L’espace - 3e
Repérage sur une sphère
Exercice 1 : Lire latitude ou longitude d'une ville sur terre à partir des parallèles et méridiens
Sur le schéma ci-dessous, le point D symbolise la ville d'Aral (Chine).
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On pourra faire pivoter la figure en cliquant dessus.
Légende
- Méridien d'origine Greenwich 0°
- Méridiens (espacés de 20°)
- Équateur 0°
- Parallèles (espacés de 20°)
- N : Pôle nord
- S : Pôle sud
- D : Ville d'Aral
Donner la latitude de la ville d'Aral (Chine).
Exemples de format de réponses attendu : \(80°N\), \(60°S\), \(80°E\) ou \(20°O\)
Exemples de format de réponses attendu : \(80°N\), \(60°S\), \(80°E\) ou \(20°O\)
Exercice 2 : Calculer la longueur de l'équateur ou d'un méridien à partir du rayon/diamètre de la planète
Sur une planète de rayon \( 2\:400\:\text{km} \), on définit l'équateur de la même manière que sur Terre.
Quelle est la longueur de l'équateur de cette planète ?
On arrondira le résultat au kilomètre près, suivi de l'unité qui convient.
On arrondira le résultat au kilomètre près, suivi de l'unité qui convient.
Exercice 3 : Lire les coordonnées géographiques d'une ville sur terre à partir des angles
Sur le schéma ci-dessous, le point D symbolise la ville de Minatitlán (Mexique).
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On pourra faire pivoter la figure en cliquant dessus.
Légende
- Méridien d'origine Greenwich 0°
- Méridien du point D
- Équateur 0°
- Parallèle du point D
- N : Pôle nord
- S : Pôle sud
- C : Centre de la terre
- D : Ville de Minatitlán
Sachant que \( \widehat{DCN} = 72 ° \), \( \widehat{ECD} = 18 ° \), \( \widehat{SCE} = 90 ° \) et \( \widehat{ABD} = 95 ° \), donner les coordonnées géographique de la ville de Minatitlán (Mexique).
Par exemple:
Par exemple:
- Pour la ville de Nippes (Allemagne) on donnera une réponse de la forme \(\left(51° N; 7° E\right)\)
- Pour la ville de São Luís (Brésil) on donnera une réponse de la forme \(\left(3° S; 44° O\right)\)
Exercice 4 : Lire latitude ou longitude d'une ville sur terre à partir des angles
Sur le schéma ci-dessous, le point D symbolise la ville d'Iochkar-Ola (Russie).
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{"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 0, "linewidth": 2}}, "PlaneSurface_19": {"position": {"x": 0.0, "y": 33.546822717816966, "z": 0.0}, "rotation": {"x": 1.5707963267948966, "y": 3.141592653589793, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": false}, "surface_render": {"visible": true, "color": 16776960, "opacity": 0.2, "depthTest": true}, "type": "PlaneSurface", "path": "Arc_18"}, "Arc_18": {"type": "Path2D", "path": [{"moveTo": {"x": 0, "y": 0}}, {"lineTo": {"x": -14.577385909852335, "y": -16.18982722497675}}, {"absArc": {"center": {"x": 0, "y": 0}, "radius": 21.785561400601082, "startAngle": 0, "endAngle": 0.8377580409572782}}, {"lineTo": {"x": 0, "y": 0}}]}, "Segment3D_20": {"type": "Segment", "pt1": {"x": 0.0, "y": 33.546822717816966, "z": 0.0}, "pt2": {"x": -26.785561400601082, "y": 33.546822717816966, "z": 0.0}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 0, "linewidth": 2}}, "Segment3D_21": {"type": "Segment", "pt1": {"x": 0.0, "y": 33.546822717816966, "z": 0.0}, "pt2": {"x": -17.92303894164663, "y": 33.546822717816966, "z": 19.90555135236372}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 0, "linewidth": 2}}, "PlaneSurface_23": {"position": {"x": 0.0, "y": 33.546822717816966, "z": 0.0}, "rotation": {"x": 1.5707963267948966, "y": 3.141592653589793, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 16776960, "linewidth": 2}, "surface_render": {"visible": false}, "opened": true, "type": "PlaneSurface", "path": "Arc_22"}, "Arc_22": {"type": "Path2D", "path": [{"absArc": {"center": {"x": 0, "y": 0}, "radius": 10.892780700300541, "startAngle": 0, "endAngle": 0.8377580409572782}}]}, 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-2.4492935982947065e-15, "y": 40.0, "z": 0.0}, "text": "N", "position_offset": {"x": 0.0, "y": 3.3941125496954276, "z": 3.3941125496954276}, "label_render": {"color": 