sub>.<\/li>\n<li>Calculer la force gravitationnelle exerc\u00e9e par la Lune sur la sonde.<\/li>\n<li>Comparer avec son poids sur Terre.<\/li>\n<\/ol>\n\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">g = G \u00d7 m<sub>Lune<\/sub> \/ R<sub>Lune<\/sub>\u00b2<\/div>\n<p class=\"step\">On calcule d\u2019abord g, puis la force :<\/p>\n<div class=\"formule bluebox\">P = m \u00d7 g<\/div>\n<\/div>\n\n<p>R<sub>Lune<\/sub> = 1738 \u00d7 10\u00b3 m.<\/p>\n<p>g<sub>Lune<\/sub> \u2248 1,6 N\u00b7kg\u207b\u00b9.<\/p>\n<p>P<sub>Lune<\/sub> = 500 \u00d7 1,6 = 800 N.<\/p>\n<p>P<sub>Terre<\/sub> = 500 \u00d7 9,81 = 4905 N.<\/p>\n<p class=\"resultat\">La sonde subit une force environ 6 fois plus faible sur la Lune que sur Terre.<\/p>\n<\/div>\n\n<div class=\"exercice\">\n<h3>Situation 2 \u2014 Force Terre-Lune<\/h3>\n<p>\nOn donne m<sub>T<\/sub> = 5,98 \u00d7 10\u00b2\u2074 kg ; m<sub>L<\/sub> = 7,35 \u00d7 10\u00b2\u00b2 kg ;\nd = 3,84 \u00d7 10\u2075 km ; G = 6,67 \u00d7 10\u207b\u00b9\u00b9.\n<\/p>\n<ol>\n<li>Convertir la distance en m\u00e8tres.<\/li>\n<li>Calculer la force gravitationnelle entre la Terre et la Lune.<\/li>\n<li>Repr\u00e9senter la force exerc\u00e9e par la Terre sur la Lune.<\/li>\n<\/ol>\n\n<p class=\"red\">Conversion :<\/p>\n<p>d = 3,84 \u00d7 10\u2075 km = 3,84 \u00d7 10\u2078 m.<\/p>\n\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">F = G \u00d7 m\u2081 \u00d7 m\u2082 \/ d\u00b2<\/div>\n<p class=\"step\">Pour Terre-Lune :<\/p>\n<div class=\"formule bluebox\">F = G \u00d7 m<sub>T<\/sub> \u00d7 m<sub>L<\/sub> \/ d\u00b2<\/div>\n<\/div>\n\n<p>F \u2248 1,99 \u00d7 10\u00b2\u2070 N.<\/p>\n<p class=\"resultat\">La force est attractive et dirig\u00e9e vers le centre de la Terre lorsqu\u2019on la repr\u00e9sente sur la Lune.<\/p>\n<\/div>\n<\/section>\n\n<section class=\"section\" id=\"fiche-bilan\">\n<h2>\ud83d\udccc Fiche bilan \u2014 La gravitation universelle<\/h2>\n<div class=\"grid3\">\n<div class=\"card\"><h3>Gravitation<\/h3><p>Interaction attractive entre deux corps qui poss\u00e8dent une masse.<\/p><\/div>\n<div class=\"card\"><h3>Newton<\/h3><p>A \u00e9tabli la loi de la gravitation universelle au XVII\u1d49 si\u00e8cle.<\/p><\/div>\n<div class=\"card\"><h3>Forces<\/h3><p>F\u2081\/\u2082 = F\u2082\/\u2081 : m\u00eame valeur, sens oppos\u00e9s.<\/p><\/div>\n<div class=\"card\"><h3>Loi<\/h3><div class=\"formule\">F = G m\u2081m\u2082 \/ d\u00b2<\/div><\/div>\n<div class=\"card\"><h3>Constante G<\/h3><p>G = 6,67 \u00d7 10\u207b\u00b9\u00b9 N\u00b7m\u00b2\u00b7kg\u207b\u00b2.<\/p><\/div>\n<div class=\"card\"><h3>Unit\u00e9s<\/h3><p>m en kg ; d en m ; F en N.<\/p><\/div>\n<div class=\"card\"><h3>Surface Terre<\/h3><div class=\"formule bluebox\">P = m \u00d7 g<\/div><\/div>\n<div class=\"card\"><h3>Champ terrestre<\/h3><div class=\"formule bluebox\">g = Gm<sub>T<\/sub>\/R<sub>T<\/sub>\u00b2<\/div><p>g \u2248 9,81 N\u00b7kg\u207b\u00b9.<\/p><\/div>\n<div class=\"card\"><h3>Altitude<\/h3><div class=\"formule bluebox\">g(h)=Gm<sub>T<\/sub>\/(R<sub>T<\/sub>+h)\u00b2<\/div><\/div>\n<div class=\"card\"><h3>Lune<\/h3><p>g<sub>Lune<\/sub> \u2248 1,6 N\u00b7kg\u207b\u00b9.<\/p><\/div>\n<div class=\"card\"><h3>Comparaison<\/h3><p class=\"red\">g<sub>Terre<\/sub> \u2248 6 \u00d7 g<sub>Lune<\/sub>.<\/p><\/div>\n<div class=\"card\"><h3>Masse \/ poids<\/h3><p>La masse ne change pas ; le poids d\u00e9pend de g.<\/p><\/div>\n<\/div>\n<\/section>\n\n<section class=\"section\">\n<h2>Carte mentale<\/h2>\n<div class=\"grid3\">\n<div class=\"mm-center\">LA GRAVITATION UNIVERSELLE<\/div>\n<div class=\"card\"><h3>Principe<\/h3><p>Deux masses s\u2019attirent.<\/p><\/div>\n<div class=\"card\"><h3>Force<\/h3><p>F = Gm\u2081m\u2082\/d\u00b2.<\/p><\/div>\n<div class=\"card\"><h3>Distance<\/h3><p>Distance de centre \u00e0 centre.<\/p><\/div>\n<div class=\"card\"><h3>Terre<\/h3><p>P = m \u00d7 g ; g = 9,81 N\u00b7kg\u207b\u00b9.<\/p><\/div>\n<div class=\"card\"><h3>Altitude<\/h3><p>g diminue quand h augmente.<\/p><\/div>\n<div class=\"card\"><h3>Lune<\/h3><p>g = 1,6 N\u00b7kg\u207b\u00b9 ; 6 fois plus l\u00e9ger.