{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "KtuLD5qNbohK" }, "source": [ "## Plotar as leis de Kepler\n", "### Adaptado de https://github.com/katiebreivik/Keplers_Laws/blob/master/Graphing%20Kepler's%20Laws%20with%20Python.ipynb" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true, "id": "F3dxmC2mbohM" }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n" ] }, { "cell_type": "markdown", "metadata": { "id": "GVF8JS35bohN" }, "source": [ "## Funções:\n", "### (1) Uma função precisa de variáveis (between parentheses) e retorna um resultado\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true, "id": "SNpMsVW9bohN" }, "outputs": [], "source": [ "def keplerIII_period_to_semimajor_axis(orbital_period):\n", " #########################################################\n", " # Units: orbital period [yr], separation [au] #\n", " #########################################################\n", " semimajor_axis_cubed = orbital_period**2\n", " semimajor_axis = semimajor_axis_cubed**(1./3.)\n", "\n", " return semimajor_axis\n", "\n", "def make_kepler_orbit(eccentricity,orbital_period):\n", " ##########################################################\n", " # Units: orbital period [years] #\n", " # returns: 500 true anomaly values throughout the orbit #\n", " ##########################################################\n", " nStep = 500\n", " tRange = np.linspace(0.0,orbital_period,nStep)\n", "\n", " theta = []\n", " for time in tRange:\n", " PsiDiff = 1.0\n", " M = 2*np.pi*time/orbital_period\n", " PsiOld = M\n", " theta0old = 180.0\n", " while PsiDiff > 1e-10:\n", " PsiNew = M + eccentricity*np.sin(PsiOld)\n", " PsiDiff = PsiNew-PsiOld\n", " PsiOld = PsiNew\n", " theta0 = 2*np.arctan(((1+eccentricity)/(1-eccentricity))**(0.5)*np.tan(PsiOld/2.))\n", " theta.append(theta0)\n", " return theta" ] }, { "cell_type": "markdown", "metadata": { "id": "oU6HaV0xbohN" }, "source": [ "## Primeiro, vamos simular a órbita da Terra. Precisamos especificar todas as variáveis ​​usadas na função ‘make_kepler_orbit’. Pela forma da 3a lei de Kepler acima, qual a unidade do período orbital (orbital_period)?\n", "\n", "##Precisamos também indicar a excentricidade da Terra (eccentricity).\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true, "id": "euEAzUSpbohO" }, "outputs": [], "source": [ "orbital_period = 1.0\n", "eccentricity = 0.02" ] }, { "cell_type": "markdown", "metadata": { "id": "4Tcs3FF0bohO" }, "source": [ "## Para plotar a órbita Kepleriana, precisamos enviar as variáveis ​​corretas para a função e usar a variável que a função envia de volta. make_kepler_orbit envia de volta uma lista de ângulos $\\theta$ ; esses são os ângulos de anomalia verdadeira para cada tempo na órbita.\n", "\n", "## A lista que é enviada de volta de make_kepler_orbit será chamada de 'list1' (se quiser pode mudar para outro nome)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true, "id": "8-tazqUJbohO" }, "outputs": [], "source": [ "list1 = make_kepler_orbit(eccentricity,orbital_period)\n" ] }, { "cell_type": "markdown", "metadata": { "id": "37kiOm26bohO" }, "source": [ "## Para fazer os plots, precisamos especificar a posição x e y de cada valor do ângulo $\\theta$ \"true anomaly\" (anomalia verdadeira). Para isso, usamos a primeira lei de Kepler (slide 34 da aula 3):\n", "\n", "# r = a (1 - e$^2$)/(1 - e cos $\\theta$)\n", "\n", "## Na equação da elipse, $\\theta$ é a 'true_anomaly'.\n", "\n", "## A função a seguir, orbit(semimajor_axis,e,true_anomaly), calcula x e y para a elipse e retorna os valores xorbit e yorbit. Com esses valores de x e y, podemos plotar a orbita!" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true, "id": "Z8XcgDcTbohO" }, "outputs": [], "source": [ "def orbit(semimajor_axis,eccentricity,true_anomaly):\n", " ##############################################\n", " # Units: separation [au] #\n", " ##############################################\n", "\n", " # define the shape equation\n", " r_orbit = semimajor_axis*(1 - eccentricity**2)/(1 + eccentricity*np.cos(true_anomaly))\n", " x_orbit = r_orbit*np.cos(true_anomaly)\n", " y_orbit = r_orbit*np.sin(true_anomaly)\n", "\n", "\n", " return x_orbit,y_orbit" ] }, { "cell_type": "markdown", "metadata": { "id": "_ukMyRrjbohP" }, "source": [ "## Observe que a função órbita precisa do semieixo maior. Isso significa que precisaremos usar a função da terceira lei de Kepler para converter o período orbital no semieixo maior.\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true, "id": "TQt0kpFKbohP" }, "outputs": [], "source": [ "semimajor_axis = keplerIII_period_to_semimajor_axis(orbital_period)" ] }, { "cell_type": "markdown", "metadata": { "id": "rfb37t0WbohP" }, "source": [ "## Agora que temos a separação (semi-eixo maior \"a\"), podemos chamar a função órbita. A função de órbita precisa do semi-eixo maior, excentricidade e anomalia verdadeira $\\theta$ (que é retornada pela função make_kepler_orbit).\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true, "id": "JVURZVNYbohP" }, "outputs": [], "source": [ "xOrbit, yOrbit = orbit(semimajor_axis,eccentricity,list1)\n" ] }, { "cell_type": "markdown", "metadata": { "id": "VBzSYAykbohP" }, "source": [ "## Graças à função orbit, podemos traçar nossos valores x_orbit e y_orbit. Neste gráfico, colocamos o Sol no centro (0,0).\n", "\n", "## Observe que definimos a seguir plt.axis('equal') na quinta linha; isso faz com que o gráfico use o mesmo tamanho para os eixos x e y. Comente a linha que iguala os eixos digitando # no começo da linha. O que acontece com a órbita da Terra? Por que isso é enganoso? Preencha sua resposta na caixa abaixo do gráfico.\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 472 }, "id": "dsS4ba3dbohP", "outputId": "528d2bdb-8225-4f6c-b381-a53ec5172e44" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": {} } ], "source": [ "plt.title('Earth orbit')\n", "# The Sun is located at the origin.\n", "plt.scatter(0,0, color='orange')\n", "plt.scatter(xOrbit,yOrbit)\n", "plt.axis('equal')\n", "plt.xlabel('x position [au]')\n", "plt.ylabel('y position [au]')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "KqWBS2h0bohQ" }, "source": [ "O plot sem o \"equal\" é errado porque:" ] }, { "cell_type": "markdown", "metadata": { "id": "PU8LsH7YbohQ" }, "source": [ "## Agora que sabemos como fazer a órbita da Terra, podemos fazer órbitas para qualquer planeta do Sistema Solar! Precisaremos saber o período orbital do planeta em anos e sua excentricidade. Estes dados estão abaixo para os outros planetas e Plutão:\n", "\n", "#### Planet = Mercury, orbital period = 0.48 years, eccentricity = 0.21\n", "#### Planet = Venus, orbital period = 0.62 years, eccentricity = 0.01\n", "#### Planet = Mars, orbital period = 1.88 years, eccentricity = 0.09\n", "#### Planet = Jupiter, orbital period = 11.86 years, eccentricity = 0.05\n", "#### Planet = Saturn, orbital period = 29.46 years, eccentricity = 0.05\n", "#### Planet = Uranus, orbital period = 84.02 years, eccentricity = 0.05\n", "#### Planet = Neptune, orbital period = 164.8 years, eccentricity = 0.01\n", "#### Planeta anão = Pluto, orbital period = 248.0 years, eccentricity = 0.25\n", "#### Cometa = Halley, orbital period = 75.3 years, eccentricity = 0.967" ] }, { "cell_type": "markdown", "metadata": { "id": "YDH3pdbhbohQ" }, "source": [ "### Quais planetas (incluindo a Terra) têm a órbita mais e menos circular?. Preencha suas respostas abaixo\n" ] }, { "cell_type": "markdown", "metadata": { "id": "UEjvfn3QbohQ" }, "source": [ "2 planetas com órbitas mais circulares:\n", "\n", "2 planetas com órbitas menos circulares:" ] }, { "cell_type": "markdown", "metadata": { "id": "GZGGP8xubohQ" }, "source": [ ":### Como exemplo, a seguir a órbita de Mercúrio. Após a órbita de Mercúrio, plotar Urano, Netuno, Plutão e o Cometa Halley." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 472 }, "id": "1c1XfssobohQ", "outputId": "b62ee009-193f-4e36-9939-6b0442a78128" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "# Define Mercury's parameters;\n", "orbital_period_Mercury = 0.48\n", "eccentricity_Mercury = 0.21\n", "\n", "# compute Mercury's true anomaly\n", "true_anomaly_Mercury = make_kepler_orbit(eccentricity_Mercury,orbital_period_Mercury)\n", "\n", "# compute Mercury's separation\n", "semimajor_axis_Mercury = keplerIII_period_to_semimajor_axis(orbital_period_Mercury)\n", "\n", "# compute Mercury's x and y orbital coordinates\n", "xOrbit_Mercury, yOrbit_Mercury = orbit(semimajor_axis_Mercury,eccentricity_Mercury,\n", " true_anomaly_Mercury)\n", "\n", "plt.title('Mercury orbit')\n", "# The Sun is located at the origin.\n", "plt.scatter(0,0, color='orange')\n", "plt.scatter(xOrbit_Mercury,yOrbit_Mercury)\n", "plt.axis('equal')\n", "plt.xlabel('x position [au]')\n", "plt.ylabel('y position [au]')\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true, "id": "CM8_hk0WbohR" }, "outputs": [], "source": [ "##### COLOCAR AQUI SEU CÓDIGO PARA PLOTAR Urano, Netuno, Plutão e o Cometa Halley #####\n", "\n", "\n" ] }, { "cell_type": "markdown", "source": [ "RESPONDA: Dos quatro corpos acima.\n", "A) Qual se aproxima mais do Sol?\n", "B) Qual se afasta mais do Sol?" ], "metadata": { "id": "-ViSqFS3oNT-" } }, { "cell_type": "markdown", "metadata": { "id": "msjNifXSbohR" }, "source": [ "# EXOPLANETAS" ] }, { "cell_type": "markdown", "metadata": { "id": "kJ-LRNfjbohR" }, "source": [ "## Vamos comparar agora o planeta WASP-18, que tem massa bem superior a Júpiter e que orbita perto da sua estrela. É um \"hot Jupiter\".\n", "\n", "## Dados de WASP-18b e de Júpiter:\n", "#### Planet = WASP-18b, orbital period = 0.24 years, eccentricity = 0.01\n", "\n", "#### Planet = Jupiter, orbital period = 11.86 years, eccentricity = 0.05\n", "\n", "## Como você compararia o Wasp 18b com Júpiter? Preencha sua resposta na célula abaixo\n" ] }, { "cell_type": "markdown", "metadata": { "id": "C1A_z4mCbohR" }, "source": [ "Como a excentricidade do Wasp-18b se compara à excentricidade de Júpiter:\n", "\n", "Como o período orbital do Wasp-18b se compara ao período orbital de Júpiter:" ] }, { "cell_type": "markdown", "metadata": { "id": "HueRetE4bohR" }, "source": [ "## Agora faça um gráfico da órbita do WASP-18b e da órbita de Júpiter. Incluir um título e nomes dos eixos!" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true, "id": "G9UrR8wibohR" }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": { "id": "0ld79RuMbohR" }, "source": [ "## Como o formato do Wasp 18b é semelhante ao de Júpiter? Como é diferente?" ] }, { "cell_type": "markdown", "metadata": { "id": "fHpkOHnmbohR" }, "source": [ "WASP-18b é semelhante a Júpiter porque:\n", "\n", "\n", "WASP-18b é diferente a Júpiter porque:" ] }, { "cell_type": "markdown", "metadata": { "id": "saSemQ8UbohR" }, "source": [ "## Por que você acha que os astrônomos chamaram planetas como WASP 18b de 'Júpiteres Quentes'? Forneça seu raciocínio para esta afirmação." ] }, { "cell_type": "markdown", "metadata": { "id": "h0rYcKpCbohR" }, "source": [ "Astrônomos chamaram planetas como WASP-18b de 'Júpiteres Quentes' porque:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true, "id": "lnSTYML_bohR" }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" }, "colab": { "provenance": [] } }, "nbformat": 4, "nbformat_minor": 0 }