108 lines
83 KiB
Plaintext
108 lines
83 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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"%matplotlib widget\n",
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"import matplotlib.pyplot as plt\n",
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"import numpy as np\n",
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"\n",
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"a = 5 # SEMI_MAJOR_AXIS Astronomical Units\n",
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"b = 2 # SEMI_MINOR_AXIS Astronomical Units\n",
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"M_star = 3 # Solar mass\n",
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"\n",
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"G = 6.67e-11\n",
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"\n",
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"E = np.sqrt(1 - b**2 / a**2)\n",
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"T = np.sqrt(a ** 3 / M_star)"
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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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"theta = np.linspace(0, 2 * np.pi, 10_000)\n",
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"r = a * (1 - E**2) / (1 + E * np.cos(theta))\n",
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"x, y = r * np.cos(theta), r * np.sin(theta)"
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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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"application/vnd.jupyter.widget-view+json": {
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"model_id": "4d54dca5c1bf4c1ea47e63b0a9d18cb4",
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"version_major": 2,
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"version_minor": 0
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},
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" <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
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" Figure\n",
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" </div>\n",
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" <img src='data:image/png;base64,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" </div>\n",
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" "
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],
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"text/plain": [
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"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
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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.ion()\n",
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"fig = plt.figure()\n",
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"\n",
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"ax = fig.add_subplot()\n",
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"ax.plot(x, y)\n",
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"ax.set_title(\"Elliptical Orbit\")\n",
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"ax.set_xlabel(\"x / AU\")\n",
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"ax.set_ylabel(\"y / AU\")\n",
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"\n",
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"plt.grid()\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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"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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"pygments_lexer": "ipython3",
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"version": "3.9.2"
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"orig_nbformat": 4,
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}
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"nbformat_minor": 2
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}
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