Ecrit par ✅ Quiz : Lois De Kepler
Ce quiz contient 20 questions.
Note : Placeholder pour valider la structure. Le JSON converti est conservé ci-dessous pour l’import final des vraies questions Tutor LMS.
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{
"quiz_title": "Lois De Kepler",
"quiz_slug": "07_lois_de_kepler_quiz",
"quiz_description": "Quiz Edu509 : Lois De Kepler",
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"questions": [
{
"question_order": 1,
"question_title": "Selon la première loi de Kepler, quelle affirmation est correcte concernant la trajectoire d'une planète autour du Soleil ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
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"question_description": "",
"question_explanation": "La première loi de Kepler affirme que les planètes décrivent des ellipses dont le Soleil occupe l’un des foyers.",
"answers": [
{
"answer_title": "La trajectoire est une ellipse dont le Soleil occupe un foyer.",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "La trajectoire est un cercle parfait centré sur le Soleil.",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "La trajectoire est une parabole.",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "La trajectoire est une droite.",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 2,
"question_title": "Si une planète a un demi-grand axe de \\\\( a = 4 \\\\ \\\\mathrm{UA} \\\\), quelle est sa période de révolution autour du Soleil en années ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Selon la troisième loi de Kepler, \\\\( T^2 = a^3 \\\\). Donc \\\\( T^2 = 4^3 = 64 \\\\), donc \\\\( T = \\\\sqrt{64} = 8 \\\\) années.",
"answers": [
{
"answer_title": "8",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "2",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "16",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "4",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 3,
"question_title": "La deuxième loi de Kepler implique que :",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La deuxième loi de Kepler stipule que le segment reliant la planète au Soleil balaie des aires égales en des temps égaux.",
"answers": [
{
"answer_title": "Le segment reliant la planète au Soleil balaie des aires égales en des temps égaux.",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "La planète se déplace toujours à vitesse constante.",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "La planète accélère toujours en s’éloignant du Soleil.",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "La planète ralentit toujours en s’approchant du Soleil.",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 4,
"question_title": "Pour une planète dont la période de révolution est de \\\\( 27 \\\\) années, quel est le demi-grand axe de son orbite en UA ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "D’après la troisième loi de Kepler : \\\\( T^2 = a^3 \\\\). Donc \\\\( a = \\\\sqrt[3]{T^2} = \\\\sqrt[3]{27^2} = \\\\sqrt[3]{729} = 9 \\\\) UA.",
"answers": [
{
"answer_title": "9",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "3",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "81",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "18",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 5,
"question_title": "Quelle grandeur reste constante selon la deuxième loi de Kepler ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La deuxième loi de Kepler affirme que la vitesse aréolaire \\\\( \\\\left( \\\\frac{dA}{dt} \\\\right) \\\\) est constante.",
"answers": [
{
"answer_title": "La vitesse aréolaire \\\\( \\\\left( \\\\frac{dA}{dt} \\\\right) \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "La vitesse linéaire",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "La distance au Soleil",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "La période orbitale",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 6,
"question_title": "Une planète a un demi-grand axe de \\\\( 2 \\\\ \\\\mathrm{UA} \\\\). Quelle est sa période de révolution en années ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Avec \\\\( T^2 = a^3 \\\\), \\\\( T^2 = 2^3 = 8 \\\\), donc \\\\( T = \\\\sqrt{8} = 2.83 \\\\) années.",
"answers": [
{
"answer_title": "2.83",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "4",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "1.41",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "8",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 7,
"question_title": "Si la période d’une planète est multipliée par 2, par combien est multiplié son demi-grand axe ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Si \\\\( T \\\\) est multiplié par 2, alors \\\\( T^2 \\\\) est multiplié par 4. Donc \\\\( a^3 = 4a_0^3 \\\\), donc \\\\( a = a_0 \\\\times \\\\sqrt[3]{4} \\\\).",
"answers": [
{
"answer_title": "La racine cubique de 4",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "2",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "4",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "8",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 8,
"question_title": "Quelle(s) affirmation(s) est/sont vraie(s) concernant l’ellipse orbitale d’une planète ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Dans l’ellipse orbitale, le Soleil occupe l’un des foyers, pas le centre.",
"answers": [
{
"answer_title": "Le Soleil occupe l’un des foyers de l’ellipse.",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "Le Soleil est au centre de l’ellipse.",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "Le demi-grand axe est toujours égal au demi-petit axe.",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "L’ellipse n’a pas de foyers.",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 9,
"question_title": "Pour une planète située à \\\\( 0{,}25 \\\\ \\\\mathrm{UA} \\\\) du Soleil, quelle est sa période de révolution en années ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Avec \\\\( T^2 = a^3 \\\\), \\\\( T^2 = (0{,}25)^3 = 0{,}015625 \\\\), donc \\\\( T = \\\\sqrt{0{,}015625} = 0{,}125 \\\\) années, donc la période est 0,125 années. Cependant, la racine de 0,015625 est 0,125, donc",
"answers": [
{
"answer_title": "0.125",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0.5",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0.25",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "0.0625",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 10,
"question_title": "Si une planète a une période de \\\\( 0{,}5 \\\\) années, quelle est la valeur de son demi-grand axe en UA ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Avec \\\\( T^2 = a^3 \\\\), \\\\( a = \\\\sqrt[3]{T^2} = \\\\sqrt[3]{0{,}25} = 0{,}63 \\\\) UA.",
