{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "![En tête general](img/En_tete_general.png)\n", "\n", "\n", "*(C) Copyright Franck CHEVRIER 2019-2021 http://www.python-lycee.com/*\n", "\n", " Pour exécuter une saisie Python, sélectionner la cellule et valider avec SHIFT+Entrée.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Géolocalisation par satellites (corrigé)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sommaire\n", "\n", "1. Principe des coordonnées géographiques
\n", "2. Système de géolocalisation par satellite
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Principe des coordonnées géographiques\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Activer la cellule Python suivante, pour obtenir une figure dynamique, où le point M est mobile." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\t\n", "\t\t\n", "\t\t\n", "\t\t\n", "\t\t\n", "\t\n", "\t\n", "\t\t
\n", "\t\t\t\t\t\t\n", "\t\t\t
\n", "\t\t\t\t
\n", "\t\t\t\t\t\t\t\t\n", "\t\t\t\t
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\n", "\t\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Sélectionner cette zone puis SHIFT+ENTREE\n", "from IPython.display import display, HTML ; display(HTML('fig_dyn_GeoGebra/Geolocalisation1.html'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La géolocalisation d'un point M sur Terre se fait à l'aide de deux coordonnées géographiques :
\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Exercice :
\n", "Activer la figure dynamique ci-dessous, qui permet de lire les coordonnées sphériques du point rouge mobile. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\t\n", "\t\t\n", "\t\t\n", "\t\t\n", "\t\t\n", "\t\n", "\t\n", "\t\t
\n", "\t\t\t\t\t\t\n", "\t\t\t
\n", "\t\t\t\t
\n", "\t\t\t\t\t\t\t\t\n", "\t\t\t\t
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\n", "\t\t
\n", "\t\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Sélectionner cette zone puis SHIFT+ENTREE\n", "from IPython.display import display, HTML ; display(HTML('fig_dyn_GeoGebra/Geolocalisation2.html'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recopier et compléter le tableau fourni ci-dessous (précision attendue : au degré près).
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Nom du point
Ville
Longitude
Latitude
Greenwich
0°
51° N
H
Jayapura
E
Los Angeles
Moscou
38° E
56° N
Karachi
67° E
25° N
Rio de Janeiro
43° O
23° S
Washington
77° O
39° N
B
Bamako
\n", "\n", "Tableau corrigé :\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Nom du point
Ville
Longitude
Latitude
A
Greenwich
0°
51° N
H
Jayapura
141° E
3° S
E
Los Angeles
118° O
34° N
F
Moscou
38° E
56° N
G
Karachi
67° E
25° N
C
Rio de Janeiro
43° O
23° S
D
Washington
77° O
39° N
B
Bamako
8° O
13° N
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Système de géolocalisation par satellite" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. Un satellite envoie des ondes radio qui se propagent à la vitesse de $300\\;000\\;km \\cdot s^{-1}=300\\;km\\cdot ms^{-1}$. En mesurant le temps que met une onde pour lui parvenir d'un satellite, un système de géolocalisation est capable de déduire sa distance à ce satellite.

\n", "Écrire une fonction Python DistSat qui reçoit en argument le temps t mis par l'onde (exprimé en $ms$) et qui renvoie la distance du satellite (exprimée en km)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "#Écrire ici la fonction DistSat\n", "\n", "def DistSat(t):\n", " \"\"\"\n", " fonction qui reçoit un temps t en ms\n", " et renvoie la distance parcourue (ondes à 300kms-1)\n", " \"\"\"\n", " return 300*t" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2. On souhaite géolocaliser un point de la surface terrestre. Pour cela, on dispose des temps mis pour atteindre ce point par des ondes envoyées par 3 satellites. Les données sont consignées dans le tableau ci-dessous.
\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Satellite
Temps (ms)
Sat1
69,9
Sat2
68,1
Sat3
72,3
\n", " \n", "À l'aide de la fonction Python DistSat, déterminer les trois distances qui séparent le point cherché de chaque satellite." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "20970.0" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Utiliser ces zones de saisie pour déterminer les distances\n", "\n", "DistSat(69.9) #distance du satellite 1" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "20430.0" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\n", "DistSat(68.1) #distance du satellite 2" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "21690.0" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\n", "DistSat(72.3) #distance du satellite 3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3. Activer la cellule Python ci-dessous pour obtenir une figure dynamique." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\t\n", "\t\t\n", "\t\t\n", "\t\t\n", "\t\t\n", "\t\n", "\t\n", "\t\t
\n", "\t\t\t\t\t\t\n", "\t\t\t
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\n", "\t\t\t\t\t\t\t\t\n", "\t\t\t\t
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\n", "\t\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Sélectionner cette zone puis SHIFT+ENTREE\n", "from IPython.display import display, HTML ; display(HTML('fig_dyn_GeoGebra/Geolocalisation3.html'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
    \n", "
  • À l'aide des curseurs, régler le plus précisément possible les distances des satellites obtenues à la question précédente.
    Pour chaque satellite, on obtient ainsi une sphère correspondant au signal émis.

    • \n", "
  • Observer l'intersection des sphères obtenues et indiquer dans quel continent puis dans quel pays se trouve le point cherché.

    • \n", "
  • Sachant que ce point est une capitale, donner le nom de cette ville.
    • \n", "
\n", "\n", "L'intersection des sphères se situe en Espagne, et la capitale cherchée est donc Madrid." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*(C) Copyright Franck CHEVRIER 2019-2021 http://www.python-lycee.com/*\n" ] } ], "metadata": { "celltoolbar": "Raw Cell Format", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.10" } }, "nbformat": 4, "nbformat_minor": 2 }