physics/elliptical_orbit_plotter.ipynb

108 lines
83 KiB
Plaintext

{
"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 = 5 # SEMI_MAJOR_AXIS Astronomical Units\n",
"b = 2 # SEMI_MINOR_AXIS Astronomical Units\n",
"M_star = 3 # Solar mass\n",
"\n",
"G = 6.67e-11\n",
"\n",
"E = np.sqrt(1 - b**2 / a**2)\n",
"T = np.sqrt(a ** 3 / M_star)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"theta = np.linspace(0, 2 * np.pi, 10_000)\n",
"r = a * (1 - E**2) / (1 + E * np.cos(theta))\n",
"x, y = r * np.cos(theta), r * np.sin(theta)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "4d54dca5c1bf4c1ea47e63b0a9d18cb4",
"version_major": 2,
"version_minor": 0
},
"image/png": "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",
"text/html": [
"\n",
" <div style=\"display: inline-block;\">\n",
" <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
" Figure\n",
" </div>\n",
" <img src='data:image/png;base64,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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, y)\n",
"ax.set_title(\"Elliptical Orbit\")\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
}