"answers": [
{
"answer_title": "0.63",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0.5",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0.25",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "1",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 11,
"question_title": "Laquelle des propositions suivantes est une conséquence directe de la troisième loi de Kepler ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La troisième loi de Kepler relie la période et la distance au Soleil : plus la planète est éloignée, plus sa période est longue.",
"answers": [
{
"answer_title": "Plus une planète est éloignée du Soleil, plus sa période de révolution est longue.",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "Toutes les planètes ont la même période de révolution.",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "La vitesse d’une planète est constante sur son orbite.",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "Le Soleil est au centre de l’ellipse.",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 12,
"question_title": "Si une planète double sa distance moyenne au Soleil, comment évolue sa période de révolution ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Si \\\\( a \\\\) est multiplié par 2, alors \\\\( T^2 = (2a_0)^3 = 8a_0^3 \\\\), donc \\\\( T = T_0 \\\\times 2.83 \\\\).",
"answers": [
{
"answer_title": "Elle est multipliée par \\\\( 2^{3/2} = 2.83 \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "Elle est multipliée par 2",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "Elle est multipliée par 4",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "Elle reste inchangée",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 13,
"question_title": "Quelle(s) grandeur(s) doit-on connaître pour appliquer la troisième loi de Kepler dans le Système solaire ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Dans le Système solaire, la troisième loi de Kepler s’applique avec le demi-grand axe en UA et la période en années.",
"answers": [
{
"answer_title": "Le demi-grand axe (en UA) et la période (en années)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "La masse de la planète",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "La vitesse aréolaire",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "La distance focale de l’ellipse",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 14,
"question_title": "Une planète a un demi-grand axe de \\\\( 3 \\\\ \\\\mathrm{UA} \\\\). Quelle est sa période de révolution en années ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Avec \\\\( T^2 = a^3 \\\\), \\\\( T^2 = 27 \\\\), donc \\\\( T = \\\\sqrt{27} = 5.20 \\\\) années.",
"answers": [
{
"answer_title": "5.20",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "3",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "9",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "1.73",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 15,
"question_title": "Parmi les propositions suivantes, laquelle correspond à la définition du demi-grand axe d’une ellipse ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le demi-grand axe est la moitié de la plus grande longueur de l’ellipse.",
"answers": [
{
"answer_title": "La moitié de la plus grande longueur de l’ellipse.",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "La distance entre les deux foyers.",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "La moitié de la plus petite longueur de l’ellipse.",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "La distance du centre au foyer.",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 16,
"question_title": "Si une planète a une période de \\\\( 27 \\\\) années, quelle est la valeur de \\\\( a^3 \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Avec \\\\( T^2 = a^3 \\\\), donc \\\\( a^3 = T^2 = 27^2 = 729 \\\\).",
"answers": [
{
"answer_title": "729",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "81",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "19683",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "243",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 17,
"question_title": "Quelle(s) affirmation(s) est/sont correcte(s) concernant la vitesse d’une planète sur son orbite elliptique ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La planète va plus vite au périhélie (plus proche du Soleil) et plus lentement à l’aphélie.",
"answers": [
{
"answer_title": "La vitesse est maximale au périhélie.",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "La vitesse est minimale au périhélie.",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "La vitesse est constante.",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "La vitesse est maximale à l’aphélie.",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 18,
"question_title": "Pour une planète dont le demi-grand axe est \\\\( 0{,}5 \\\\ \\\\mathrm{UA} \\\\), quelle est la période de révolution en années ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Avec \\\\( T^2 = (0{,}5)^3 = 0{,}125 \\\\), donc \\\\( T = \\\\sqrt{0{,}125} = 0{,}35 \\\\) années.",
"answers": [
{
"answer_title": "0.35",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0.5",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0.25",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "0.71",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 19,
"question_title": "Laquelle des lois de Kepler permet d’expliquer pourquoi une planète accélère en s’approchant du Soleil ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La deuxième loi explique que la planète balaie des aires égales en des temps égaux, donc elle accélère près du Soleil.",
"answers": [
{
"answer_title": "La deuxième loi (loi des aires)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "La première loi (loi des orbites)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "La troisième loi (loi des périodes)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "Aucune loi de Kepler",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 20,
"question_title": "Si une planète a une période de \\\\( 64 \\\\) années, quelle est la valeur de son demi-grand axe en UA ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Avec \\\\( T^2 = a^3 \\\\), \\\\( a = \\\\sqrt[3]{T^2} = \\\\sqrt[3]{4096} = 16 \\\\) UA.",
"answers": [
{
"answer_title": "16",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "8",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "32",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "4",
"is_correct": false,
"answer_order": 4
}
]
}
]
}