<\/p><\/div>\n<\/div>\n<\/section>\n\n<\/div>\n\n<script>\nlet utterance;\nfunction playAudioSummary(){\n speechSynthesis.cancel();\n const text=document.getElementById(\"audioText\").innerText;\n utterance=new SpeechSynthesisUtterance(text);\n utterance.lang=\"fr-FR\";\n utterance.rate=0.90;\n speechSynthesis.speak(utterance);\n}\nfunction stopAudioSummary(){speechSynthesis.cancel();}\n<\/script>\n\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>Seconde \u2014 La gravitation universelle La gravitation universelle Seconde physique-chimie \u2022 Attraction gravitationnelle \u2022 Force entre deux corps \u2022 Champ de pesanteur \u2022 Terre \u2022 Lune...<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-778","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pcwallis.malo.wf\/index.php\/wp-json\/wp\/v2\/pages\/778","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pcwallis.malo.wf\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pcwallis.malo.wf\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pcwallis.malo.wf\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/pcwallis.malo.wf\/index.php\/wp-json\/wp\/v2\/comments?post=778"}],"version-history":[{"count":1,"href":"https:\/\/pcwallis.malo.wf\/index.php\/wp-json\/wp\/v2\/pages\/778\/revisions"}],"predecessor-version":[{"id":780,"href":"https:\/\/pcwallis.malo.wf\/index.php\/wp-json\/wp\/v2\/pages\/778\/revisions\/780"}],"wp:attachment":[{"href":"https:\/\/pcwallis.malo.wf\/index.php\/wp-json\/wp\/v2\/media?parent=778"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

{"id":778,"date":"2026-05-28T03:49:28","date_gmt":"2026-05-28T01:49:28","guid":{"rendered":"https:\/\/pcwallis.malo.wf\/?page_id=778"},"modified":"2026-05-28T03:49:28","modified_gmt":"2026-05-28T01:49:28","slug":"gravitation","status":"publish","type":"page","link":"https:\/\/pcwallis.malo.wf\/index.php\/gravitation\/","title":{"rendered":"gravitation"},"content":{"rendered":"\n\n\n\n\n\nSeconde \u2014 La gravitation universelle<\/title>\n<style>\n:root{\n --deep:#101828;\n --blue:#2563EB;\n --cyan:#0891B2;\n --teal:#14B8A6;\n --purple:#7C3AED;\n --pink:#DB2777;\n --orange:#F97316;\n --red:#B83227;\n --green:#0F766E;\n --amber:#F59E0B;\n --ink:#1F2937;\n --paper:#FFFFFF;\n --line:#D9E2EC;\n}\n*{box-sizing:border-box}\nhtml{scroll-behavior:smooth}\nbody{\n margin:0;\n font-family:Arial, Helvetica, sans-serif;\n background:\n radial-gradient(circle at top left, rgba(37,99,235,.12), transparent 28%),\n linear-gradient(180deg,#f8fbff,#eef4f8);\n color:var(--ink);\n 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display:inline-block;\n}\nbutton.stop{background:#333}.cyanbtn{background:var(--cyan)}.pinkbtn{background:var(--pink)}.greenbtn{background:#0f766e}.orangebtn{background:var(--orange)}\ntable{border-collapse:collapse;width:100%;margin:14px 0;background:white}\nth,td{border:1px solid #9aa7bd;padding:10px;text-align:center}\nth{background:#f0f4fb}\n.card{\n border:2px solid #e1e8f0;\n border-top:6px solid var(--teal);\n border-radius:18px;\n padding:18px;\n background:#fff;\n}\n.mm-center{\n grid-column:1\/-1;\n text-align:center;\n background:linear-gradient(135deg,var(--deep),var(--teal));\n color:white;\n border-radius:18px;\n padding:18px;\n font-size:1.3rem;\n font-weight:900;\n}\n.small{font-size:.92rem;color:#5b6770}\n@media print{button,.btns,.linkbtn{display:none}body{background:white}.section{box-shadow:none;break-inside:avoid}}\n<\/style>\n<\/head>\n<body>\n\n<header>\n<h1>La gravitation universelle<\/h1>\n<p>Seconde physique-chimie \u2022 Attraction gravitationnelle \u2022 Force entre deux corps \u2022 Champ de pesanteur \u2022 Terre \u2022 Lune \u2022 Altitude<\/p>\n<\/header>\n\n<div class=\"container\">\n\n<div class=\"btns\">\n<button onclick=\"playAudioSummary()\">\ud83d\udd0a \u00c9couter le r\u00e9sum\u00e9 audio clair<\/button>\n<button class=\"stop\" onclick=\"stopAudioSummary()\">\u23f9 Arr\u00eater<\/button><br>\n<a class=\"linkbtn cyanbtn\" href=\"#fiche-bilan\">\ud83d\udccc Aller \u00e0 la fiche bilan<\/a>\n<a class=\"linkbtn pinkbtn\" href=\"#exercices\">\ud83d\ude80 Exercices contextualis\u00e9s<\/a>\n<a class=\"linkbtn greenbtn\" href=\"#type-bac\">\ud83c\udf93 Partie type bac \/ \u00e9valuation<\/a>\n<a class=\"linkbtn orangebtn\" href=\"#lune\">\ud83c\udf19 Terre \/ Lune<\/a>\n<\/div>\n\n<div id=\"audioText\" style=\"display:none;\">\nBienvenue dans le chapitre la gravitation universelle.