Lesson4-4_skipthis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AAAAAAKATTJpUfF6zJl0OAMaMohMApFT/NMmnPhWxbFm6LAAAAAAA0K7q35zwve9F9PamywLAmFF0AoDUnnmm+Nzfny4HAAAAAAC0o9NPL89ve1uaHACMOUUnAEht8uSISy4p5vqnTgAAAAAAgGf3t79FnHxyMde/SQGAjqPoBACt4PDDy/Nb35omBwAAAAAAtJONNy4+P/VUuhwANIWiEwC0ivqnTC6/POLhh9NlAQAAAACAVlf/hoRzzonYZJN0WQBoCkUnAGglS5YUn2fMSJcDAAAAAABa2SGHlOfjjkuTA4CmUnQCgFYyZUrEVVcVc/3TKAAAAAAAQMRf/hLxox8Vc/0bEwDoaIpOANBq5syJmDatmJWdAAAAAAAgV6tFvPjFxfz00+myANB0ik4A0IoWLizPv/pVmhwAAAAAANBKKnU/cV95ZcRGG6XLAkDTKToBQKuqVovPr3tdxJo16bIAAAAAAEBq9W9AmDEj4k1vSpcFgCQUnQCgVWVZxJIlxTxuXLosAAAAAACQ0mWXlef589PkACApRScAaGVTpkRceGEx1z+tAgAAAAAA3WDZsoi3va2Y69+IAEBXUXQCgFZ3xBHl+eij0+QAAAAAAIAU+vuLz08/7aFggC6m6AQA7aBWKz5fcEHEvHnJogAAAAAAQNPUl5quuipio43SZQEgOUUnAGgXAwPF55kzy+UnAAAAAADoNK94RXmeMydNDgBahqITALSLnp6IO+8s5oq/xgEAAAAA6FC33BLx298Ws4d/AQhFJwBoL7vuGrH//sXsPeQAAAAAAHSawcGIPfcs5mo1XRYAWoqiEwC0m+uuK8+f+1yaHAAAAAAAMBZ6e4vPjz7qoV8A/o+iEwC0o/qnVz796YgnnkiXBQAAAAAARkt9qelzn4vYcst0WQBoOYpOANCOsixiwYJi3mKLdFkAAAAAAGA07LVXef7Up9LkAKBlKToBQLuaPj3ie98rZlf3AgAAAADQrubOjfjNb4q5VkuXBYCWpegEAO3sbW+LeOELi1nZCQAAAACAdjMwELH33sW8bFm6LAC0NEUnAGh3f/lLeT711DQ5AAAAAABgffT1FZ9vuSVi0qR0WQBoaYpOANAJqtXi82c+E/HII+myAAAAAADA2qp/U8EJJ0TssUe6LAC0PEUnAOgEWRaxZk0xb7ut95cDAAAAANDapkwpz1/6UpocALQNRScA6BS9vREPPFDMFX/NAwAAAADQoi6/POLpp4vZw7sArAW/gAJAJ5k5M+Kkk4q5/spfAAAAAABoBYsXR7z1rcU8OJguCwBtRdEJADrNaaeV5zlz0uQAAAAAAICRbLJJ8XnZMm8oAGCt+RsDADpR/RW/P/1pxNy56bIAAAAAAMCQ+jcR3HxzxKRJ6bIA0HYUnQCgUw0MFJ/33jtixYp0WQAAAAAAoL7kdPDBEa96VbosALQlRScA6FQ9PRHz5hWzp2IAAAAAAEjln/+5PP/wh2lyANDWFJ0AoJNtt13EmWcWc/3TMgAAAAAA0Ay33RbxrW8Vc62WLgsAbU3RCQA63Sc+UZ6VnQAAAAAAaJY1ayL22KOYV69OlwWAtqfoBADdYPjTMR/8YJocAAAAAAB0l3Hjis933x3R15cuCwBtT9EJALpFtVp8Pu+8/KpgAAAAAAAYK/VvGDjjjIiddkqXBYCOoOgEAN0iyyKefrqY99gjYuXKdHkAAAAAAOhc9SWniIh///c0OQDoKIpOANBNNtqofJPTxInpsgAAAAAA0Jne+c7yXKulyQFAx1F0AoBus9tuEWedVczDn6oBAAAAAID1ddNNEd/5TjFXq+myANBxFJ0AoBudeGLEtGnFrOwEAAAAAMCGWrYsYp99innpUufPAIwqRScA6FYLF5bn2bPT5AAAAAAAoP3VahH9/cX88MPlGQBGgaITAHSz+vei33xzxBVXpMsCAAAAAED7qtT99HzttRHbbJMuCwAdS9EJALpdfdnp0EMjHn00XRYAAAAAANpP/evpjj464tWvTpcFgI6m6AQARAwMFJ+32ipicDBdFgAAAAAA2kdvb3k+//w0OQDoCopOAEBET0/E/PnFPHxjCgAAAAAAw33hC+UHZ+vfIAAAY0DRCQDIzZhRftKm/qphAAAAAACod9ddEZ/4RDErOQHQBIpOAEDh6KMjpk0rZmUnAAAAAACGW7YsYtddi3lgIF0WALqKohMAULZwYXmeOTNNDgAAAAAAWlN/f/F5/vyInp50WQDoKopOAECjarX4PG9exJe+lCwKAAAAAAAtpP5NAN/4RsSMGemyANB1FJ0AgEZZFrF6dTH/27/l71sHAAAAAKB71ZecXv7yiKOOSpcFgK6k6AQAjKyvr/wau113jVi+PF0eAAAAAADSqS85RUT89rdpcgDQ1RSdAIBnN21axK23FvPkyRG1Wro8AAAAAAA034EHlmfnxAAkougEADy33XePuOCCYq745wMAAAAAQNe48MKIX/6ymKvVdFkA6Hp+qQQAnt+RR0YcfngxD7+iGAAAAACAzvOnP0UcdVQxL1/ufBiApBSdAIC1c8kl5dlmFgAAAACgcz3zTMROOxXzggUREyemywMAoegEAKyL4e9d7+tLkwMAAAAAgLFTrUZstFEx33prxPTp6fIAwN8pOgEA66a+7DQwEHHccemyAAAAAAAw+np6is+XXRax++7psgBAHUUnAGDd1Zedzj034ic/SZcFAAAAAIDRk2XF5xNPjDjssHRZAGAYRScAYP1Uq8XnN70pYt68ZFEAAAAAABgF9SWn7baLOOusdFkAYASKTgDA+smyiKVLi3nmzIgVK9LlAQAAAABg/dWXnCI83ApAS1J0AgDWX39/xN13F/OkSeXX2gEAAAAA