physics/gravitational_field_earth.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"Gravitational field strength vs range (Earth).\"\"\"\n",
    "\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "IN_STEPS = 20\n",
    "OUT_STEP = 0.25\n",
    "OUT_COUNT = 40\n",
    "G = 6.67 * 10e-11\n",
    "M = 5.97 * 10e24\n",
    "R = 6.38 * 10e6\n",
    "\n",
    "density = M / ((4/3) * math.pi * R**3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "inside_x = []\n",
    "inside_y = []\n",
    "for i in range(IN_STEPS):\n",
    "    r = R * i / IN_STEPS\n",
    "    g = (4/3) * math.pi * G * r * density\n",
    "    inside_x.append(r)\n",
    "    inside_y.append(g)\n",
    "\n",
    "outside_x = []\n",
    "outside_y = []\n",
    "for i in range(OUT_COUNT):\n",
    "    r = R * (1 + i*OUT_STEP)\n",
    "    g = G * M / r**2\n",
    "    outside_x.append(r)\n",
    "    outside_y.append(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9OQCAtJDWQee9997TnDlzdOGFF+rZZ5/VqFGjtGvXLp122mlml2YtWXap+HyzqwAAIGZpHXTuuOMOFRUVqba2tvdacXGxiRUBAIBUktZzdDZs2KDp06friiuuUH5+vqZOnao1a9ac8DXd3d3q6OgI+0lHgaChbbvf1TPN+7Vt97vxO8ATAAALSesenb/+9a+qqanRqlWrdMstt2j79u264YYbNHz4cC1ZsqTf16xevVrV1dVJrjS+Glp8qq73hB3s6XI6VFXhHvr+OQAAWIjNMIy07QoYPny4pk+frq1bPz6G4IYbbtD27du1bdu2fl/T3d2t7u7u3scdHR0qKiqS3+9Xbm5uwmseqoYWnyrrmvrsbNOzc05cNgsEACDFdXR0yOl0Dvj9ndZDVy6XS263O+zapz/9ae3duzfia7Kzs5Wbmxv2ky4CQUPV9Z4THbOp6noPw1gAAPxDXILOhx9+qH379umNN95Qe3t7PG4ZlTlz5uiNN94Iu/bmm29q3LhxSashmRq97WHDVcczJPn8XWr0Ju/fAQAAqWzQQaezs1M1NTX63Oc+p9zcXI0fP16f/vSnNWrUKI0bN07XX3+9tm/fHs9a+/jGN76hP/zhD/rRj36kt956S4899pgeeughLVu2LKHva5a2zsghZzDtAACwukEFnbvvvlvjx49XbW2t5s6dq/Xr16u5uVlvvvmmtm3bpqqqKn300Ue65JJLVF5erl27dsW7bknSjBkztG7dOj3++OMqKSnR97//fd1zzz1atGhRQt7PbPk5joEbxdAOAACrG9Rk5GuuuUbf+973NGnSpBO26+7uVm1trYYPH67rrrtu0EUmUrSTmVJBIGjovDt+p1Z/V6RjNlXgdOjlGy+Kz8GeAACkqGi/v9N61VU8pFPQkT5edSX1e8wmq64AABkh6auuXnnllXjdCidQXuJSzeJSFTjDh6cKnA5CDgAAx4lbj87YsWNPuKw7VaVbj06PQNBQo7ddbZ1dys9xqKw4j+EqAEDGiPb7O6adka+88sp+rxuGkdRl5ZDsWTbNmjDS7DIAAEhpMQWdF154Qb/61a80YsSIsOuGYeill16Ka2EAAABDFVPQueCCC5STk6PPfvazfZ6bPHly3IoCAACIB1ZdpekcHQAAMllSVl21trYO5eUAAAAJNaSgc8kll8SrDgAAgLiLaY7O8TJ81MsULCsHACB6Qwo6NhtfsMnU0OJTdb0n7ARzl9Ohqgo3GwUCANCPuO2MjMTqOfrh2JAjSa3+LlXWNamhxWdSZQAApC6CThoIBA1V13v6Pciz51p1vUeBIEOJAAAca0hBx263x6sOnECjt71PT86xDEk+f5cavexODQDAsYYUdF577bV41YETaOuMHHIG0w4AgEzB0FUayM9xDNwohnYAAGSKIQcdj8ejYDAYj1oQQVlxnlxOhyKtcbMptPqqrDgvmWUBAJDyhrS8XJJKSkrkcDjkdrs1ZcqUsJ9TTz01DiXCnmVTVYVblXVNsklhk5J7wk9VhZv9dAAAOM6Qe3Q2b96s3NxcjRkzRp2dnVqzZo0uvPBCjRw5UmeffbZuvfVWHTp0KA6lZrbyEpdqFpeqwBk+PFXgdKhmcSn76AAA0I8hH+pZWlqqW2+9VV/4whd6r23atElf+9rXtGTJEr3wwgvau3evGhsbNWrUqCEXHG/pdqgnOyMDABD99/eQg84nPvEJNTc366yzzgq7Xl9fr4cffli//vWvdeWVV+rUU0/VmjVrhvJWCZFuQQcAACTp9HJJmjZtmh599NE+10tKSvTcc8/JZrPp29/+tl544YWhvhUAAEBMhhx0fvzjH+vuu+/Wv/zLv+j111+XJB09elQ/+clPlJcXWgU0atQoHTx4cKhvBQAAEJMhr7qaOXOmtm3bphUrVsjtdis7O1sfffSRhg0bptraWkmhjQULCwuHXCwAAEAshhx02traVFJSok2bNmnv3r1qbm6W3W7XtGnTVFBQICnUo3P77bcPuVgAAIBYDHky8mc/+1m9+OKL/Z571dOzk8qYjAwAQPpJ2mTkU089VTfccEOf6++++67mzp071NvjHwJBQ9t2v6tnmvdr2+53OakcAIAoDLm75ZFHHlFZWZl+8Ytf6LrrrpMk/eUvf9E//dM/aeLEiUMuEFJDi0/V9Z6wE8xdToeqKtxsFAgAwAnEpUfn6aef1re//W01NjZq48aNmjVrlhYuXKj6+vp41JjRGlp8qqxrCgs5ktTq71JlXZMaWnwmVQYAQOobVI/OF7/4RZ177rm9P+ecc47uv/9+ff7zn1dXV5fuu+8+LV26NN61ZpxA0FB1vUf9DVIZCp1zVV3v0Tx3AbsjAwDQj0EFnQkTJmjLli26//779c477+i0007TlClTZBiGvvzlL6u0tFQffvihTjrppHjXm1Eave19enKOZUjy+bvU6G3XrAkjk1cYAABpYlBB56677ur95/3796u5uVnNzc0aOXKkXnzxRf385z/XsGHDNHHiRP3xj3+MW7GZpq0zcsgZTDsAADLNkCcjjxkzRmPGjNGCBQt6rx0+fFjNzc2EnCHKz3EM3CiGdgAAZJqEbHIzYsQInXfeeTrvvPMScfuMUVacJ5fToVZ/V7/zdGySCpyhE8wBAEBfQ151hcSxZ9lUVeGWFAo1x+p5XFXhZiIyAAAREHRSXHmJSzWLS1XgDB+eKnA6VLO4lH10AAA4gdQ+nwGSQmFnnrtAjd52tXV2KT8nNFxFTw4AACcWt6Aze/Zs7d69WwcPHozXLXEMe5aNJeQAAMQobkHnqquu0jvvvBOv2wEAAAxZ3ILOihUr4nUrAACAuGAyMgAAsCyCDgAAsCyCDgAAsKxBz9EZM2aMpk2bpmnTpqm0tFSlpaUaM2ZMPGuDQieYs6wcAIDBsRmG0d/pAgO677771NTUpKamJv3lL39RIBDQqFGjVFpaGhZ+xo0bF++a46qjo0NOp1N+v1+5ublmlxOmocWn6npP2AnmLqdDVRVuNgoEAGS0aL+/Bx10jtXd3a3m5ube4NPU1CSPx6MPP/xQH3300VBvn1CpGnQaWnyqrGvqc8ZVT19Oyu6KHAxIe7ZKhw9KI0ZL42ZLWXazqwIAWEy0399xWV6enZ2tmTNnqrS0VBs3btSHH34or9er4cOHx+P2GScQNFRd7+n3IE9DobBTXe/RPHdBag1jeTZIDTdKHQc+vpZbKJXfIbkvM68uAEDGGvJk5K6uLq1bt06LFi3SqFGjtHTpUtntdv3qV7/S22+/HY8aM06jtz1suOp4hiSfv0uN3vbkFTUQzwZp7bXhIUeSOnyh654N5tQFAMhog+7RefLJJ/X000/r2WefVU5Ojr7whS/o6aef1gUXXCC7naGKoWjrjBxyBtMu4YKBUE/OifqgGm6SJi5gGAsAkFSDDjrXXHONCgsLddddd+mrX/2qhg3jfNB4yc9xDNwohnYJt2dr356cMIbUsT/Urvj8pJUFAMCgh67OP/98dXZ26utf/7qcTqdmzZqlZcuW6Re/+IWam5tTfhJyKisrzpPL6VCk2Tc2hVZflRXnJbOsyA5HeZBrtO0AAIiTQXfDbN68WZK0a9cu7dixo3e11eOPP65Dhw4pOztb55xzjhobG+NWbKawZ9lUVeFWZV2TbAofEOoJP1UV7tSZiDxidHzbAQAQJ0MebzrzzDN15pln6uqrr+695vV69eqrr+q1114b6u0zVnmJSzWLS/vso1OQivvojJsdWl3V4VP/83RsoefHzU52ZQCADDeofXT27t2rsWPHRt1+//79Kbtrcqruo9MjbXZG7ll1JanfPqgrH2GJOQAgbqL9/h7UHJ0ZM2boa1/7mrZv3x6xjd/v15o1a1RSUqKnn356MG8DhYaxZk0YqcvPHaNZE0amZsiRQiHmykek3ON6mnILCTkAANMMaujK4/Hohz/8oebNmyeHw6Fp06apsLBQDodD7733njwej/785z+rtLRUd955pz7/+c/Hu26kIvdloSXk7IwMAEgRQzoC4oMPPtBvf/tbvfzyy9qzZ48++OADnX766Zo6daouvfRSlZSUxLPWhEj1oSsAANBXUs+6SmcEHQAA0k9C5+ikqttvv102m00rV640uxQAAJACLBN0tm/frp/97GeaPHmy2aUAAIAUMeSg4/F4FAwG41HLoB0+fFiLFi3SmjVrdNppp5laS7wEgoa27X5XzzTv17bd7yoQzOgRRgAABmXIGwaWlJTI4XDI7XZrypQpYT+nnnpqHEoc2LJly7RgwQLNnTtXP/jBD07Ytru7W93d3b2POzo6El1ezBpafH02CnSl4kaBAACkuCH36GzevFm5ubkaM2aMOjs7tWbNGl144YUaOXKkzj77bN166606dOhQHErt3xNPPKGmpiatXr06qvarV6+W0+ns/SkqKkpYbYPR0OJTZV1TWMiRpFZ/lyrrmtTQ4jOpMgAA0s+Qg86KFStUU1OjZ555RmvXrtXOnTv1/PPPq7i4WIsXL9ZLL72kqVOn6u23345HvWH27dunFStW6NFHH5XDEd1J3jfffLP8fn/vz759++Je12AFgoaq6z39HqLQc6263sMwFgAAURpy0Hn99dc1adKksGsXX3yxfvKTn+iPf/yjfv/732v69Om65ZZbhvpWfezYsUNtbW0qLS3VsGHDNGzYMG3evFn33nuvhg0bpkAg0Oc12dnZys3NDftJFY3e9j49OccyJPn8XWr0tievKAAA0tiQg860adP06KOP9rleUlKi5557TjabTd/+9rf1wgsvDPWt+rj44ou1c+dONTc39/5Mnz5dixYtUnNzs+z29NqRt60zcsgZTDsAADLdkCcj//jHP9bcuXP117/+Vd/97nc1ceJEHT16VD/5yU+Ul5cnSRo1apQOHjw45GKPl5OT02f35VNOOUUjR45Mi12Zj5efE93wW7TtAADIdEMOOjNnztS2bdu0YsUKud1uZWdn66OPPtKwYcNUW1srSXrttddUWFg45GKtrqw4Ty6nQ63+rn7n6dgkFThDJ5gDAICBxfUIiL179/YOGU2bNk0FBQWSpC1btujgwYP60pe+FK+3iptUOwKiZ9WVpLCw03Nmec3iUpaYAwAyHmddRSnVgo7EPjoAAAwk2u/vIQ9dIf7KS1ya5y5Qo7ddbZ1dys8JDVfZs2wDvxgAAPQi6KQoe5ZNsyaMNLsMAADSmmUO9QQAADgeQQcAAFgWQQcAAFgWQQcAAFgWk5FTTCBosNoKAIA4IeikEPbPAQAgvhi6ShE9OyIff3p5q79LlXVNamjxmVQZAADpi6CTAgJBQ9X1nn7Pt+q5Vl3vUSCY0ZtYAwAQM4JOCmj0tvfpyTmWIcnn71Kjtz15RQEAYAEEnRTQ1hk55AymHQAACCHopID8HEdc2wEAgBCCTgooK86Ty+lQpEXkNoVWX5UV5yWzLAAA0h5BJwXYs2yqqnBLUp+w0/O4qsJtrf10ggHJu0Xa+VTo12DA7IoAABbEPjoporzEpZrFpX320Smw4j46ng1Sw41Sx4GPr+UWSuV3SO7LzKsLAGA5NsMwMnrNckdHh5xOp/x+v3Jzc80ux/o7I3s2SGuvlfospv/H7/HKRwg7AIABRfv9TY9OirFn2TRrwkizy0iMYCDUkxNxxyCb1HCTNHGBlGVPcnEAACtijg6SZ8/W8OGqPgypY3+oHQAAcUDQQfIcPhjfdgAADICgg+QZMTq+7QAAGABBB8kzbnZoddWJdgzKHRNqBwBAHBB0kDxZ9tASckkRdwwqv52JyACAuCHopIhA0NC23e/qmeb92rb7XeueVO6+LLSEPPe4fYFyC1laDgCIO5aXp4CGFl+fjQJdVtwosIf7stAS8j1bQxOPR4wODVfRkwMAiDM2DDR5w8CGFp8q65oibZ+nmsWl1gw7AAAMQbTf3wxdmSgQNFRd74m4fZ4kVdd7rDuMBQBAghF0TNTobQ8brjqeIcnn71Kjtz15RQEAYCEEHRO1dUYOOYNpBwAAwhF0TJSf44hrOwAAEI6gY6Ky4jy5nI4TbZ8nlzN0gjkAAIgdQcdE9iybqirckiJun6eqCrfsWZGiEAAAOBGCjsnKS1yqWVyqAmf48FSB08HScgAAhogNA1NAeYlL89wFavS2q62zS/k5oeEqenIAABgagk6KsGfZNGvCSLPLAADAUhi6AgAAlkXQAQAAlkXQAQAAlkXQAQAAlkXQAQAAlsWqK5MFggbLygcSDEh7tkqHD0ojRkvjZktZdrOrAgCkAYKOiRpafKqu94SdYO5yOlRV4WajwB6eDVLDjVLHgY+v5RZK5XdI7svMqwsAkBYYujJJQ4tPlXVNYSFHklr9Xaqsa1JDi8+kylKIZ4O09trwkCNJHb7Qdc8Gc+oCAKQNgo4JAkFD1fUeGf0813Otut6jQLC/FhkiGAj15JzoU2q4KdQOAIAICDomaPS29+nJOZYhyefvUqO3PXlFpZo9W/v25IQxpI79oXYAAERA0DFBW2fkkDOYdpZ0+GB82wEAMhJBxwT5OY6BG8XQzpJGjI5vOwBARiLomKCsOE8up0ORFpHbFFp9VVacl8yyUsu42aHVVSf6lHLHhNoBABABQccE9iybqirckvp+jfc8rqpwZ/Z+Oln20BJySRE/pfLb2U8HAHBCBB2TlJe4VLO4VAXO8OGpAqdDNYtL2UdHCu2Tc+UjUu5xn0VuYeg6++gAAAZgMwwjg9cwSx0dHXI6nfL7/crNzU36+7MzchTYGRkAcJxov7/ZGdlk9iybZk0YaXYZqS3LLhWfb3YVAIA0xNAVAACwLIIOAACwLIIOAACwLIIOAACwLIIOAACwrLQOOqtXr9aMGTOUk5Oj/Px8LVy4UG+88YbZZQ0oEDS0bfe7eqZ5v7btfjezTykHACCB0np5+ebNm7Vs2TLNmDFDH330kW655RZdcskl8ng8OuWUU8wur18NLT5V13vCTi93OR2qqnCzSeBQsd8OAOA4ltow8O2331Z+fr42b96sz372s/226e7uVnd3d+/jjo4OFRUVJWXDwIYWnyrrmnT8B96zPSA7Ig+BZ4PUcKPUceDja7mFoWMk2EEZACwn2g0D03ro6nh+v1+SlJcX+TDM1atXy+l09v4UFRUlpbZA0FB1vadPyJHUe6263sMw1mB4Nkhrrw0POZLU4Qtd92wwpy4AgOksE3SCwaBWrlypOXPmqKSkJGK7m2++WX6/v/dn3759Samv0dseNlx1PEOSz9+lRm97UuqxjGAg1JNzogjZcFOoHQAg46T1HJ1jLVu2TC0tLXr55ZdP2C47O1vZ2dlJqupjbZ2RQ85g2uEf9mzt25MTxpA69ofacYwEAGQcSwSd5cuX6ze/+Y1eeuklnXHGGWaX06/8HMfAjWJoh384fDC+7QAAlpLWQ1eGYWj58uVat26dfve736m4uNjskiIqK86Ty+lQpHPJbQqtviorjjy/CP0YMTq+7QAAlpLWQWfZsmWqq6vTY489ppycHLW2tqq1tVUffPCB2aX1Yc+yqarCLUl9wk7P46oKt+xZkaIQ+jVudmh11YkiZO6YUDsAQMZJ66BTU1Mjv9+vCy64QC6Xq/fnySefNLu0fpWXuFSzuFQFzvDhqQKng6Xlg5VlDy0hlxQxQpbfzn46AJChLLWPzmBEuw4/ngJBQ43edrV1dik/JzRcRU/OEPW7j86YUMhhHx0AsJxov78tMRk53dizbJo1YaTZZViL+zJp4gJ2RgYAhCHowDqy7CwhBwCEIeggM3EuFgBkBIIOMg/nYgFAxkjrVVdAzDgXCwAyCkEHmYNzsQAg4xB0kigQNLRt97t6pnm/tu1+l5PKky2Wc7EAAJbAHJ0kaWjxqbreE3aCucvpUFWFm40Ck4VzsQAg49CjkwQNLT5V1jWFhRxJavV3qbKuSQ0tPpMqyzCciwUAGYegk2CBoKHqes+JZoWout7DMFYycC4WAGQcgk6CNXrb+/TkHMuQ5PN3qdHbnryiMhXnYgFAxiHoJFhbZ+SQM5h2GCL3ZdKVj0i5x82Lyi0MXT9+H51gQPJukXY+FfqVFVkAkFaYjJxg+TmOgRvF0A5xEO25WGwsCABpj6CTYGXFeXI5HWr1d/U7T8cmqcAZOsEcSTTQuVg9Gwse/2+tZ2PB/np/AAAph6GrBLNn2VRV4ZYUcVaIqircsmdFmiCLpGNjQQCwDIJOEpSXuFSzuFQFzvDhqQKnQzWLS9lHJ9WwsSAAWAZDV0lSXuLSPHeBGr3tauvsUn5OaLiKnpwUxMaCAGAZBJ0ksmfZNGvCSLPLwEDYWBAALIOhK+B4bCwIAJZB0AGON9iNBdlzBwBSDkNXQH96Nhbsdx+d2/suLWfPHQBISTbDMDL6kKWOjg45nU75/X7l5uaaXQ5STTAQ3caC/e2509P7w547ABB30X5/06OTBIGgwWqrdDXQxoID7rljC+25M3EBZ2gBgAkIOgnW0OJTdb0n7GBPl9Ohqgo3++dYQSx77pwoMAEAEoLJyAnU0OJTZV1Tn9PLW/1dqqxrUkOLz6TKEDeD2XOHScsAkDT06CRIIGiout5zogENVdd7NM9dwDBWOot1zx0mLQNAUtGjkyCN3vY+PTnHMiT5/F1q9LYnryjEXyx77vRMWj5+qKvnoFDPhkRXCwAZh6CTIG2dkUPOYNohRUW7547EQaEAYAKCToLk5zgGbhRDO6Swnj13co+bXJ5b+PHS8sEeFMp8HgAYEuboJEhZcZ5cToda/V39/h3eptDp5WXFeckuDYngviy0hDzSnjuDmbTMfB4AGDJ6dBLEnmVTVYVbUsQBDVVVuJmIbCU9e+6c86XQr8fumzOYScvM5wGAISPoJFB5iUs1i0tV4AwfnipwOlSzuJR9dDJJLJOWB9yEUMznAYAoMXSVYOUlLs1zF7AzcqbrmbS89lqFws6xIea4g0K9W2LfhDCaoyoAIAMRdJLAnmXTrAkjzS4DZov2oNBY5/MwlwcAIiLoAMk00KRlKbb5PJEOFO2Zy8OBogAyHEEHSLaBDgrtmc/T4VP/83RsoeeLZkr3TonQ5gQHijLMBSCDEHSAVBPtfJ59r8Q+l4dhLgAZhlVXQCqKZhPCwczliWXJOpsVArAAenSAVDXQfJ5Y5vIMuGT9uGEuen4AWARBJ4ECQYNl5RiaE83niXYuz7jZsR1B8cF7sU9wZt4PgBRF0EmQhhafqus9YSeYu5wOVVW42SgQ8RHL3jzRDnN1+qQXqhTTBGd6fwCkMOboJEBDi0+VdU1hIUeSWv1dqqxrUkOLz6TKYDnRzOWRoh/mOvJ2bIePMu8HQIqjRyfOAkFD1fWeE/19WNX1Hs1zFzCMhfiIZm+eaIe5ThkV3XsePpj4eT8MhwGIA4JOnDV62/v05BzLkOTzd6nR285uyYifgfbmiXaY6+TTonu/EaMTO++H4TAAccLQVZy1dUYOOYNpB8RNNMNcsRw+Gsu8n1gOKWU4DEAc0aMTZ/k5joEbxdAOiKuBhrlimeCciHk/42YzHAYgrgg6cVZWnCeX06FWf1ekmRAqcIaWmgOmGGiYK9rDRxMx7ydVhsMIRIBlEHTizJ5lU1WFW5V1TZH+PqyqCjcTkZHaopngnIh5P4laBh/L4aeJ6iUiPAGmIOgkQHmJSzWLS/vso1PAPjpIJwP1/EjR9f4EA7FtbBiNRA2Hvf7bxPQSMcQGmIagkyDlJS7NcxewMzKsL57zfswcDvNuiX1+UDShKJbeJClxQ2yEJ2Qogk4C2bNsLCFHZojXvB8zh8P2vBz/XqKzyhMTnqTYApHZ4YmQBRMRdAAkRzTzfnramTEc1t