physics/binary_orbits.ipynb

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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib widget\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"a = 3 # Semi major axis (AU)\n",
"r_1 = 1 # Planet 1 initial orbit radius (AU)\n",
"M_1 = 3 # Star 1 mass (Solar masses)\n",
"M_2 = 2 # Star 2 mass (Solar masses)\n",
"\n",
"r_2 = a - r_1\n",
"T = np.sqrt(a ** 3 / (M_1 + M_2))\n",
"v_1 = 2 * np.pi * r_1 / T\n",
"v_2 = 2 * np.pi * (a - r_1) / T"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"t = np.linspace(0, T, 10000)\n",
"theta = 2 * np.pi * t / T\n",
"x_1, y_1 = -r_1 * np.sin(theta), -r_1 * np.cos(theta)\n",
"x_2, y_2 = -r_2 * np.sin(theta), -r_2 * np.cos(theta)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "407c30b67cad4a12a48103840009b82d",
"version_major": 2,
"version_minor": 0
},
"image/png": 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",
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" <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
" Figure\n",
" </div>\n",
" <img 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' width=640.0/>\n",
" </div>\n",
" "
],
"text/plain": [
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.ion()\n",
"fig = plt.figure()\n",
"\n",
"ax = fig.add_subplot()\n",
"ax.plot(x_1, y_1)\n",
"ax.plot(x_2, y_2)\n",
"ax.set_xlabel(\"x / AU\")\n",
"ax.set_ylabel(\"y / AU\")\n",
"\n",
"plt.grid()\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"
},
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "31f2aee4e71d21fbe5cf8b01ff0e069b9275f58929596ceb00d14d90e3e16cd6"
}
}
},
"nbformat": 4,
"nbformat_minor": 2
}