0Pr23LM8O+cFoEUpOgEAG2annSIuvLCYK/55AQAAAADQNk4/PeKWW4pZyQmAFuaXSABgwx1xRMQhhxTz8CuOAQAAAABoPb/8ZcTJJxdztZouCwCsBUUnAGB0XHFFeVZ2AgAAAABoXfPmRRx4YDEvX+5cF4CWp+gEAIye4Vca2xQDAAAAALSe5csjZs4s5vvvj5g4MV0eAFhLik4AwOgaXnaq+OcGAAAAAEDLqFYjJk8u5muvjZg1K10eAFgHfnkEAEZf/Xvca7WIt789XRYAAAAAAHK1WkRPTzH/139FvPrV6fIAwDpSdAIARl+WlctO3/9+xNe+li4PAAAAAADlG/iPPjri2GPTZQGA9aDoBACMjSyLGBws5g9/OOL669PlAQAAAADoZllWfH7RiyLOPz9dFgBYT4pOAMDYqVQi1qwp5v32i3jwwXR5AAAAAAC6UX3JKSLivvvS5ACADaToBACMrd7eiOXLi3nWrIglS9LlAQAAAADoJsNLTrVamhwAMAoUnQCAsTdxYsSjjxbz1KkRq1alywMAAAAA0A2UnADoMIpOAEBzbLllxB13FPOECRHVaro8AAAAAACdbIcdyrOSEwAdQNEJAGieV7wi4pJLirmnx+YaAAAAAGC0HXlkxH33FbNzWAA6hKITANBchx8eccwxxVzxzxEAAAAAgFHz5S9HXHRRMSs5AdBB/LIIADTfeedFTJ9ezMPfEw8AAAAAwLq74oqIE04o5sHBdFkAYAwoYH+h2AAAIABJREFUOgEAaSxYUJ6VnQAAAAAA1t+tt0Ycemgxr1jhRn0AOo6/2QCAdIZfmazsBAAAAACw7ubNi3jVq4p54cKICROSxQGAsaLoBACkpewEAAAAALD+Fi+OmDmzmO+6K2LatHR5AGAMKToBAOkpOwEAAAAArLuVKyM22aSYr7suYpdd0uUBgDGm6AQAtAZlJwAAAACAtTc4GDFxYjFfdlnE/vsniwMAzaDoBAC0jmq1PG+/fZIYAAAAAAAtrVqN6O0t5m98I+Kww9LlAYAmUXQCAFpHlpXLTvPnR7zmNenyAAAAAAC0mlotoqenmM8+O+Koo9LlAYAmUnQCAFrL8LLTtddGHHFEujwAAAAAAK2iVouo1P3Ee9ppEccfny4PADSZohMA0HqGl52++c2Ik09OFgcAAAAAoCXUl5xOPDHipJPSZQGABBSdAIDWNLzsdPrpEV/+cro8AAAAAAApZVnx+YgjIs46K10WAEhE0QkAaF3Dy04nnBBxwQXp8gAAAAAApFBfcjrwwIgLL0yXBQASUnQCAFpblkUMDhbz0UdHfOc76fIAAAAAADRTfclphx0ifv7zdFkAIDFFJwCg9VUqEStXFvM73xnxox+lywMAAAAA0Az1JaeIiD//OU0OAGgRik4AQHsYPz7ib38r5kMOibj66nR5AAAAAADG0vCSU62WJgcAtBBFJwCgfbzgBRELFhTzQQdFXHNNujwAAAAAAGNByQkARqToBAC0l+nTI+6/v5hf+9qI669PlwcAAAAAYDQpOQHAs1J0AgDaz6xZEX/8YzHvt1/E3Lnp8gAAAAAAjAYlJwB4TopOAEB72nHHiLvvLua99464+eZ0eQAAAAAANoSSEwA8L0UnAKB97bRT+Wan2bMjbrklXR4AAAAAgPWh5AQAa0XRCQBobzvuGHH//cW8554Rt96aLg8AAAAAwLpQcgKAtaboBAC0v1mzIhYuLOZXvcrNTgAAAABA61NyAoB1ougEAHSGadMiFi0q5j33jJg7N10eAAAAAIDnouQEAOtM0QkA6BxTp0Y8/XQx7713xPXXp8sDAAAAADASJScAWC+KTgBAZ9loo4hnninm/faL+NWv0uUBAAAAAKin5AQA603RCQDoPJMnRyxdWsyve13ElVemywMAAAAAEKHkBAAbSNEJAOhM/f0RS5YU81veEvGd76TLAwAAAAB0NyUnANhgik4AQOeaMiXi8ceL+Z3vjPj619PlAQAAAAC6k5ITAIwKRScAoLNtvnnEI48U8zHHRHzxi+nyAAAAAADdRckJAEaNohMA0Pm23jpiwYJiPvHEiJNOSpcHAAAAAOgOSk4AMKoUnQCA7jB9esTChcV8xhkRH/hAujwAAAAAQGdTcgKAUafoBAB0j2nTIhYtKubzz484+OB0eQAAAACAzlOrlUtOEyYoOQHAKFF0AgC6y9SpEUuXFvOPfxzxj/+YLg8AAAAA0Dmq1YhK3U+w220XsWJFujwA0GEUnQCA7tPfH7F6dTH/7nf5GgAAAADA+hoYiOjpKeZ9942YNy9ZHADoRIpOAEB36uvLn64asmxZ+TppAAAAAIC1tXx5fuY45H3vi7j++mRxAKBTKToBAN0ryyJqtcY1AAAAAIC1tWhRxOTJxXz66REXXZQuDwB0sN7UAQAAkqvVygWnkQpQAAAAAADDPfRQxHbbFfNll0Ucdli6PADQ4RSdAAAilJ0AAAAAgHXz+99HvOxlxXzrrRG7754uDwB0Aa+uAwAY4jV2AAAAAMDa+OUvyyWnefOUnACgCRSdAADqKTsBAAAAAM/l/PMjDjywmBcvLr++DgAYM4pOAADDjVR28ho7AAAAAOBjH4v4wAeKefnyiI03TpcHALpMb+oAAAAtqVYr3+ZUqURUq254AgAAAIButc8+ETfdVMyrVkWMG5cuDwB0IUUnAIBnU6tFTJsW8dhj+VypOLwAAAAAgG40/AHI1asj+vrSZAGALubVdQAAz+XRRyNe//piHj8+YtGidHkAAAAAgOZScgKAlqHoBADwfK6+OuKTnyzmTTeNuPfedHkAAAAAgOYYXnIaHFRyAoCEFJ0AANbG6adHfPObxfySl0Rcc02yOAAAAADAGBtecqpWIyp+XgWAlPxNDACwtt773oi5c4v5ta+N+OpX0+UBAAAAAMbG8JJTrda4BgA0naITAMC6