102 lines
22 KiB
Plaintext
102 lines
22 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"\"\"\"Gravitational field strength vs range (Earth).\"\"\"\n",
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"\n",
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"import math\n",
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"import matplotlib.pyplot as plt\n",
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"\n",
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"IN_STEPS = 20\n",
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"OUT_STEP = 0.25\n",
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"OUT_COUNT = 40\n",
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"G = 6.67 * 10e-11\n",
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"M = 5.97 * 10e24\n",
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"R = 6.38 * 10e6\n",
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"\n",
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"density = M / ((4/3) * math.pi * R**3)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"inside_x = []\n",
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"inside_y = []\n",
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"for i in range(IN_STEPS):\n",
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" r = R * i / IN_STEPS\n",
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" g = (4/3) * math.pi * G * r * density\n",
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" inside_x.append(r)\n",
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" inside_y.append(g)\n",
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"\n",
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"outside_x = []\n",
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"outside_y = []\n",
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"for i in range(OUT_COUNT):\n",
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" r = R * (1 + i*OUT_STEP)\n",
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" g = G * M / r**2\n",
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" outside_x.append(r)\n",
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" outside_y.append(g)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"plt.scatter(inside_x, inside_y)\n",
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"plt.scatter(outside_x, outside_y)\n",
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"\n",
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"plt.xlabel(\"r (m)\")\n",
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"plt.ylabel(\"$g \\/ (N \\cdot kg^{-1})$\")\n",
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"\n",
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"plt.show()"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3.9.2 64-bit",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.9.2 (default, Feb 28 2021, 17:03:44) \n[GCC 10.2.1 20210110]"
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},
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"orig_nbformat": 4,
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"vscode": {
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"interpreter": {
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"hash": "31f2aee4e71d21fbe5cf8b01ff0e069b9275f58929596ceb00d14d90e3e16cd6"
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}
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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