9t+hNLL9H2NeYPsZkdnlJhzhNBK6MRdAAkTzTzfiRzhsOKz5e23DVwbbH0Er33t+jaJWqITTI3PCVq2M6qvVn0kCUEQQdAakr2cNj48+LfS3Ta+OjaJWqITTIvPCVq2C7WHqp06c1KxD3NDlkpEsgIOgDSVzyHw6T49xLNuF7adr95Q2zRSkR4SsSwXSzhSUqf3qxE3TMdglsScAQEgPTW0/NzzpdCv0b6G6P7Mmlli7TkN9I//zz068qd4X/oRnsafE8vkaS+x2UcE4qGDY+u3bHhaaDjN6IZ+pNCoS/a3atjCU9mDtvFEp7iNhSoj48oGfAg23+0/eioufeM5RiVaNsm4p5JQtBJgEDQ0Lbd7+qZ5v3atvtdBYLR/ikCIKGiCUXRBKKedtGEoniHp54htmjOIzMzPCVi2C6W8JSIoUAzA1m090yX4JbEM+ksMXT1wAMP6K677lJra6umTJmi++67T2VlZabU0tDi67NRoIuNAoH0Eq9J04NpF88htmjbxjI/qaceM4btYglP0UrEUGAsgSze9zR7GDLae+7ZGn3AHqK079F58skntWrVKlVVVampqUlTpkzRpZdeqra2tqTX0tDiU2VdU1jIkaRWf5cq65rU0OJLek0AEizaoTMzhtiibRttb1KW3dxhuxnXW683K973NHsYMtp7xhLyhijtg87dd9+t66+/XkuXLpXb7daDDz6oT3ziE/rFL36R1DoCQUPV9Z4Tddaput7DMBaAgcVziC3atvEOT7G0S0R4MnMoMBGBLNp7pktwi6XXbYjSeujq6NGj2rFjh26++ebea1lZWZo7d662bdvW72u6u7vV3d3d+7ijoyMutTR62/v05BzLkOTzd6nR285uyQDiI9ohtmjbRjvEFkvbeA/bRdsulrbxHgrsCWRm3NPsYcho79nTNgnSOui88847CgQCGj06PBmOHj1ar7/+er+vWb16taqrq+NeS1tn5JAzmHYAYIp4h6dY2sU7PEXbNhHhycx7pkNwS+J+OjbDMNJ2LOXAgQMaM2aMtm7dqlmzZvVe/853vqPNmzfrlVde6fOa/np0ioqK5Pf7lZubO+hatu1+V9es+cOA7R6//jP06ABAKkqXDfaiadfvPjZj+oasWNom4p5D0NHRIafTOeD3d1oHnaNHj+oTn/iEnnrqKS1cuLD3+pIlS3To0CE988wzA94j2g9qIIGgofPu+J1a/V2ROutU4HTo5Rsv4gRzAEDipUtwG6Rov7/Teuhq+PDhmjZtmjZt2tQbdILBoDZt2qTly5cntRZ7lk1VFW5V1jVF6qxTVYWbkAMASA4zhyFjbZtAab/qatWqVVqzZo0efvhh/eUvf1FlZaWOHDmipUuXJr2W8hKXahaXqsDpCLte4HSoZnEp++gAAJBkad2jI0lXXXWV3n77bd12221qbW3Vueeeq4aGhj4TlJOlvMSlee4CNXrb1dbZpfwch8qK8+jJAQDABGk9Ryce4jVHBwAAJE+0399pP3QFAAAQCUEHAABYFkEHAABYFkEHAABYFkEHAABYFkEHAABYFkEHAABYFkEHAABYFkEHAABYVtofATFUPRtDd3R0mFwJAACIVs/39kAHPGR80Ons7JQkFRUVmVwJAACIVWdnp5xOZ8TnM/6sq2AwqAMHDignJ0c2W/wO3uzo6FBRUZH27duX0Wdo8TmE8DnwGfTgcwjhcwjhcxj8Z2AYhjo7O1VYWKisrMgzcTK+RycrK0tnnHFGwu6fm5ubsf/xHovPIYTPgc+gB59DCJ9DCJ/D4D6DE/Xk9GAyMgAAsCyCDgAAsCyCToJkZ2erqqpK2dnZZpdiKj6HED4HPoMefA4hfA4hfA6J/wwyfjIyAACwLnp0AACAZRF0AACAZRF0AACAZRF0AACAZRF0EuSBBx7Q+PHj5XA4NHPmTDU2NppdUlK99NJLqqioUGFhoWw2m9avX292SUm3evVqzZgxQzk5OcrPz9fChQv1xhtvmF1W0tXU1Gjy5Mm9m4HNmjVLzz77rNllmer222+XzWbTypUrzS4lqf7zP/9TNpst7GfixIlml2WK/fv3a/HixRo5cqROPvlknXPOOXr11VfNLiupxo8f3+e/B5vNpmXLlsX1fQg6CfDkk09q1apVqqqqUlNTk6ZMmaJLL71UbW1tZpeWNEeOHNGUKVP0wAMPmF2KaTZv3qxly5bpD3/4g55//nl9+OGHuuSSS3TkyBGzS0uqM844Q7fffrt27NihV199VRdddJEuv/xy/fnPfza7NFNs375dP/vZzzR58mSzSzHFpEmT5PP5en9efvlls0tKuvfee09z5szRSSedpGeffVYej0f//d//rdNOO83s0pJq+/btYf8tPP/885KkK664Ir5vZCDuysrKjGXLlvU+DgQCRmFhobF69WoTqzKPJGPdunVml2G6trY2Q5KxefNms0sx3WmnnWb8z//8j9llJF1nZ6dx5plnGs8//7zxuc99zlixYoXZJSVVVVWVMWXKFLPLMN2NN95onHfeeWaXkXJWrFhhTJgwwQgGg3G9Lz06cXb06FHt2LFDc+fO7b2WlZWluXPnatu2bSZWBrP5/X5JUl5ensmVmCcQCOiJJ57QkSNHNGvWLLPLSbply5ZpwYIFYX8+ZJpdu3apsLBQn/zkJ7Vo0SLt3bvX7JKSbsOGDZo+fbquuOIK5efna+rUqVqzZo3ZZZnq6NGjqqur03XXXRfXA7Ylhq7i7p133lEgENDo0aPDro8ePVqtra0mVQWzBYNBrVy5UnPmzFFJSYnZ5STdzp07NWLECGVnZ+vf//3ftW7dOrndbrPLSqonnnhCTU1NWr16tdmlmGbmzJn65S9/qYaGBtXU1Mjr9er8889XZ2en2aUl1V//+lfV1NTozDPP1MaNG1VZWakbbrhBDz/8sNmlmWb9+vU6dOiQ/vVf/zXu987408uBZFi2bJlaWloycj6CJJ199tlqbm6W3+/XU089pSVLlmjz5s0ZE3b27dunFStW6Pnnn5fD4TC7HNPMnz+/958nT56smTNnaty4cVq7dq2+8pWvmFhZcgWDQU2fPl0/+tGPJElTp05VS0uLHnzwQS1ZssTk6szx85//XPPnz1dhYWHc702PTpydfvrpstvtOnjwYNj1gwcPqqCgwKSqYKbly5frN7/5jV588UWdccYZZpdjiuHDh+tTn/qUpk2bptWrV2vKlCn66U9/anZZSbNjxw61tbWptLRUw4YN07Bhw7R582bde++9GjZsmAKBgNklmuLUU0/VWWedpbfeesvsUpLK5XL1Cfmf/vSnM3IYT5L27NmjF154QV/96lcTcn+CTpwNHz5c06ZN06ZNm3qvBYNBbdq0KSPnJGQywzC0fPlyrVu3Tr/73e9UXFxsdkkpIxgMqru72+wykubiiy/Wzp071dzc3Pszffp0LVq0SM3NzbLb7WaXaIrDhw9r9+7dcrlcZpeSVHPmzOmz1cSbb76pcePGmVSRuWpra5Wfn68FCxYk5P4MXSXAqlWrtGTJEk2fPl1lZWW65557dOTIES1dutTs0pLm8OHDYX9L83q9am5uVl5ensaOHWtiZcmzbNkyPfbYY3rmmWeUk5PTO0fL6XTq5JNPNrm65Ln55ps1f/58jR07Vp2dnXrsscf0+9//Xhs3bjS7tKTJycnpMzfrlFNO0ciRIzNqzta3vvUtVVRUaNy4cTpw4ICqqqpkt9t1zTXXmF1aUn3jG9/Q7Nmz9aMf/UhXXnmlGhsb9dBDD+mhhx4yu7SkCwaDqq2t1ZIlSzRsWIIiSVzXcKHXfffdZ4wdO9YYPny4UVZWZvzhD38wu6SkevHFFw1JfX6WLFlidmlJ09/vX5JRW1trdmlJdd111xnjxo0zhg8fbowaNcq4+OKLjeeee87sskyXicvLr7rqKsPlchnDhw83xowZY1x11VXGW2+9ZXZZpqivrzdKSkqM7OxsY+LEicZDDz1kdkmm2LhxoyHJeOONNxL2HjbDMIzERCgAAABzMUcHAABYFkEHAABYFkEHAABYFkEHAABYFkEHAABYFkEHAABYFkEHAABYFkEHAADE3UsvvaSKigoVFhbKZrNp/fr1Md9j48aN+sxnPqOcnByNGjVK//zP/6y//e1vMd2DoAPAEo4ePapPfepT2rp165Duc9NNN+k//uM/4lQVkLmOHDmiKVOm6IEHHhjU671ery6//HJddNFFam5u1saNG/XOO+/oi1/8Ykz3YWdkAJZw7733qr6+Xs8///yQ7vPOO+/ok5/8pJqbm/XJT34yTtUBmc1ms2ndunVauHBh