{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"4. Mouvement de Mercure, variations du vecteur vitesse et masse du Soleil.ipynb","version":"0.3.2","provenance":[],"collapsed_sections":[]},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.7.1"},"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"}},"cells":[{"metadata":{"id":"wJhQTsCtWPz-","colab_type":"text"},"cell_type":"markdown","source":["# FICHE n°4 : Mouvement de Mercure, variations du vecteur vitesse et masse du Soleil\n","\n","L’étude porte sur le mouvement de Mercure, les positions étant obtenues sur le site des éphémérides pour 11 dates démarrant le 1/1/2017 et espacées de 8 jours. Les variations du vecteur vitesse au cours du temps permettent d’estimer une valeur de la masse solaire. \n","\n","**Capacité numérique mise en œuvre** : Utiliser un langage de programmation pour étudier la relation approchée entre la variation du vecteur vitesse d’un système modélisé par un point matériel entre deux instants voisins et la somme des forces appliquées sur celui-ci.\n","\n","## 1. Représentation des vecteurs vitesse"]},{"metadata":{"id":"8-UUojf1v8HC","colab_type":"code","colab":{}},"cell_type":"code","source":["import numpy as np\n","import matplotlib.pyplot as plt\n","\n","t=8*np.arange(11)\n","Xmes=np.array([-0.2,2.9,5.4,6.4,5,1.2,-3.4,-6.4,-6.9,-5.7,-3.3])\n","Ymes=np.array([-8.2,-7.3,-4.9,-1.2,2.9,5.3,4.7,1.5,-2.3,-5.5,-7.5])\n","x=Xmes*0.46/8.2\n","y=Ymes*0.46/8.2"],"execution_count":0,"outputs":[]},{"metadata":{"id":"Nsu3SFqhc3ia","colab_type":"text"},"cell_type":"markdown","source":["**Calcul des vitesses et des accélérations**"]},{"metadata":{"id":"XwqcNYVjWOer","colab_type":"code","colab":{}},"cell_type":"code","source":["vxl=[]\n","m=np.arange(len(t)-2)\n","for i in m :\n"," vx=(x[i+2]-x[i])/(t[i+2]-t[i])\n"," vxl.append(vx)\n","\n","vyl=[]\n","m=np.arange(len(t)-2)\n","for i in m :\n"," vy=(y[i+2]-y[i])/(t[i+2]-t[i])\n"," vyl.append(vy)\n","\n","axl=[]\n","m=np.arange(len(t)-4)\n","for i in m :\n"," ax=(vxl[i+2]-vxl[i])/(t[i+2]-t[i])\n"," axl.append(ax)\n","\n","ayl=[]\n","m=np.arange(len(t)-4)\n","for i in m :\n"," ay=(vyl[i+2]-vyl[i])/(t[i+2]-t[i])\n"," ayl.append(ay)"],"execution_count":0,"outputs":[]},{"metadata":{"id":"MDtAPxvtdUOo","colab_type":"text"},"cell_type":"markdown","source":["**Réprésentation des vecteurs vitesse**"]},{"metadata":{"id":"EZFx5KlFWOet","colab_type":"code","outputId":"4c186c88-e74a-48bd-cecf-8c89d6ddf56c","executionInfo":{"status":"ok","timestamp":1556614590235,"user_tz":-540,"elapsed":761,"user":{"displayName":"Laurent Abbal","photoUrl":"https://lh6.googleusercontent.com/-p69Q6bgsEu8/AAAAAAAAAAI/AAAAAAAAB48/MjyqeBqYC-A/s64/photo.jpg","userId":"10222764443389714306"}},"colab":{"base_uri":"https://localhost:8080/","height":281}},"cell_type":"code","source":["for i in m :\n"," plt.arrow(x[i+1],y[i+1],5*vxl[i],5*vyl[i],head_width=0.05)\n","\n","plt.axis('equal')\n","plt.xlim(-1,1)\n","plt.ylim(-1,1)\n","plt.title(\"Vecteurs vitesse\")\n","plt.grid()\n","plt.plot(x,y,'bo')\n","plt.show()"],"execution_count":31,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAYcAAAEICAYAAAC0+DhzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n9uygvSm+8+1vYWX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2s7vDPpOAk4DJZlYafo1Mcr0ikgbPPPMMAC+88IKuRspySX3Owd0/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\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"metadata":{"id":"oZAAKJgBvrgF","colab_type":"text"},"cell_type":"markdown","source":["## 2. Détermination de la masse du Soleil\n","\n","\n"]},{"metadata":{"id":"OUGpt99hUznr","colab_type":"text"},"cell_type":"markdown","source":["* Le script précédent fournit les directions et sens des vecteurs vitesse, mais il y a un problème d’échelle\n","* Pour rendre notre étude quantitative, on convertit les valeurs de vitesses dans les unités correctes pour pouvoir définir les vecteurs variation de la vitesse. Cette manipulation des listes axl et ayl nécessite de les transformer préalablement en tableau numpy (en effet, on ne peut pas effectuer d’opérations numériques sur des listes) : c’est le sens des lignes type : ayln=1.5*10**11*np.array(ayl)/(24*3600)**2\n","* Dans un deuxième temps, le script calcule, pour tous les points de mesure, la norme de la variation du vecteur vitesse. Ensuite, le produit de cette norme par le carré de la distance d2 est calculé. D’après le principe fondamental de la dynamique, en considérant Mercure uniquement soumis à l’action du Soleil, ce produit doit être égal à GMs où G est la constante de gravitation universelle et Ms la masse du soleil. Il faut ici prendre garde à redimensionner les listes de distances pour qu’elles contiennent autant de valeurs que de valeurs calculées d’accélération. \n","* Il faut aussi prendre garde à bien faire correspondre les valeurs de distance et d’accélération calculée (il faut ainsi décaler la liste des distances (c’est le sens de la commande dr=d[ 2:] qui enlève les 2 premiers termes de la liste d) et de x[ :-2], qui enlève les 2 derniers termes de la liste x).