\nC\u2019est la gravitation universelle qui r\u00e9git le mouvement des plan\u00e8tes et des \u00e9toiles de notre univers.\nC\u2019est Newton, au dix-septi\u00e8me si\u00e8cle, qui a \u00e9tabli la loi de la gravitation universelle.\nTout corps qui poss\u00e8de une masse exerce sur un autre corps qui poss\u00e8de lui aussi une masse une force attractive appel\u00e9e attraction gravitationnelle.\nLes deux forces gravitationnelles exerc\u00e9es entre deux corps ont la m\u00eame valeur, mais des sens oppos\u00e9s.\nLa valeur de la force gravitationnelle s\u2019\u00e9crit F \u00e9gale G fois m un fois m deux divis\u00e9 par d au carr\u00e9.\nG est la constante universelle de gravitation.\nLes masses doivent \u00eatre en kilogrammes et la distance entre les centres des objets doit \u00eatre en m\u00e8tres.\n\u00c0 la surface de la Terre, on peut simplifier l\u2019attraction gravitationnelle : la force exerc\u00e9e par la Terre sur un objet est son poids, P \u00e9gale m fois g.\nLe champ de pesanteur terrestre vaut environ 9,81 newtons par kilogramme.\nEn altitude, le champ gravitationnel diminue l\u00e9g\u00e8rement car la distance au centre de la Terre augmente.\nSur la Lune, le champ de pesanteur vaut environ 1,6 newton par kilogramme.\nOn se sent donc environ six fois plus l\u00e9ger sur la Lune.\nFin du r\u00e9sum\u00e9.\n<\/div>\n\n<section class=\"section\">\n<h2>Objectifs du chapitre<\/h2>\n<p>\nCe cours reprend les phrases du cahier comme base : gravitation universelle, force gravitationnelle,\nloi de Newton, repr\u00e9sentation des forces, gravitation \u00e0 la surface de la Terre,\nchamp gravitationnel, variation avec l\u2019altitude et comparaison Terre-Lune.\n<\/p>\n<div class=\"grid3\">\n<div class=\"card\"><h3>Comprendre<\/h3><p>La gravitation comme interaction attractive entre deux corps poss\u00e9dant une masse.<\/p><\/div>\n<div class=\"card\"><h3>Calculer<\/h3><p>Une force gravitationnelle, un champ g, un poids P.<\/p><\/div>\n<div class=\"card\"><h3>Repr\u00e9senter<\/h3><p>Des forces gravitationnelles avec une direction, un sens et une \u00e9chelle.<\/p><\/div>\n<\/div>\n<\/section>\n\n<section class=\"section\">\n<h2>\ud83d\udd34 M\u00e9thode obligatoire pour les exercices<\/h2>\n<p>\nOn part toujours de la <span class=\"red\">formule du cours<\/span>, puis on fait le\n<span class=\"blue\">travail litt\u00e9ral<\/span>, et seulement ensuite l\u2019application num\u00e9rique.\n<\/p>\n<div class=\"litteral\">\n<p class=\"start\">Exemple : isoler une masse \u00e0 partir du poids<\/p>\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">P = m \u00d7 g<\/div>\n<p class=\"step\">On veut isoler m. On divise par g :<\/p>\n<div class=\"formule bluebox\">m = P \/ g<\/div>\n<p class=\"red\">Ensuite seulement, on remplace par les valeurs num\u00e9riques.<\/p>\n<\/div>\n<\/section>\n\n<section class=\"section\">\n<h2>I. Force gravitationnelle<\/h2>\n\n<p>\nC\u2019est la gravitation universelle qui r\u00e9git le mouvement des plan\u00e8tes et \u00e9toiles de notre univers.\n<\/p>\n<p class=\"red\">\nC\u2019est Newton au XVII\u1d49 si\u00e8cle qui a \u00e9tabli la loi de la gravitation universelle.\n<\/p>\n<p class=\"red\">\nTout corps qui poss\u00e8de une masse exerce sur un autre corps qui poss\u00e8de lui aussi une masse\nune force attractive appel\u00e9e attraction gravitationnelle.