77Xu7m5997vf1eOPP65Dhw6ppKREd9xxhy644AJJ0lNPPaVrrrlG3d3dysoK9cvU19fr8ssvV3d3t0466aSo3pseHQBp4+jRo/1eNwxD999/v77yla8M+T1OP/10XXrppaqpqRnyvQBEtnz5cm3btk1PPPGE/vSnP+mKK65QeXm5du3aJUmaNm2asrKyVFtbq0AgIL/fr1/96leaO3du1CFHIugASGEXXHCBli9frpUrV/YGkP7s2LFDu3fv1oIFC3qv/e1vf5PNZtPatWt1/vnn6+STT9aMGTP05ptvavv27Zo+fbpGjBih+fPn6+233w67X0VFhZ544omE/t6ATLZ3717V1tbq17/+tc4//3xNmDBB3/rWt3TeeeeptrZWklRcXKznnntOt9xyi7Kzs3Xqqafq73//u9auXRvTexF0AKS0hx9+WMOHD9f//d//6cEHH+y3zZYtW3TWWWcpJyenz3NVVVX63ve+p6amJg0bNkxf/vKX9Z3vfEc//elPtWXLFr311lu67bbbwl5TVlamv//97zFPegQQnZ07dyoQCOiss87SiBEjen82b96s3bt3S5JaW1t1/fXXa8mSJdq+fbs2b96s4cOH60tf+pJimXUzLFG/CQCIhzPPPFN33nnnCdvs2bNHhYWF/T73rW99q7cnaMWKFbrmmmu0adMmzZkzR5L0la98Rb/85S/DXtNzrz179mj8+PFD+w0A6OPw4cOy2+3asWOH7HZ72HMjRoyQJD3wwANyOp1h///X1dWpqKhIr7zyij7zmc9E9V4EHQApbdq0aQO2+eCDD+RwOPp9bvLkyb3/PHr0aEnSOeecE3atra0t7DUnn3yyJOn999+PuV4AA5s6daoCgYDa2tp0/vnn99vm/fff752E3KMnFAWDwajfi6ErACntlFNOGbDN6aefrvfee6/f546dtGiz2fq9dvwfmu3t7ZKkUaNGxVwvgJDDhw+rublZzc3NkkLLxZubm7V3716dddZZWrRoka699lr97//+r7xerxobG7V69Wr99re/lSQtWLBA27dv13/9139p165dampq0tKlSzVu3DhNnTo16joIOgDS3tSpU/X666/HNG5/Ii0tLTrppJM0adKkuNwPyESvvvqqpk6d2htKVq1apalTp/bOiautrdW1116rb37zmzr77LO1cOFCbd++XWPHjpUkXXTRRXrssce0fv16TZ06VeXl5crOzlZDQ0Nvr2s0GLoCkPYuvPBCHT58WH/+859VUlIy5Ptt2bKld6UWgMG54IILTviXj5NOOknV1dWqrq6O2Obqq6/W1VdfPaQ66NEBkPZGjhypL3zhC3r00Ufjcr8nnnhC119/fVzuBcBc7IwMwBL+9Kc/ad68edq9e3fvqo3BePbZZ/XNb35Tf/rTnzRsGJ3eQLqjRweAJUyePFl33HGHvF7vkO5z5MgR1dbWEnIAi6BHBwAAWBY9OgAAwLIIOgAAwLIIOgAAwLIIOgAAwLIIOgAAwLIIOgAAwLIIOgAAwLIIOgAAwLIIOgAAwLL+H0MmN31qTp/hAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(inside_x, inside_y)\n",
    "plt.scatter(outside_x, outside_y)\n",
    "\n",
    "plt.xlabel(\"r (m)\")\n",
    "plt.ylabel(\"$g \\/ (N \\cdot kg^{-1})$\")\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.9.2 64-bit",
   "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": "3.9.2 (default, Feb 28 2021, 17:03:44) \n[GCC 10.2.1 20210110]"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "31f2aee4e71d21fbe5cf8b01ff0e069b9275f58929596ceb00d14d90e3e16cd6"
   }
  }
 },
 "nbformat": 4,
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