mD074uGHi/nYYyPe8Y50eQAAAACA0TNSoalWS5MFAGig6AQAsK622SZi5cpi/u53Pc0FAAAAAO1u9eryq+lmzlRyAoAWo+gEALA+xo+PqFbLa8pOAAAAANCennoqP/Mb8olPRDzwQLo8AMCIelMHAABoW1nWeJX10BoAAAAA0B7uuiti112L+Sc/iXjjG9PlAQCelRudAAA21PBik5udAAAAAKA9fPvb5ZLT/fcrOQFAC3OjEwDAaBjpZqdqVekJAAAAAFrVkUdGXHRRMS9dGtHfny4PAPC8FJ0AAEZLrZY//XXXXflcqUSsXBkxfnzaXAAAAABA2bhxEWvWFPOaNRG9fjoFgFbn1XUAAKPp97+POOGEYp4wIeLBB9PlAQAAAADKsqxcchocVHICgDah6AQAMNq+9KXyldezZkVcfnm6PAAAAABALsvKc7Wa38wOALQFf2sDAIyF970v4vrri/mtb4046qhkcQAAAACgq9VqjSWnkdYAgJam6AQAMFb23TfivvuK+cILHZwAAAAAQLOtWdN4a1OtliYLALBBFJ0AAMbSi14UsXRpeU3ZCQAAAACa45FHIsaNK+bNN1dyAoA2pugEADDW+vsjBgbKa8pOAAAAADC2fvaziG23Lebjjot4/PF0eQCADaboBADQDD09jU+KZZmnxwAAAABgLHz4wxFvfGMx//CHEeecky4PADAqelMHAADoKrVaxMYbR/ztb/lcqUQsWRIxZUraXAAAAADQKYbfpn7ffREvelGaLADAqHKjEwBAsy1ZEnHaacW88cYRd9yRLg8AAAAAdIrhJadly5ScAKCDKDoBAKRw0kkRt91WzLvtFvH5z6fLAwAAAADtbnjJqVqNmDQpTRYAYEwoOgEApLLbbhGLFxfzKadE9PenywMAAAAA7WjNmsaSU63WuAYAtD1FJwCAlDbeOGL16mJetswBDAAAAACsrYceihg3rpgPOCAvOQEAHUnRCQAgtb6+iMHB8pqyEwAAAAA8t299K2K77Yr5u9+NuOaadHkAgDHXmzoAAAARUalEVKv5n0OyLGJgIKKnJ10uAAAAAGhFu+0WcccdxfzAAxEzZ6bLAwA0haITAECryLL8Wu3625x6eyMefDBi++2TxQIAAACAljL8NvRnnomYPDlNFgCgqby6DgCg1dRqEccdV8wzZ0acd166PAAAAADQKoaXnAYGlJwAoIsoOgEAtKJzzon41a+K+YMfjJg1K10eAAAAAEhpYKCx5FStRvT0pMkDACSh6AQA0Kpe85qIhQuL+cEHGw9zAAAAAKDT3XdfRF9fea1Wc1YGAF1I0QkAoJVNmxYxOFhec4ADAAAAQLc444yIHXYo5o9/PC85AQBdqTd1AAAAnkel0viEWpZFPPNMxOTJ6XIBAAAAwFga/sDfr38dsd9+SaIAAK3BjU4AAO2iVos45JBi7u+PuO22dHkAAAAAYKwMLzktWqTkBAAoOgEAtJUrrsifXBuyxx4RRx6ZLA4AAAAAjKpqtbHkVK1GTJ2aJg8A0FIUnQAA2s1++0X87W/FfNFFjYc/AAAAANBuFiyI6Okpr9Vqzr4AgP+j6AQA0I5e8IKIgYHymgMfAAAAANrV+edHbLNNMZ92Wl5yAgCo05s6AAAA66mnJ7+2u1LXXc+yiBUrIiZMSJcLAAAAANbF8Af47r034sUvTpMFAGhpbnQCAGhnWdb4ZNvEiRG//nWSOAAAAACwToaXnFatUnICAJ6VohMAQCeo1SI+97lifvWrI+bMSZcHAAAAAJ5LrdZYcqpWI8aNS5MHAGgLik4AAJ3iU5+KuO22Yv7pTxsPiwAAAAAgtXvuiagM+5lypOITAMAwik4AAJ1kt90iVqwor430ejsAAAAASOHYYyN23LGYP/QhZ1cAwFrrTR0AAIBRNmFCfs13/VNxlUrEggUR06enywUAAABAdxt+Y9N110Xsv3+SKABAe3KjEwBAJxq6xWmffYq1rbeOOPvsdJkAAAAA6E4jvZZu8WIlJwBgnSk6AQB0shtuiLj++mL++McbD5UAAAAAYKwsXly+eTwiv418443T5AEA2pqiEwBAp9t334hVq8prQzc+AQAAAMBYufDCiE02Keb99x/5dicAgLXUmzoAAABNMG5c4yFSpRKxaFHE1KnpcgEAAADQmYaXmW6/PeKVr0yTBQDoGG50AgDoJrVaxD/9UzFvsknEeeelywMAAABA5xleclq9WskJABgVik4AAN3mBz+IuPvuYv7gB10XDgAAAMCGW7y48ZypVovo60uTBwDoOIpOAADdaKedIlatKq9lWX7wBAAAAADr6n/+J789fMj/+3/OmgCAUdebOgAAAImMGxdRrUZU6rrvlUrEwoUR06alywUAAABAexl+i9PcuRGzZ6fJAgB0NDc6AQB0s6FbnF72smJtq60iPvrRdJkAAAAAaB/DS07PPKPkBACMGUUnAAAifve7iKuuKuavfKXxkAoAAAAAhsyb13h+VK1GTJ6cJA4A0B0UnQAAyM2ZE/Hkk+W1LMsPqAAAAABgyPvfHzFzZjFPn57fGu7BOQBgjCk6AQBQ2HTTxmJTT0/ETTelyQMAAABAa8myiG98o5gvuyxiwYJ0eQCArqLoBABAWZblT+B96EPF2j77RGy5ZbpMAAAAAKS1enXjjU1LlkQcdliaPABAV1J0AgBgZF/9asT8+cX8+OOuHwcAAADoRldeGTF+fHmtWo2YMiVNHgCgayk6AQDw7GbMaHyVXZZFPPpomjwAAAAANFeWRbzlLcV8/PH5beAeiAMAElB0AgDguQ29yu6VryzWttoq4thj02UCAAAAYGyNVGZ65JGIs89OkwcAIBSdAABYW7ffHnHXXcX81a96cg8AAACgE/3xjxGVYT8jVqsRW2+dJg8AwN8pOgEAsPZ22SViYKC8lmURK1akyQMAAADA6Npll4iddy7mo4/2qjoAoGX0pg4AAECb6elpPNyaNCniK1+J+Nd/TZcLAAAAgA0zvMz02GMRW2yRJgsAwAjc6AQAwPqp1SL++7+L+bjjPNkHAAAA0I7mz28816nVlJwAgJaj6AQAwPr78IcjHnqovJZlja+3AwAAAKA1HXBAxPbbF/NOO+UlJwCAFqToBADAhtl224hqtbzW1xdxySVp8gAAAACwdrIs4rrrinnu3Ii7706XBwDgeSg6AQCw4bIsf9LvuOOKtfe8x6vsAAAAAFrRww83ntssWxYxe3aaPAAAa0nRCQCA0XPOOREPPlhey7KINWvS5AEAAACgbK+9ImbMKK/VahGTJqXJAwCwDhSdAAAYXdtv3/gqu3HjvMoOAAAAIKVaLX8g7Te/KdYuuyxfBwBoE4pOAACMvqFX2Z13XrHmVXYAAAAAadxzT0Rl2M+CS5dGHHZYmjwAAOtJ0QkAgLFzzDERq1aV17IsYtmyNHkAAAAAus1mm0XsuGMxT5uWP6DW358uEwDAelJ0AgBgbI0b13gFen9/xKmnpskDAAAA0A2GXlX31FPF2p/+FLFwYbpMAAAbSNEJAIDmqNUifvjDYv7MZ7zKDgAAAGAsXHNN46vqqtWIl740TR4AgFGi6AQAQPMcfHDE8uXltSyL+Otf0+QBAAAA6DRZFvHa1xbzsccWtzsBALS53tQBAADoMhMnNh6ubb11xOzZEXPnpssFAAAA0M5WrYqYMKG8tmRJxJQpafIAAIwBNzoBAJBGrRbx7W8X829+k5efarV0mQAAAADa0SmnNJacajUlJwCg4yg6AQCQzjveEbFsWXmtUom4+uo0eQAAAADaTZZFfP7zxXz22R4kAwA6llfXAQCQ1qRJ+eHb5ptHPPlkvnbQQfmfDuUAAAAARvbAAxEvfGF57bHHIrbYIk0eAIAmcKMTAACt4YknIm6/vbyWZRFPP50mDwAAAECrGjeuseRUqyk5AQAdT9EJAIDW8cpXRlSr5bUpUyLe+c40eQAAAABayeBg/mDYmjXF2lVXuRUbAOgaik4AALSWLMsP5y66qFj7zneKdQAAAIBudO65Eb295bVVqyLmzEmTBwAgAUUnAABa0/veFzEwUF6rVCJ+8YskcQAAAACSybKI444r5pNOyh8IGzcuXSYAgAQUnQAAaF09Pfmh3eGHF2uvf31+uAcAAADQ6e65p/EcZNmyiNNOS5MHACAxRScAAFrfJZdErFhRXsuyiL/+NU0eAAAAgLGWZRE77ljMW2yRPxA2aVK6TAAAiSk6AQDQHiZMyA/z6m29tdudAAAAgM7y9NON5x2PPZb/BwDQ5RSdAABoL7VaxJ13lteyLGL16jR5AAAAAEbLQQdFTJlSXqvV8tucAABQdAIAoA3tumvEwEB5bfz4iLe/PU0eAAAAgA1RreYPcl19dbH2ve813m4NANDlFJ0AAGhPPT35Yd8ppxRr3/9+fijoEBAAAABoF2eckZ9z1Fu1KuJtb0uTBwCghSk6AQDQ3k49NWLRovJapRLx5S+nyQMAAACwNmq1/IGtk04q1vbfP18fNy5ZLACAVqboBABA+5s6NT8EnD27WDvhhPywEAAAAKDV/OAH+YNa9ebPj7juujR5AADaRG/qAAAAMGrmzo14+OGIGTOKtSyL+PGPI9785nS5AAAAAIaM9GBWrdb8HAAAbciNTgAAdJZtt80PB7feulh7y1vc7gQAAACkdfPNjecTt9+u5AQAsA7c6AQAQGd65JGIRYsiNt20WMuyiBtvjNh773S5AAAAgO4z0gNY1aoHswAA1pEbnQAA6FybbJI/FdnXV6zts49DRAAAAKA5/vCHxnOIO+/MzyucTwAArDM3OgEA0PlWr4548smIzTcv1rIs4rbbInbbLV0uAAAAoHONVGTymjoAgA3iRicAALrDZps1HibuvrunJwEAAIDRdffdjecN8+crOQEAjAJFJwAAukutll8bX2/odicAAACADZFlEbvsUl6r1SJmzEiTBwCgwyg6AQDQfXbeOWJwsLy2xx5udwIAAADWzx13NJ4r3H+/W5wAAEaZohMAAN2pUskPG3/xi/J6lkXceGOaTAAAAED7ybKI3XYrr9VqEbNmpckDANDBFJ0AAOhur3td4+1O++7rdicAAADguV1zTeP5wY03usUJAGAMKToBAMDQ7U433FBez7KIn/40TSYAAACgdWVZxGtfW16rViP23jtNHgCALqHoBAAAQ/bZJz+UrDdnTn546WlMAAAA4JJLGm9xuvba/NzA7dAAAGOuN3UAAABoKUOlpscei5g2rVivVCLOOy/imGPSZQMAAADSqNXys4HhqlUFJwCAJnKjEwAAjGTLLfNDzF12Kdb+5V/yw8vBwXS5AAAAgOb65CcbS0733ecWJwCABBSdAADgudx1V8TKleW13t6I970vSRwAAACgSVatyotMZ55ZrO2zT15wetGL0uUCAOhiik4AAPB8xo/PDzHf+95i7eKL88POZcvS5QIAAADGxs47R0yYUF5btSrihhvS5AEAICIUnQAAYO1985sRy5eX1/r7I8aNSxIHAAAAGGWPP54/2PTHPxZrX/xi/gCU/T8AQHKKTgAAsC4mTswPN48/vlhbsyY/BP3zn9PlAgAAADZMlkVsuWV5rVqN+PjH0+QBAKCBohMAAKyPs8+OWLGivPbSl+aHogAAAED7uO66xv38j36UP+hknw8A0FIUnQAAYH1NmJAfen796+X1LIu46KI0mQAAAIC1M1RkOuCA8vrgYMRb3pImEwAAz0nRCQAANtT7359fZV/vyCPzw9KBgTSZAAAAgGf3oQ9FVIb9THbDDXn5afg6AAAtozd1AAAA6AhZlh+G/ulPETvtVKz39UXsumvEnXemywYAAADkli2L6O9vXK9WvaYOAKANqKQDAMBo2nHHvPD0xjcWa7//fX5YOm9eslgAAADQ9bKsseT0178Wr7ADAKDlKToBAMBY+MlPGl9bN3Omg1MAAABothtuaNyPn3NOXnDaaqs0mQAAWC9eXQcAAGOlpyc/NL3rrvz1dUOyLOLzn484+eR02QAAAKDTVav53nykdQ8iAQC0JTc6AQDAWPuHf8gLTxttVKx96lP5oeqyZelyAQAAQKfad9/GktMTT3hNHQBAm1N0AgCAZnn66YhVq8pr/f0OWAEAAGC03Hdfvs++8cZi7T3vyQtOm22WLhcAAKNC0QkAAJpp3Lj8cPXCC8vrWRZxwQVpMgEAAEAnyLKIHXYor1WrERdfnCYPAACjTtEJAABSOOKIiIGB8trRR+eHsqtXp8kEAAAA7eg972m8LfnXv/aaOgCADtSbOgAAAHStnp780PX3v4942cuK9fHj8z9rtTS5AAAAoB3Mmxcxc2bjerWq4AQA0KHc6AQAAKntumteanrXu8rrWdb4ijsAAADodkM3NQ0vOT32mFucAAA6nKITAAC0iksvjVizprx21FH5Ae3SpWkyAQAAQCs59NCIyrCft846Ky84bbFFmkwAADSNV9cBAEAr6e3ND2cffDBi1qxi/QUvyP/0OjsAAAC60T33ROy4Y+O619QBAHQVNzoBAEArmjkzLzWde255PcsiPvvZNJkAAACg2QYH873w8JLTwoVeUwcA0IUUnQAAoJV95CONtzj9x3/kB7kLFiSJBAAAAE0xdWp+83G9K6/M98nTpqXJBABAUopOAADQDmq1iBUrymvbbJMXnrzODgAAgE5y5ZX5fnfJkmJt9ux8//umN6XLBQBAcr3P/78AAAAtYcKE/FD3qqsi3vzmYr1Sidhhh4g//zldNgAAANhQS5dGvOAFjeuDg/neFwCArudfhQAA0G7e9KaIarW8du+9+dOuP/1pmkwAAACwIbKsseT0xBP5Az9KTgAA/J1/GQIAQDsaemXdE0+U1+fMyb9bvjxNLgAAAFgXBx6Y72PrnXNOvufdbLM0mQAAaFleXQcAAO1ss83yw9+f/SzijW8s1idPzv+s1dLkAgAAgOdy3XURBxzQuF6tNhafAADg79zoBAAAneCgg/JS07veVV7Psvw7AAAAaAXLl+d71eElp4UL832tkhMAAM9B0QkAADrJpZdGDA6W166+Oj8ovvbaNJkAAABgqMQ0dAPxkMsvz7+bNi1NLgAA2oqiEwAAdJpKJT8kXrGivP6a1+SHykuWpMkFAABAd9p553yvWu+ww/K966GHpskEAEBb6k0dAAAAGCMTJuSHxg8/HDFjRrE+dWr+Z7XqlQAAAACMnUsvjTj88Mb1NWsiev1EBQDAunOjEwAAdLptt80LT9/4Rnm9UnGwDAAAwOibPz9/sGZ4yWn58nx/ai8KAMB6UnQCAIBucdRR+YFyf3+xNjiYHz5/5jPpcgEAANAZBgbyPeb225fXH3ss349OnJgkFgAAnUPRCQAAus3SpRErV5bXTj01P4z+zW/SZAIAAKC9ZVlEX1957eqr84LTFlukyQQAQMdRdAIAgG40fnx+2PyHP5TX99orP5xesiRNLgAAANrLTjvl+8h6hx6a7zlf//o0mQAA6FiKTgAA0M123jk/fP7618vrU6fmB9W1WppcAAAAtLYvfjHfN/7pT+X1ajXi8svTZAIAoOMpOgEAABHvf39eanrzm8vrlUrjk7kAAAB0rzvuyPeJJ55YXn/iiXxfaQ8JAMAYUnQCAAAKP/5x/vTtcFkW8fKXNz8PAAAArWHJknxvuNtu5fWbb84LTpttliYXAABdRdEJAAAoG3pl3erV5fU778y/+9zn0uQCAACg+QYG8r3g1Knl9UsvzfeOr3pVmlwAAHQlRScAAGBkfX35ofXKleX1T386P+T++c/T5AIAAGDsDb2Grq+vvP7pT+ffvetdaXIBANDVelMHAAAAWtz48fkh9ooVEZMmFetveEP+55//HLHDDmmyAQAAMPqyrHFtzpyIq65qfhYAAKjjRicAAGDtTJyYF54efbS8/pKX5IfgixalyQUAAMDomD175JJTrabkBABAS1B0AgAA1s2WW+aH3DfdVF7fdNP8QHz16jS5AAAAWD8f+1i+n7v55vJ6rZb/BwAALULRCQAAWD977ZUfeH/pS+X18ePzA3KH4QAAAK3ta1/L92/nnFNeX7PGng4AgJak6AQAAGyYE06IqFYj9t67vF6pjPzKAwAAANL68Y/z/dqHP1xeX7gwLzj19qbJBQAAz0PRCQAA2HBZFnHjjRGDgyN/p/AEAACQ3s035/uzgw8ur8+dmxecpk1LkwsAANaSohMAADB6KpX8cHxgoPE7hScAAIA07rkn34/Nnl1ev/jifA83fB0AAFqUohMAADD6enryw/LVqxu/U3gCAABojoceyvdfO+5YXj/zzHzP9p73pMkFAADrSdEJAAAYO319+eH5s73Srq+v+ZkAAAA63cKF+Z5ru+3K65/+dL5H+8Qn0uQCAIANpOgEAACMvaFX2lWr5fWBgfzwfbPN0uQCAADoJI8/nu+xpk8vr596ar4n++xn0+QCAIBRougEAAA0T5blh+sDA+X1p57Kv9t66zS5AAAA2tkTT+R7qi23LK//53/me7BTTkmTCwAARpmiEwAA0Hw9Pflh+/Ll5fW//nXkp48BAABoNFRw2mKL8vq55+Z7ro9+NE0uAAAYI4pOAABAOhMn5ofvjz1WXl+4cOTDegAAACIefXTkPdPZZ+d7rI98JE0uAAAYY4pOAABAeltskR/Gz5tXXh96OnnSpCSxAAAAWsrDD+d7pK22Kq+fckq+pzr++DS5AACgSRSdAACA1rHddiMXnlasyA/zsyyOnoKFAAAgAElEQVRJLAAAgKTuvTffD82YUV4/+uh8D3XqqWlyAQBAkyk6AQAArWeo8PToo43fKTwBAADd4vbb8/3PS15SXj/yyHzPdP75aXIBAEAiik4AAEDr2nLL/PB+5crG74YKT7Va83MBAACMpV/8It/v7L57ef344/M90AUXpMkFAACJKToBAACtb/z4/DC/Wm38rlLJfwAYHGx+LgAAgNF08cX5/ub1ry+vf+Ur+Z7o7LPT5AIAgBbRmzoAAADAWhu6walWywtO9Xr/vr1ZuTIvRgEAALSLk0+OOP30xvVrr4149aubnwcAAFqUohMAANB+nqvwNGFC/ufixREbb9z8bAAAAGvrNa/Jy0zD/eUvES98YfPzAABAi1N0AgAA2tdQ4alajejpKX83dWr+5733Rrz4xc3PBgAA8GyybOT1J5+M2HTT5mYBAIA2Unn+/wUAAKDFVSpF4Wn77cvf7bBD/iPC1VcniQYAABAR+Z4ly0YuOS1Zkn+v5AQAAM9J0QkAAOgcWRbx4IN54emQQ8rfHXRQ/v2ZZ6bJBgAAdKeBgXwvMvy12xERTz2VF5ymTGl+LgAAaEOKTgAAQOfJsogrrsh/MDjttPJ3n/xk/v3ee6fJBgAAdIcnn8z3Hn19jd8tXZrvVzbZpPm5AACgjSk6AQAAne2kk/IfEK67rrw+d27x2ohaLU02AACg89xyS77P2Hzzxu9Wr873H/39zc8FAAAdQNEJAADoDvvvn/+gsHhx43eVSv5DxMqVTY8FAAB0iC98Id9X7Llnef3d744YHMz3IyPd7gQAAKy13tQBAAAAmmrjjfMfGGq1vOBUb+LE/M8HHoiYObP52QAAgPazzTYRCxY0rv/sZxFveEPz8wAAQAdzoxMAANCdhl5ZV6tF7LVX+btZs/Lvv/71NNkAAIDWNjhYvAp7eMnp8cfzfYaSEwAAjDpFJwAAgJtuyn+IOPfc8voxx+Q/XGy3XZpcAABAa1m4MN8j9I7wwow1a/J9xeabNz8XAAB0CUUnAACAIR/5SP7DxM9/Xl5/6KHiae1qNU02AAAgnf/933w/MH1643eDg/k+YqTyEwAAMKoUnQAAAIY78MD8h4o//rHxu56e/AeOBx9sfi4AAKC5XvGK/N//7353ef2Vr8wfgqjVIip+agEAgGb5/+zde5RlVX0n8O+u6m4aunkjiggokZeAj9AqURF1HAR1KbJCEKIjIT7GPNRxdAZfkYkoJktjIis6cUaF+ECdKDKOihqUKGrURhQRRMThbRRbkKabbrqr9vxxbs+tom49uqrurVNdn89atTj37n3v/tUC7j6n9vfu4+wbAABgMkcc0SxcrF8/se3gg5sFj3e9a/B1AQAA/bNlS3dH16uuGt923nnNNcLatU07AAAwUIJOAAAA01m9ulnMGB1NXvKS8W2vf313EaTWhakPAACYu+uua87rV6yY2Pbd7zbn+2efPfi6AACA/0/QCQAAYKZKSS64oFng+OEPJ7YPDTV9fvObgZcGAADM0qte1ZzHP+pRE9vuuac5/3/84wdfFwAAMIGgEwAAwGw8+tHNgsfWrRPb9t67WSj58IcHXxcAADC9kZHuzqznnz++7VWvanZzrTXZddeFqQ8AAOhJ0AkAAGAuhoebBZBakxNOGN921lluawcAAG1yzTXN+fmyZRPbbrqpOW//u79r+gAAAK0j6AQAADBfvvSlZmHk4osntm27rd2ddw6+LgAAWOpOOqk5Hz/66Ilt23ZvOuigwdcFAABsF0EnAACA+Xbyyc1CyU9+MrFt332bBZY3v3nwdQEAwFKyeXN3h9VLLx3f9o53dHdmtXsTAAAsGoJOAAAA/XLYYc3CyebNyR57jG97+9u7iy4jIwtTHwAA7IguvLA5z165cmLbD37QnKO/4Q2DrwsAAJgzQScAAIB+W7EiueuuZkHlU5+a2L5sWbMQc8UVg68NAAB2BNt2ZiolOfPMie333tv0ecxjBl4aAAAwfwSdAAAABunUU5sFlk2bJrYdd1x3cabWwdcGAACLzZVXNufPQz2WO972tu7t6VatGnxtAADAvFu20AUAAAAsSTvt1A0zffzjyR/+4fj2bQs111+fHHroYGsDAIC2W7Uq2bixd9uttyYPe9hg6wEAAAbCjk4AAAAL7YwzmtDThg0T2w47rPmG+iMfOfi6AACgTa6/vrsD6gNDTm9/e3f3JiEnAADYYdnRCQAAoC122aW7OPPCFyaf+lS37cYbmwWdJPnpT5NDDlmYGgEAYNAe8pDkl7/s3XbvvW5LBwAAS4gdnQAAANqmlOSTn2wCT1//+sT2Qw9t+hx00OBrAwCAQfjJT7q7Nz0w5PQnf9L9goCQEwAALCl2dAIAAGiz445rFnDuvz/Zffdk06Zu2y23dHd5+v73k8c9bmFqBACA+VBrMjTF97Ovv74J/QMAAEuWHZ0AAAAWgxUrkvvuaxZ/vvrVie2/+7vdb7yPjg6+PgAAmK0rrmjOY3uFnNasSUZGmvNgIScAAFjyBJ0AAAAWm6c/vVnoGR1tjh9oeLhZKPqnfxp8bQAAMBNbtnSD+scdN7F97drmnPd735t6lycAAGBJcXUAAACwWJXS7O5Ua3LPPRPbTz21u3i0YcPg6wMAgAf6679uzk9XrJjYdvbZ3d2bjjlm8LUBAACtt2yhCwAAAGAe7LprsyCUJJdempx00vj21aubf65Z03wrHgAABuW225IDDpi8/b77kpUrB1cPAACwaNnRCQAAYEdz4olN6GlkZGLb2rXdXZ6+8pXB1wYAwNJQa/e8s1fI6aqrmj61CjkBAAAzJugEAACwoxoa6i4erV07sf2EE7qLTxs3Dr4+AAB2PO98Z3N+OdRj+eHww5PR0eb89LGPHXxtAADAoifoBAAAsBQcc0yzoLRlS3LyyRPbV61qFqQe9KDB1wYAwOJ2ww3dAP0b3jCx/dprm3PR665r+gAAAMySoBMAAMBSsmxZcvHFzULT7bdPbP/1r7uLVOefP/j6AABYHDZv7p43HnroxPZXvrK7e9MRRwy