0}}, "Point3D_S": {"type": "Point", "position": {"x": -2.4492935982947065e-15, "y": -40.0, "z": 0.0}, "point_render": {"color": 0, "size": 64}, "label_render": {"color": 0}}, "Label_for_Point3D_S": {"type": "Label", "position": {"x": -2.4492935982947065e-15, "y": -40.0, "z": 0.0}, "text": "S", "position_offset": {"x": 0.0, "y": 3.3941125496954276, "z": 3.3941125496954276}, "label_render": {"color": 0}}, "PlaneSurface_30": {"position": {"x": 0.0, "y": 0.0, "z": 0.0}, "rotation": {"x": 1.5707963267948966, "y": 0.0, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 255, "linewidth": 4}, "surface_render": {"visible": false}, "type": "PlaneSurface", "path": "Circle_29"}, "Circle_29": {"type": "Path2D", "path": [{"absEllipse": {"center": {"x": 0.0, "y": 0.0}, "startAngle": 0, "endAngle": 6.28318530718, "radius": {"x": 40.5, "y": 40.5}}}]}, "PlaneSurface_32": {"position": {"x": 0.0, "y": 33.546822717816966, "z": 0.0}, "rotation": {"x": 1.5707963267948966, "y": 0.0, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 8487415, "linewidth": 4}, "surface_render": {"visible": false}, "type": "PlaneSurface", "path": "Circle_31"}, "Circle_31": {"type": "Path2D", "path": [{"absEllipse": {"center": {"x": 0.0, "y": 0.0}, "startAngle": 0, "endAngle": 6.28318530718, "radius": {"x": 22.285561400601082, "y": 22.285561400601082}}}]}, "Point3D_C": {"type": "Point", "position": {"x": 0.0, "y": 0.0, "z": 0.0}, "point_render": {"color": 0, "size": 64}, "label_render": {"color": 0}}, "Label_for_Point3D_C": {"type": "Label", "position": {"x": 0.0, "y": 0.0, "z": 0.0}, "text": "C", "position_offset": {"x": 0.0, "y": 3.3941125496954276, "z": 3.3941125496954276}, "label_render": {"color": 0}}, "Point3D_E": {"type": "Point", "position": {"x": -26.76522425435433, "y": 0.0, "z": 29.725793019095768}, "point_render": {"color": 0, "size": 64}, "label_render": {"color": 0}}, "Label_for_Point3D_E": {"type": "Label", "position": {"x": -26.76522425435433, "y": 0.0, "z": 29.725793019095768}, "text": "E", "position_offset": {"x": 0.0, "y": 3.3941125496954276, "z": 3.3941125496954276}, "label_render": {"color": 0}}, "Point3D_A": {"type": "Point", "position": {"x": -21.785561400601082, "y": 33.546822717816966, "z": 0.0}, "point_render": {"color": 0, "size": 64}, "label_render": {"color": 0}}, "Label_for_Point3D_A": {"type": "Label", "position": {"x": -21.785561400601082, "y": 33.546822717816966, "z": 0.0}, "text": "A", "position_offset": {"x": 0.0, "y": 3.3941125496954276, "z": 3.3941125496954276}, "label_render": {"color": 0}}, "Point3D_D": {"type": "Point", "position": {"x": -14.577385909852339, "y": 33.546822717816966, "z": 16.18982722497675}, "point_render": {"color": 16711680, "size": 128}, "label_render": {"color": 16711680}}, "Label_for_Point3D_D": {"type": "Label", "position": {"x": -14.577385909852339, "y": 33.546822717816966, "z": 16.18982722497675}, "text": "D", "position_offset": {"x": 0.0, "y": 3.3941125496954276, "z": 3.3941125496954276}, "label_render": {"color": 16711680}}}}
On pourra faire pivoter la figure en cliquant dessus.
Légende
- Méridien d'origine Greenwich 0°
- Méridien du point D
- Équateur 0°
- Parallèle du point D
- N : Pôle nord
- S : Pôle sud
- C : Centre de la terre
- D : Ville d'Iochkar-Ola
Sachant que \( \widehat{ABD} = 48 ° \), \( \widehat{ECD} = 57 ° \), \( \widehat{DCN} = 33 ° \) et \( \widehat{SCE} = 90 ° \), donner la longitude de la ville d'Iochkar-Ola (Russie).
Exemples de format de réponses attendu : \(80°N\), \(60°S\), \(80°E\) ou \(20°O\)
Exemples de format de réponses attendu : \(80°N\), \(60°S\), \(80°E\) ou \(20°O\)
Exercice 5 : Calculer le rayon d'un parallèle
On assimile la Terre à une sphère de rayon \( 6\:400\:\text{km} \).
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On pourra faire pivoter la figure en cliquant dessus.
Légende
- Équateur 0°
- Parallèle passant par D
- N : Pôle nord
- S : Pôle sud
- D : Ville de Tema
Déterminer le rayon du parallèle passant à Tema de coordonnées (6° N, 0°).
On arrondira donnera un résultat arrondi au \( km \).
On arrondira donnera un résultat arrondi au \( km \).