\n","* On peut ensuite faire modéliser la fonction précédente par une constante et faire afficher la valeur expérimentale de la masse du Soleil. Pour pouvoir faire varier l’échelle à loisir, il vaut mieux définir des grandeurs plus petites (ce qui explique la présence de 1020).\n","* Remarque : la commande \"%.1e\"%M sert à ne garder qu’un chiffre après la virgule pour M."]},{"metadata":{"id":"pa65gEmiWOex","colab_type":"code","outputId":"1e6c1b16-7f84-44aa-dc3b-5b3d9504321b","executionInfo":{"status":"ok","timestamp":1556614599080,"user_tz":-540,"elapsed":784,"user":{"displayName":"Laurent Abbal","photoUrl":"https://lh6.googleusercontent.com/-p69Q6bgsEu8/AAAAAAAAAAI/AAAAAAAAB48/MjyqeBqYC-A/s64/photo.jpg","userId":"10222764443389714306"}},"colab":{"base_uri":"https://localhost:8080/","height":317}},"cell_type":"code","source":["ayln=1.5*10**11*np.array(ayl)/(24*3600)**2 # on convertit les échelles de distance et de temps en unités SI\n","axln=1.5*10**11*np.array(axl)/(24*3600)**2 # idem\n","norma=(ayln**2+axln**2)**(1/2) # on calcule la norme de l'accélération\n","dx=x[:-2]*1.5*10**11 # on enlève les deux dernières valeurs de dx\n","dy=y[:-2]*1.5*10**11 # idem pour uy\n","d=(dx**2+dy**2)**(1/2) # on calcule la distance pour les listes coupées\n","\n","dr=d[2:] # on enlève les deux premières valeurs\n","GM=dr**2*norma # on calcule la valeur du produit GM\n","GMth=6.67*10**(-11)*2*10**30 # valeur tabulée de GM\n","n=np.arange(len(t)-4) \n","plt.plot(n,GM*10**(-20),'bo',label=\"points expérimentaux\")\n","plt.legend()\n","plt.grid()\n","\n","mod=np.polyfit(n,GM,0) # on modélise la liste des valeurs de GM par une constante (polynôme d'ordre 0) \n","M=float(mod[0]/(6.67*10**(-11))) # on calcule la masse du soleil\n","print('La masse du soleil est de l ordre de',\"%.1e\"%M,'kg') # la commande \"%.1e\"%M sert à ne garder qu'1 seul CS pour M \n","GMmod=0*n+mod[0] # on définit une fonction à partir de la valeur modélisée, pour pouvoir tracer. \n","plt.plot(n,(GMmod)*10**(-20),'r-',label=\"modèle\")\n","plt.legend()\n","plt.ylim(0,5)\n","plt.xlabel(\"point de mesure\")\n","plt.ylabel(\"valeur du produit GMs x10^20\")"],"execution_count":32,"outputs":[{"output_type":"stream","text":["La masse du soleil est de l ordre de 1.7e+30 kg\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["Text(0, 0.5, 'valeur du produit GMs x10^20')"]},"metadata":{"tags":[]},"execution_count":32},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAXwAAAEKCAYAAAARnO4WAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n3UfWsc14YDxA+/bti2bNSm6If2VlJa1atUpq36YmV9qSK+0AtaUpypV2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iEieUMIXEckT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\nB1J1cKdoS3rWAAAAAElFTkSuQmCC\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"metadata":{"id":"sWpsSD9eBD25","colab_type":"text"},"cell_type":"markdown","source":["**Conclusion** : la masse obtenue est très proche de la valeur tabulée.\n","\n","**Remarque** : on peut aussi faire tracer la norme de l’accélération en fonction de $1/distance^2$, pour vérifier que l’on a bien une évolution linéaire, la pente de la fonction modèle étant alors le facteur GMs avec Ms obtenue précédemment. \n"]},{"metadata":{"id":"bmOzUq0LWOe0","colab_type":"code","outputId":"1b534cbe-55c6-4c48-b1a2-f36bcc328df8","executionInfo":{"status":"ok","timestamp":1556612644353,"user_tz":-540,"elapsed":1641,"user":{"displayName":"Laurent Abbal","photoUrl":"https://lh6.googleusercontent.com/-p69Q6bgsEu8/AAAAAAAAAAI/AAAAAAAAB48/MjyqeBqYC-A/s64/photo.jpg","userId":"10222764443389714306"}},"colab":{"base_uri":"https://localhost:8080/","height":300}},"cell_type":"code","source":["drci=1/(dr)**2\n","plt.plot(drci,norma,'bo',label=\"points expérimentaux\")\n","plt.legend()\n","plt.grid()\n","model=6.67*10**(-11)*1.7*10**30*drci\n","plt.plot(drci,model,'r-',label=\"modèle\")\n","plt.legend()\n","plt.xlabel(\"1/d^2\")\n","plt.ylabel(\"accélération\")\n"],"execution_count":19,"outputs":[{"output_type":"execute_result","data":{"text/plain":["Text(0, 0.5, 'accélération')"]},"metadata":{"tags":[]},"execution_count":19},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAZIAAAEKCAYAAAA4t9PUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrFmzWLJkCYMGDQIgPz+fli1bFvmehad8B9ixY8d+dUSkGnzyC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kcAH5nZy4DH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\n","text/plain":["
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