\n<\/p>\n\n<div class=\"schema\">\n<svg width=\"820\" height=\"370\" viewBox=\"0 0 820 370\">\n<rect x=\"50\" y=\"45\" width=\"720\" height=\"250\" rx=\"22\" fill=\"#fbfdff\" stroke=\"#D9E2EC\"\/>\n<circle cx=\"230\" cy=\"165\" r=\"60\" fill=\"#dbeafe\" stroke=\"#2563EB\" stroke-width=\"4\"\/>\n<text x=\"205\" y=\"100\" font-size=\"18\" fill=\"#2563EB\" font-weight=\"900\">m\u2081<\/text>\n<circle cx=\"590\" cy=\"165\" r=\"70\" fill=\"#fef3c7\" stroke=\"#F59E0B\" stroke-width=\"4\"\/>\n<text x=\"570\" y=\"85\" font-size=\"18\" fill=\"#F97316\" font-weight=\"900\">m\u2082<\/text>\n<circle cx=\"230\" cy=\"165\" r=\"5\" fill=\"#111827\"\/>\n<circle cx=\"590\" cy=\"165\" r=\"5\" fill=\"#111827\"\/>\n<line x1=\"230\" y1=\"165\" x2=\"590\" y2=\"165\" stroke=\"#0F766E\" stroke-width=\"4\"\/>\n<polygon points=\"590,165 568,153 568,177\" fill=\"#0F766E\"\/>\n<polygon points=\"230,165 252,153 252,177\" fill=\"#0F766E\"\/>\n<text x=\"372\" y=\"190\" fill=\"#0F766E\" font-size=\"18\" font-weight=\"900\">d = G\u2081G\u2082<\/text>\n<line x1=\"230\" y1=\"135\" x2=\"325\" y2=\"135\" stroke=\"#B83227\" stroke-width=\"5\"\/>\n<polygon points=\"325,135 303,123 303,147\" fill=\"#B83227\"\/>\n<text x=\"260\" y=\"125\" fill=\"#B83227\" font-size=\"17\" font-weight=\"900\">F\u2082\/\u2081<\/text>\n<line x1=\"590\" y1=\"135\" x2=\"495\" y2=\"135\" stroke=\"#7C3AED\" stroke-width=\"5\"\/>\n<polygon points=\"495,135 517,123 517,147\" fill=\"#7C3AED\"\/>\n<text x=\"525\" y=\"125\" fill=\"#7C3AED\" font-size=\"17\" font-weight=\"900\">F\u2081\/\u2082<\/text>\n<text x=\"150\" y=\"325\" fill=\"#B83227\" font-size=\"17\" font-weight=\"900\">Forces attractives, m\u00eame valeur, sens oppos\u00e9s.<\/text>\n<\/svg>\n<\/div>\n\n<div class=\"formule\">F\u2081\/\u2082 = F\u2082\/\u2081<\/div>\n\n<h3>Loi de la gravitation universelle<\/h3>\n<div class=\"formule\">F\u2081\/\u2082 = G \u00d7 m\u2081 \u00d7 m\u2082 \/ d\u00b2<\/div>\n\n<ul>\n<li><span class=\"red\">G<\/span> : constante universelle de la gravitation ;<\/li>\n<li><span class=\"red\">G = 6,67 \u00d7 10\u207b\u00b9\u00b9 N\u00b7m\u00b2\u00b7kg\u207b\u00b2<\/span> ;<\/li>\n<li><span class=\"red\">m\u2081<\/span> : masse de l\u2019objet 1 en kg ;<\/li>\n<li><span class=\"red\">m\u2082<\/span> : masse de l\u2019objet 2 en kg ;<\/li>\n<li><span class=\"red\">d<\/span> : distance entre les deux objets, de centre \u00e0 centre, en m.<\/li>\n<\/ul>\n\n<div class=\"note\">\n<p class=\"red\">Attention unit\u00e9s :<\/p>\n<p>Les masses doivent \u00eatre en <span class=\"red\">kg<\/span>.<\/p>\n<p>La distance doit \u00eatre en <span class=\"red\">m<\/span>, m\u00eame si elle est souvent donn\u00e9e en km.<\/p>\n<\/div>\n\n<div class=\"exercice\">\n<h3>Exercice type \u2014 Force exerc\u00e9e par la Terre sur la Lune<\/h3>\n<p>\nCalculer et repr\u00e9senter la force qu\u2019exerce la Terre sur la Lune.\n<\/p>\n<p>Donn\u00e9es : m<sub>T<\/sub> = 5,98 \u00d7 10\u00b2\u2074 kg ; m<sub>L<\/sub> = 7,2 \u00d7 10\u00b2\u00b2 kg ; d<sub>T\/L<\/sub> = 3,84 \u00d7 10\u2075 km.<\/p>\n<p>\u00c9chelle : 1 cm \u2194 1 \u00d7 10\u00b2\u2070 N.<\/p>\n\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">F = G \u00d7 m\u2081 \u00d7 m\u2082 \/ d\u00b2<\/div>\n<p class=\"step\">Pour Terre-Lune :<\/p>\n<div class=\"formule bluebox\">F<sub>T\/L<\/sub> = G \u00d7 m<sub>T<\/sub> \u00d7 m<sub>L<\/sub> \/ d\u00b2<\/div>\n<\/div>\n\n<p class=\"red\">Conversion :<\/p>\n<p>d = 3,84 \u00d7 10\u2075 km = 3,84 \u00d7 10\u2078 m<\/p>\n\n<p>Application num\u00e9rique :<\/p>\n<p>F<sub>T\/L<\/sub> = (6,67 \u00d7 10\u207b\u00b9\u00b9 \u00d7 5,98 \u00d7 10\u00b2\u2074 \u00d7 7,2 \u00d7 10\u00b2\u00b2) \/ (3,84 \u00d7 10\u2078)\u00b2<\/p>\n<p class=\"resultat\">F<sub>T\/L<\/sub> \u2248 1,95 \u00d7 10\u00b2\u2070 N<\/p>\n<p>Avec l\u2019\u00e9chelle propos\u00e9e, cela correspond \u00e0 environ 1,95 cm.<\/p>\n\n<div class=\"schema\">\n<svg width=\"760\" height=\"250\" viewBox=\"0 0 760 250\">\n<circle cx=\"180\" cy=\"125\" r=\"55\" fill=\"#dbeafe\" stroke=\"#2563EB\" stroke-width=\"4\"\/>\n<text x=\"150\" y=\"195\" font-size=\"16\" font-weight=\"900\">Terre<\/text>\n<circle cx=\"570\" cy=\"125\" r=\"38\" fill=\"#f1f5f9\" stroke=\"#64748b\" stroke-width=\"4\"\/>\n<text x=\"545\" y=\"195\" font-size=\"16\" font-weight=\"900\">Lune<\/text>\n<line x1=\"570\" y1=\"125\" x2=\"430\" y2=\"125\" stroke=\"#B83227\" stroke-width=\"6\"\/>\n<polygon points=\"430,125 452,113 452,137\" fill=\"#B83227\"\/>\n<text x=\"455\" y=\"110\" fill=\"#B83227\" font-size=\"18\" font-weight=\"900\">F<sub>T\/L<\/sub><\/text>\n<\/svg>\n<\/div>\n<\/div>\n<\/section>\n\n<section class=\"section\">\n<h2>II. Force gravitationnelle \u00e0 la surface de la Terre<\/h2>\n\n<p>\nAu niveau de la mer, on cherche la force gravitationnelle qu\u2019exerce la Terre sur un homme de masse m<sub>H<\/sub>.