+PgAAYIck6AQAALBUPfSh3Vvbfe97E9tf9aru4tWPfjT4+gAAaJdakyc8oTk/XLmyd5/165t+73uf3ZsAAIB5J+gEAABAsmZNN/T0yU9ObH/0o7uhp/XrB18fAAAL5/zzm/PAoaHeAfkf/7h7Lrl69eDrAwAAlgxBJwAAAMb7gz9oFqlGR5PnP39i+267dUNPo6ODrw8AgP674oruOd+rXjWxfe3abrjpUY8afH0AAMCSJOgEAABAb6Ukn/1ss3j129/27jM83PQ79tjB1gYAwPy75ZZuuOm44ya2f/rT3XDTMccMvj4AAGDJE3QCAABgervt1l3Uuuyyie3f+U53UexNbxp8fQAAzM769d3zuIMOmtj+kpd0zwNPOWXw9QEAAIwh6AQAAMD2ecYzure2e897Jra/4x3dxbKPfnTw9QEAMLVNm7rna7vt1rvPvfc253wXXDDQ0gAAAKYi6AQAAMDslJK85jXNAtjISHLOORP7vPjF3UW0r3xl4CUCANCxZUv3vGznnXv3ue667u5Nq1YNtj4AAIAZEHQCAABg7oaGkre+tbswdu65E/uccEJ3ce0b3xh8jQAAS83ISPf8a8WK3n2++c3uOdzhhw+2PgAAgO0k6AQAAMD8e9Obugtmf/ZnE9uf+tTuotvllw+8PACAHdboaPc8a9my3n2uuaZ7rvakJw22PgAAgDkQdAIAAKC/zj+/WUTbujV5ylMmtj/96d3FuC98YfD1AQAsdmPDTcPDvfvcfns33HTkkYOtDwAAYJ4IOgEAADAYw8PNLetqTX7zm+Z2dw/0nOd0F+kuumjwNQIALBZjb0s3Wbjp5z/vhpse+tDB1gcAANAHgk4AAAAM3p57NotztSbr1vXuc8YZ3cW7v/mbwdYHANBGGzZMf1u6K67ohpse8YjB1gcAANBngk4AAAAsrL326i7GbdyYPOQhE/v85//cXdQ744ymLwDAUnDbbd3zoNWre/f5/Oe751NPfvJg6wMAABggQScAAADaY+edk1/8olmk27o1ecUrJva56KLmtnfbFvy2bh18nQAA/fTNb3bPdQ44oHefb3+7G2569rMHWx8AAMACEXQCAACgnYaHk//+37sLeF/8Yu9+y5d3FwLvvnuwNQIAzJdzz+2e0zzlKb373HVX99zo2GMHWx8AAEALCDoBAACwOJx4Yndh74YbevfZc8/uAuFXvjLY+gAAtketyd57d89d3vKWiX2OPz4ZHe2eA+2xx+DrBAAAaBFBJwAAABafRz6yu+B3/fW9+5xwQnfh8JRTBlsfAEAvv/hF9/xkaCj5zW8m9jn77G646fLLm74AAAAkEXQCAABgsTv00G7o6ZZbeve5+OLuoqJb3AEAg/ShD3XPQR760N59/vqvu+Gm884TbgIAAJiEoBMAAAA7jgMO6Iae7r8/efGLe/cbe4u7iy8ebI0AwI5t8+Zk5cruucYf/3Hvfl/8Yve85fWvF24CAACYAUEnAAAAdkzLlyf/+I/dBcRrrund75RTuguRy5YlW7cOtk4AYPH79re75xMrVzZhp17uuKN7bnLiiYOtEQAAYAcg6AQAAMDScOSR3YXFkZHk6KMn9hkZaQJS2xYqL7984GUCAIvA6Giy//7dc4YnPal3v499rDm/2HYOst9+g60TAABgByPoBAAAwNIzNJRcfXWz4Dg6mlx4Ye9+T396dwGzlGahEgBYmr785e45wfBwsztTL/fd1w02nXFGc94BAADAvHCFBQAAwNJWSvIf/kN3QfI735m877Jl3QXOiy4aXI0AwOBt3Dg+8PysZ/Xu98EPds8jam1uXQcAAEBfCDoBAADAWE94Qneh8v77kz//8979zjhj/OLnv/3bYOsEAOZXrcnrXted21etmrzvD37QPV8466zB1QgAALDECToBAADAZJYvT9773u5C5l13JatX9+67337dhdE1a5KtWwdbKwCw/b7xje78PTSUvPvdvfv91/+abN7cPSd4zGMGWycAAABJBJ0AAABg5vbYI1m/vrvI+ZOf9O535ZVNSGrbwum55w62TgCgtzvvHL8j41Of2rvfk5/c9N0257/zncmKFYOtFQAAgAkEnQAAAGC2DjusuwC6ZUvy6lf37veWt4xfVP3c5wZbJwAsVVu3jp+D99138r7r1nXn9SuuSPbZZ3B1AgAAMCOCTgAAADAfli1L/vZvuwukV189ed/nPW/8ouvatYOrEwB2ZCMjzS1kt82xy5dP3vcrX+nO27Ume+01uDoBAACYFUEnAAAA6Iejjx6/ePqZz0ze9/GPHx98uuaawdUJAIvZyEjy+7/fnUOXLWtuIdvLi16U3Htvd25+5jMHWysAAABzJugEAAAAg/CCF3QXVkdHp7593dFHjw8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      "text/plain": [
       "<Figure size 2880x2880 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# %load course_materials/ODE.py\n",
    "#python>=3.7.2\n",
    "#this program calculates and plots the orbits of 2 point sources interacting only gravitationally, integrating the equation of motion with the scipy package \"odeint\"\n",
    "\n",
    "\n",
    "#modules needed\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import numpy as np\n",
    "from scipy.integrate import odeint\n",
    "\n",