\n<\/p>\n\n<div class=\"schema\">\n<svg width=\"760\" height=\"420\" viewBox=\"0 0 760 420\">\n<rect x=\"55\" y=\"45\" width=\"650\" height=\"300\" rx=\"22\" fill=\"#fbfdff\" stroke=\"#D9E2EC\"\/>\n<circle cx=\"360\" cy=\"210\" r=\"120\" fill=\"#dbeafe\" stroke=\"#2563EB\" stroke-width=\"4\"\/>\n<circle cx=\"360\" cy=\"210\" r=\"5\" fill=\"#111827\"\/>\n<text x=\"348\" y=\"215\" font-size=\"17\" fill=\"#111827\" font-weight=\"900\">T<\/text>\n<circle cx=\"455\" cy=\"115\" r=\"12\" fill=\"#F97316\"\/>\n<line x1=\"360\" y1=\"210\" x2=\"455\" y2=\"115\" stroke=\"#0F766E\" stroke-width=\"4\"\/>\n<text x=\"405\" y=\"155\" fill=\"#0F766E\" font-size=\"16\" font-weight=\"900\">R<sub>T<\/sub><\/text>\n<line x1=\"455\" y1=\"115\" x2=\"415\" y2=\"155\" stroke=\"#B83227\" stroke-width=\"5\"\/>\n<polygon points=\"415,155 438,148 424,134\" fill=\"#B83227\"\/>\n<text x=\"460\" y=\"105\" fill=\"#B83227\" font-size=\"16\" font-weight=\"900\">F<sub>T\/H<\/sub><\/text>\n<text x=\"85\" y=\"375\" font-size=\"16\" fill=\"#0f172a\" font-weight=\"900\">\u00c0 la surface de la Terre, la distance au centre vaut R<sub>T<\/sub>.<\/text>\n<\/svg>\n<\/div>\n\n<p>\nLorsqu\u2019on est au niveau de la mer, <span class=\"red\">d = R<sub>T<\/sub><\/span>.\n<\/p>\n\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">F<sub>T\/H<\/sub> = G \u00d7 m<sub>T<\/sub> \u00d7 m<sub>H<\/sub> \/ d\u00b2<\/div>\n<p class=\"step\">\u00c0 la surface de la Terre, d = R<sub>T<\/sub> :<\/p>\n<div class=\"formule bluebox\">F<sub>T\/H<\/sub> = G \u00d7 m<sub>T<\/sub> \u00d7 m<sub>H<\/sub> \/ R<sub>T<\/sub>\u00b2<\/div>\n<p class=\"step\">On factorise la masse m<sub>H<\/sub> :<\/p>\n<div class=\"formule bluebox\">F<sub>T\/H<\/sub> = m<sub>H<\/sub> \u00d7 (G \u00d7 m<sub>T<\/sub> \/ R<sub>T<\/sub>\u00b2)<\/div>\n<\/div>\n\n<p>On d\u00e9finit alors le champ gravitationnel terrestre :<\/p>\n<div class=\"formule\">g<sub>T<\/sub> = G \u00d7 m<sub>T<\/sub> \/ R<sub>T<\/sub>\u00b2<\/div>\n\n<p class=\"red\">\ng<sub>T<\/sub> est le champ gravitationnel \u00e0 la surface de la Terre.\n<\/p>\n\n<p>\nOn pourra dans ce cas particulier simplifier l\u2019attraction gravitationnelle :\n<\/p>\n<div class=\"formule\">F<sub>T\/objet<\/sub> = P = m \u00d7 g<\/div>\n\n<div class=\"note\">\n<p class=\"red\">\u00c0 retenir :<\/p>\n<div class=\"formule bluebox\">g = 9,81 N\u00b7kg\u207b\u00b9<\/div>\n<p>N\u2019importe quel objet \u00e0 la surface de la Terre subit une force appel\u00e9e poids.<\/p>\n<\/div>\n\n<div class=\"exercice\">\n<h3>Exercice type \u2014 Poids d\u2019une personne au niveau de la mer<\/h3>\n<p>\nCalculer la force gravitationnelle exerc\u00e9e par la Terre sur une personne de masse <span class=\"red\">m = 70 kg<\/span>.\n<\/p>\n\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">P = m \u00d7 g<\/div>\n<p class=\"step\">On cherche P : la formule est d\u00e9j\u00e0 sous la bonne forme.<\/p>\n<div class=\"formule bluebox\">P = m \u00d7 g<\/div>\n<\/div>\n\n<p>Application num\u00e9rique :<\/p>\n<p>P = 70 \u00d7 9,81<\/p>\n<p class=\"resultat\">P \u2248 687 N<\/p>\n<\/div>\n<\/section>\n\n<section class=\"section\">\n<h2>III. Force gravitationnelle en altitude<\/h2>\n\n<p>\nEn altitude, la distance entre l\u2019objet et le centre de la Terre augmente.\n<\/p>\n<p>\nOn n\u2019a plus d = R<sub>T<\/sub>, mais :\n<\/p>\n<div class=\"formule bluebox\">d = R<sub>T<\/sub> + h<\/div>\n\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">F = G \u00d7 m<sub>T<\/sub> \u00d7 m \/ d\u00b2<\/div>\n<p class=\"step\">En altitude, d = R<sub>T<\/sub> + h :<\/p>\n<div class=\"formule bluebox\">F = G \u00d7 m<sub>T<\/sub> \u00d7 m \/ (R<sub>T<\/sub> + h)\u00b2<\/div>\n<p class=\"step\">On d\u00e9finit le champ gravitationnel \u00e0 l\u2019altitude h :<\/p>\n<div class=\"formule bluebox\">g(h) = G \u00d7 m<sub>T<\/sub> \/ (R<sub>T<\/sub> + h)\u00b2<\/div>\n<\/div>\n\n<p class=\"red\">\ng : le champ gravitationnel de la Terre varie avec l\u2019altitude h.\n<\/p>\n\n<div class=\"exercice\">\n<h3>Exercice type \u2014 Calculer g \u00e0 10 000 m<\/h3>\n<p>\nDonn\u00e9es : R<sub>T<\/sub> = 6378 km ; m<sub>T<\/sub> = 5,98 \u00d7 10\u00b2\u2074 kg ; G = 6,67 \u00d7 10\u207b\u00b9\u00b9 N\u00b7m\u00b2\u00b7kg\u207b\u00b2.\nCalculer g(h = 10 000 m).\n<\/p>\n\n<p class=\"red\">Conversions :<\/p>\n<p>R<sub>T<\/sub> = 6378 km = 6378 \u00d7 10\u00b3 m.<\/p>\n\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">g(h) = G \u00d7 m<sub>T<\/sub> \/ (R<sub>T<\/sub> + h)\u00b2<\/div>\n<p class=\"step\">On cherche g(h) : la formule est d\u00e9j\u00e0 sous la bonne forme.<\/p>\n<div class=\"formule bluebox\">g(h) = G \u00d7 m<sub>T<\/sub> \/ (R<sub>T<\/sub> + h)\u00b2<\/div>\n<\/div>\n\n<p>Application num\u00e9rique :<\/p>\n<p>g(h) = (6,67 \u00d7 10\u207b\u00b9\u00b9 \u00d7 5,98 \u00d7 10\u00b2\u2074) \/ (6378 \u00d7 10\u00b3 + 10 000)\u00b2<\/p>\n<p class=\"resultat\">g(h = 10 000 m) \u2248 9,77 N\u00b7kg\u207b\u00b9<\/p>\n<p>\nM\u00eame \u00e0 10 km d\u2019altitude, g a tr\u00e8s peu diminu\u00e9 par rapport \u00e0 9,81 N\u00b7kg\u207b\u00b9.\n<\/p>\n<\/div>\n<\/section>\n\n<section class=\"section\" id=\"lune\">\n<h2>IV. Force gravitationnelle sur la Lune<\/h2>\n\n<p>\nComparons la pesanteur sur Terre et sur la Lune.\n<\/p>\n<p class=\"red\">\nPesanteur : c\u2019est le fait de subir l\u2019attraction gravitationnelle de la Terre ou de la Lune.\n<\/p>\n\n<div class=\"schema\">\n<svg width=\"780\" height=\"380\" viewBox=\"0 0 780 380\">\n<rect x=\"55\" y=\"45\" width=\"660\" height=\"270\" rx=\"22\" fill=\"#fbfdff\" stroke=\"#D9E2EC\"\/>\n<circle cx=\"240\" cy=\"180\" r=\"105\" fill=\"#e5e7eb\" stroke=\"#64748b\" stroke-width=\"4\"\/>\n<circle cx=\"240\" cy=\"180\" r=\"5\" fill=\"#111827\"\/>\n<line x1=\"240\" y1=\"180\" x2=\"315\" y2=\"105\" stroke=\"#0F766E\" stroke-width=\"4\"\/>\n<circle cx=\"315\" cy=\"105\" r=\"10\" fill=\"#F97316\"\/>\n<text x=\"170\" y=\"305\" font-size=\"18\" fill=\"#111827\" font-weight=\"900\">Lune<\/text>\n<text x=\"280\" y=\"145\" fill=\"#0F766E\" font-size=\"16\" font-weight=\"900\">R<sub>Lune<\/sub><\/text>\n<text x=\"430\" y=\"115\" font-size=\"17\" fill=\"#B83227\" font-weight=\"900\">g<sub>Lune<\/sub> = G \u00d7 m<sub>Lune<\/sub> \/ R<sub>Lune<\/sub>\u00b2<\/text>\n<\/svg>\n<\/div>\n\n<div class=\"formule\">g<sub>Lune<\/sub> = G \u00d7 m<sub>Lune<\/sub> \/ R<sub>Lune<\/sub>\u00b2<\/div>\n\n<p>Donn\u00e9es du cahier :<\/p>\n<ul>\n<li>m<sub>Lune<\/sub> = 7,35 \u00d7 10\u00b2\u00b2 kg ;<\/li>\n<li>R<sub>Lune<\/sub> = 1738 km ;<\/li>\n<li>G = 6,67 \u00d7 10\u207b\u00b9\u00b9 USI.<\/li>\n<\/ul>\n\n<p class=\"red\">Conversion :<\/p>\n<p>R<sub>Lune<\/sub> = 1738 km = 1738 \u00d7 10\u00b3 m.<\/p>\n\n<p>Application num\u00e9rique :<\/p>\n<p>g<sub>Lune<\/sub> = (6,67 \u00d7 10\u207b\u00b9\u00b9 \u00d7 7,35 \u00d7 10\u00b2\u00b2) \/ (1738 \u00d7 10\u00b3)\u00b2<\/p>\n<p class=\"resultat\">g<sub>Lune<\/sub> \u2248 1,6 N\u00b7kg\u207b\u00b9<\/p>\n\n<p>Or, sur Terre :<\/p>\n<div class=\"formule bluebox\">g<sub>Terre<\/sub> = 9,8 N\u00b7kg\u207b\u00b9<\/div>\n\n<div class=\"formule\">g<sub>Terre<\/sub> \u2248 6 \u00d7 g<sub>Lune<\/sub><\/div>\n<p class=\"red\">\nOn se sent donc 6 fois plus l\u00e9ger sur la Lune.\n<\/p>\n\n<div class=\"exercice\">\n<h3>Exercice type \u2014 Poids sur Terre et sur la Lune<\/h3>\n<p>\nUn astronaute a une masse de <span class=\"red\">m = 80 kg<\/span>.\nComparer son poids sur Terre et sur la Lune.\n<\/p>\n\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">P = m \u00d7 g<\/div>\n<p class=\"step\">On l\u2019applique une fois avec g<sub>Terre<\/sub>, puis une fois avec g<sub>Lune<\/sub>.<\/p>\n<div class=\"formule bluebox\">P<sub>Terre<\/sub> = m \u00d7 g<sub>Terre<\/sub><\/div>\n<div class=\"formule bluebox\">P<sub>Lune<\/sub> = m \u00d7 g<sub>Lune<\/sub><\/div>\n<\/div>\n\n<p>P<sub>Terre<\/sub> = 80 \u00d7 9,81 = 785 N.<\/p>\n<p>P<sub>Lune<\/sub> = 80 \u00d7 1,6 = 128 N.<\/p>\n<p class=\"resultat\">L\u2019astronaute a la m\u00eame masse, mais son poids est environ 6 fois plus faible sur la Lune.