    "\n",
    "#define the differential system d(r_i,v_i)/dt\n",
    "def dAdt(data,t):\n",
    "\t\n",
    "\td12=np.linalg.norm([data[1]-data[0],data[2]-data[3]])\n",
    "\t\n",
    "\tdatadot=np.zeros(len(data)) \n",
    "\t\n",
    "\tdatadot[0]=data[4]\n",
    "\tdatadot[1]=data[6]\n",
    "\n",
    "\tdatadot[2]=data[5]\n",
    "\tdatadot[3]=data[7]\n",
    "\n",
    "\tdatadot[4]=-G*m[1]*(data[0]-data[1])/((d12+eps)**3) \n",
    "\tdatadot[5]=-G*m[1]*(data[2]-data[3])/((d12+eps)**3) \n",
    "\n",
    "\tdatadot[6]=-G*m[0]*(data[1]-data[0])/((d12+eps)**3) \n",
    "\tdatadot[7]=-G*m[0]*(data[3]-data[2])/((d12+eps)**3) \n",
    "\t\t\n",
    "\t\t\n",
    "\t\n",
    "\treturn datadot \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "#changing units of measurement (A.U.=1, year=1, Msun=1)\n",
    "Kg=1./(1.988E+30)\n",
    "m=1./(1.496E11)\n",
    "s=1./(3.153E+07)\n",
    "G=(6.674E-11)*(m**3)*(Kg**-1)*(s**-2)\n",
    "\n",
    "\n",
    "\n",
    "#generate random initial positions and velocities for the 2 bodies\n",
    "x1=1 \n",
    "y1=0 \n",
    "\n",
    "x2=0 \n",
    "y2=0 \n",
    "\n",
    "vx1= 0 \n",
    "vy1= 0 \n",
    "\n",
    "\n",
    "\n",
    "vx2= 2*np.pi #np.random.uniform(-2.,2.,1)[0]*3.14\n",
    "vy2= 0 #np.random.uniform(-2.,2.,1)[0]*3.14\n",
    "\n",
    "\n",
    "\n",
    "#masses (in solar unit)\n",
    "m=[1e-6,1.]\n",
    "\n",
    "\n",
    "#store all the data in a single list\n",
    "data0=[x1,x2,y1,y2,vx1,vx2,vy1,vy2] #[x],[y],[vx],[vy]\n",
    "\n",
    "#softening parameter (to avoid divergent forces)\n",
    "eps=1.E-10 \n",
    "\n",
    "#time vector\n",
    "t=np.linspace(0,10,1000)  \n",
    "\n",
    "#solution from odeint as a datacube\n",
    "sol=odeint(dAdt,data0,t)  \n",
    "\n",
    "#set general fontsize\n",
    "plt.rc('font',size=30)\n",
    "\n",
    "#create the figure\n",
    "fig=plt.figure(1,figsize=(40,40))\n",
    "#add axis\n",
    "ax=fig.add_subplot(111)\n",
    "\n",
    "#plot initial positions \n",
    "ax.scatter(sol[0,1],sol[0,3],marker='s',s=40)\n",
    "ax.scatter(sol[0,0],sol[0,2],marker='s',s=40)\n",
    "\n",
    "#plot the orbits\n",
    "ax.plot(sol[:,1],sol[:,3],color='blue',label=r'$log\\ M/M_{\\odot}\\ :\\ %.1f\\ $'%(math.log10(m[1])))\n",
    "ax.plot(sol[:,0],sol[:,2],color='red',label=r'$log\\ M/M_{\\odot}\\ :\\ %.1f\\ $'%(math.log10(m[0])))\n",
    "plt.legend()\n",
    "\n",
    "ax.set_xlabel('x [A.U.]')\n",
    "ax.set_ylabel('y [A.U.]')\n",
    "ax.set_title('2 BODY INTERACTION')\n",
    "#save the figure\n",
    "#plt.savefig('2body.png')\n",
    "\n",
    "plt.xlim(-1.2,1.2)\n",
    "plt.ylim(-1.2,1.2)\n",
    "#plt.xlim(-2e-4, 2e-4)\n",
    "#plt.ylim(-2e-4, 2e-4)\n",
    "#show on screen\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python",
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   "nbconvert_exporter": "python",
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