<\/p>\n<\/div>\n<\/section>\n\n<section class=\"section\" id=\"exercices\">\n<h2>V. Exercices contextualis\u00e9s<\/h2>\n\n<div class=\"exercice\">\n<h3>1. Satellite autour de Wallis et Futuna<\/h3>\n<p>\nUn petit satellite de masse <span class=\"red\">m = 250 kg<\/span> est \u00e0 une altitude de\n<span class=\"red\">h = 500 km<\/span>.\nOn donne R<sub>T<\/sub> = 6378 km, m<sub>T<\/sub> = 5,98 \u00d7 10\u00b2\u2074 kg et G = 6,67 \u00d7 10\u207b\u00b9\u00b9.\nCalculer le champ gravitationnel \u00e0 cette altitude puis la force gravitationnelle exerc\u00e9e sur le satellite.\n<\/p>\n\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">g(h) = G \u00d7 m<sub>T<\/sub> \/ (R<sub>T<\/sub> + h)\u00b2<\/div>\n<p class=\"step\">On calcule d\u2019abord g(h), puis on utilise :<\/p>\n<div class=\"formule bluebox\">F = m \u00d7 g(h)<\/div>\n<\/div>\n\n<p class=\"red\">Conversions :<\/p>\n<p>R<sub>T<\/sub> = 6378 \u00d7 10\u00b3 m ; h = 500 \u00d7 10\u00b3 m.<\/p>\n<p>g(h) = (6,67 \u00d7 10\u207b\u00b9\u00b9 \u00d7 5,98 \u00d7 10\u00b2\u2074) \/ (6378 \u00d7 10\u00b3 + 500 \u00d7 10\u00b3)\u00b2<\/p>\n<p>g(h) \u2248 8,43 N\u00b7kg\u207b\u00b9<\/p>\n<p>F = 250 \u00d7 8,43<\/p>\n<p class=\"resultat\">F \u2248 2,11 \u00d7 10\u00b3 N<\/p>\n<\/div>\n\n<div class=\"exercice\">\n<h3>2. Va\u2019a et poids d\u2019une rameuse<\/h3>\n<p>\nUne rameuse a une masse de <span class=\"red\">m = 62 kg<\/span>.\nCalculer son poids sur Terre.\n<\/p>\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">P = m \u00d7 g<\/div>\n<p class=\"step\">On cherche P : la formule est d\u00e9j\u00e0 sous la bonne forme.<\/p>\n<div class=\"formule bluebox\">P = m \u00d7 g<\/div>\n<\/div>\n<p>P = 62 \u00d7 9,81<\/p>\n<p class=\"resultat\">P \u2248 608 N<\/p>\n<\/div>\n\n<div class=\"exercice\">\n<h3>3. Mission lunaire<\/h3>\n<p>\nUn objet p\u00e8se <span class=\"red\">120 N<\/span> sur la Lune.\nOn donne g<sub>Lune<\/sub> = 1,6 N\u00b7kg\u207b\u00b9.\nCalculer sa masse.\n<\/p>\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">P = m \u00d7 g<\/div>\n<p class=\"step\">On veut isoler m. On divise par g :<\/p>\n<div class=\"formule bluebox\">m = P \/ g<\/div>\n<\/div>\n<p>m = 120 \/ 1,6<\/p>\n<p class=\"resultat\">m = 75 kg<\/p>\n<\/div>\n<\/section>\n\n<section class=\"section\" id=\"type-bac\">\n<h2>VI. Partie type bac \/ \u00e9valuation \u2014 niveau seconde<\/h2>\n\n<div class=\"exercice\">\n<h3>Situation 1 \u2014 Une sonde autour de la Lune<\/h3>\n<p>\nUne sonde de masse m = 500 kg se trouve \u00e0 la surface de la Lune.\nOn donne m<sub>Lune<\/sub> = 7,35 \u00d7 10\u00b2\u00b2 kg, R<sub>Lune<\/sub> = 1738 km et G = 6,67 \u00d7 10\u207b\u00b9\u00b9.\n<\/p>\n<ol>\n<li>Calculer g<sub>Lune<\/sub>.<\/li>\n<li>Calculer la force gravitationnelle exerc\u00e9e par la Lune sur la sonde.<\/li>\n<li>Comparer avec son poids sur Terre.<\/li>\n<\/ol>\n\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">g = G \u00d7 m<sub>Lune<\/sub> \/ R<sub>Lune<\/sub>\u00b2<\/div>\n<p class=\"step\">On calcule d\u2019abord g, puis la force :<\/p>\n<div class=\"formule bluebox\">P = m \u00d7 g<\/div>\n<\/div>\n\n<p>R<sub>Lune<\/sub> = 1738 \u00d7 10\u00b3 m.<\/p>\n<p>g<sub>Lune<\/sub> \u2248 1,6 N\u00b7kg\u207b\u00b9.<\/p>\n<p>P<sub>Lune<\/sub> = 500 \u00d7 1,6 = 800 N.<\/p>\n<p>P<sub>Terre<\/sub> = 500 \u00d7 9,81 = 4905 N.<\/p>\n<p class=\"resultat\">La sonde subit une force environ 6 fois plus faible sur la Lune que sur Terre.<\/p>\n<\/div>\n\n<div class=\"exercice\">\n<h3>Situation 2 \u2014 Force Terre-Lune<\/h3>\n<p>\nOn donne m<sub>T<\/sub> = 5,98 \u00d7 10\u00b2\u2074 kg ; m<sub>L<\/sub> = 7,35 \u00d7 10\u00b2\u00b2 kg ;\nd = 3,84 \u00d7 10\u2075 km ; G = 6,67 \u00d7 10\u207b\u00b9\u00b9.\n<\/p>\n<ol>\n<li>Convertir la distance en m\u00e8tres.<\/li>\n<li>Calculer la force gravitationnelle entre la Terre et la Lune.<\/li>\n<li>Repr\u00e9senter la force exerc\u00e9e par la Terre sur la Lune.<\/li>\n<\/ol>\n\n<p class=\"red\">Conversion :<\/p>\n<p>d = 3,84 \u00d7 10\u2075 km = 3,84 \u00d7 10\u2078 m.<\/p>\n\n<div class=\"litteral\">\n<p class=\"start\">Formule du cours :<\/p>\n<div class=\"formule\">F = G \u00d7 m\u2081 \u00d7 m\u2082 \/ d\u00b2<\/div>\n<p class=\"step\">Pour Terre-Lune :<\/p>\n<div class=\"formule bluebox\">F = G \u00d7 m<sub>T<\/sub> \u00d7 m<sub>L<\/sub> \/ d\u00b2<\/div>\n<\/div>\n\n<p>F \u2248 1,99 \u00d7 10\u00b2\u2070 N.<\/p>\n<p class=\"resultat\">La force est attractive et dirig\u00e9e vers le centre de la Terre lorsqu\u2019on la repr\u00e9sente sur la Lune.<\/p>\n<\/div>\n<\/section>\n\n<section class=\"section\" id=\"fiche-bilan\">\n<h2>\ud83d\udccc Fiche bilan \u2014 La gravitation universelle<\/h2>\n<div class=\"grid3\">\n<div class=\"card\"><h3>Gravitation<\/h3><p>Interaction attractive entre deux corps qui poss\u00e8dent une masse.<\/p><\/div>\n<div class=\"card\"><h3>Newton<\/h3><p>A \u00e9tabli la loi de la gravitation universelle au XVII\u1d49 si\u00e8cle.<\/p><\/div>\n<div class=\"card\"><h3>Forces<\/h3><p>F\u2081\/\u2082 = F\u2082\/\u2081 : m\u00eame valeur, sens oppos\u00e9s.<\/p><\/div>\n<div class=\"card\"><h3>Loi<\/h3><div class=\"formule\">F = G m\u2081m\u2082 \/ d\u00b2<\/div><\/div>\n<div class=\"card\"><h3>Constante G<\/h3><p>G = 6,67 \u00d7 10\u207b\u00b9\u00b9 N\u00b7m\u00b2\u00b7kg\u207b\u00b2.<\/p><\/div>\n<div class=\"card\"><h3>Unit\u00e9s<\/h3><p>m en kg ; d en m ; F en N.<\/p><\/div>\n<div class=\"card\"><h3>Surface Terre<\/h3><div class=\"formule bluebox\">P = m \u00d7 g<\/div><\/div>\n<div class=\"card\"><h3>Champ terrestre<\/h3><div class=\"formule bluebox\">g = Gm<sub>T<\/sub>\/R<sub>T<\/sub>\u00b2<\/div><p>g \u2248 9,81 N\u00b7kg\u207b\u00b9.<\/p><\/div>\n<div class=\"card\"><h3>Altitude<\/h3><div class=\"formule bluebox\">g(h)=Gm<sub>T<\/sub>\/(R<sub>T<\/sub>+h)\u00b2<\/div><\/div>\n<div class=\"card\"><h3>Lune<\/h3><p>g<sub>Lune<\/sub> \u2248 1,6 N\u00b7kg\u207b\u00b9.<\/p><\/div>\n<div class=\"card\"><h3>Comparaison<\/h3><p class=\"red\">g<sub>Terre<\/sub> \u2248 6 \u00d7 g<sub>Lune<\/sub>.<\/p><\/div>\n<div class=\"card\"><h3>Masse \/ poids<\/h3><p>La masse ne change pas ; le poids d\u00e9pend de g.<\/p><\/div>\n<\/div>\n<\/section>\n\n<section class=\"section\">\n<h2>Carte mentale<\/h2>\n<div class=\"grid3\">\n<div class=\"mm-center\">LA GRAVITATION UNIVERSELLE<\/div>\n<div class=\"card\"><h3>Principe<\/h3><p>Deux masses s\u2019attirent.<\/p><\/div>\n<div class=\"card\"><h3>Force<\/h3><p>F = Gm\u2081m\u2082\/d\u00b2.<\/p><\/div>\n<div class=\"card\"><h3>Distance<\/h3><p>Distance de centre \u00e0 centre.<\/p><\/div>\n<div class=\"card\"><h3>Terre<\/h3><p>P = m \u00d7 g ; g = 9,81 N\u00b7kg\u207b\u00b9.<\/p><\/div>\n<div class=\"card\"><h3>Altitude<\/h3><p>g diminue quand h augmente.<\/p><\/div>\n<div class=\"card\"><h3>Lune<\/h3><p>g = 1,6 N\u00b7kg\u207b\u00b9 ; 6 fois plus l\u00e9ger.<\/p><\/div>\n<\/div>\n<\/section>\n\n<\/div>\n\n<script>\nlet utterance;\nfunction playAudioSummary(){\n speechSynthesis.cancel();\n const text=document.getElementById(\"audioText\").innerText;\n utterance=new SpeechSynthesisUtterance(text);\n utterance.lang=\"fr-FR\";\n utterance.rate=0.90;\n speechSynthesis.speak(utterance);\n}\nfunction stopAudioSummary(){speechSynthesis.cancel();}\n<\/script>\n\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>Seconde \u2014 La gravitation universelle La gravitation universelle Seconde physique-chimie \u2022 Attraction gravitationnelle \u2022 Force entre deux corps \u2022 Champ de pesanteur \u2022 Terre \u2022 Lune...<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-778","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pcwallis.malo.wf\/index.php\/wp-json\/wp\/v2\/pages\/778","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pcwallis.malo.wf\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pcwallis.malo.wf\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pcwallis.malo.wf\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/pcwallis.malo.wf\/index.php\/wp-json\/wp\/v2\/comments?post=778"}],"version-history":[{"count":1,"href":"https:\/\/pcwallis.malo.wf\/index.php\/wp-json\/wp\/v2\/pages\/778\/revisions"}],"predecessor-version":[{"id":780,"href":"https:\/\/pcwallis.malo.wf\/index.php\/wp-json\/wp\/v2\/pages\/778\/revisions\/780"}],"wp:attachment":[{"href":"https:\/\/pcwallis.malo.wf\/index.php\/wp-json\/wp\/v2\/media?parent=778"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}