{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "720e7493",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t=0.0, r=30000000000.0, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407407408e-24\n",
      "t=1e-06, r=30000000000.0, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407407408e-24\n",
      "t=1.9999999999999998e-05, r=29999999999.99999, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407407414e-24\n",
      "t=2.9999999999999997e-05, r=29999999999.999985, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407407415e-24\n",
      "t=7.999999999999999e-05, r=29999999999.99996, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407407427e-24\n",
      "t=8.888888888888888e-05, r=29999999999.999954, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407407431e-24\n",
      "t=9.999999999999999e-05, r=29999999999.99995, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407407433e-24\n",
      "t=9.999999999999999e-05, r=29999999999.99995, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407407433e-24\n",
      "t=0.00030000000000000003, r=29999999999.99985, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407407481e-24\n",
      "t=0.00039999999999999996, r=29999999999.9998, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407407506e-24\n",
      "t=0.0009, r=29999999999.99955, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.40740740740763e-24\n",
      "t=0.0009888888888888888, r=29999999999.999508, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.40740740740765e-24\n",
      "t=0.0011, r=29999999999.99945, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407407678e-24\n",
      "t=0.0011, r=29999999999.99945, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407407678e-24\n",
      "t=0.0031000000000000003, r=29999999999.99845, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407408173e-24\n",
      "t=0.0041, r=29999999999.99795, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.40740740740842e-24\n",
      "t=0.0091, r=29999999999.995453, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407409654e-24\n",
      "t=0.00998888888888889, r=29999999999.995007, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407409873e-24\n",
      "t=0.0111, r=29999999999.99445, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.40740740741015e-24\n",
      "t=0.0111, r=29999999999.99445, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.40740740741015e-24\n",
      "t=0.031100000000000003, r=29999999999.98445, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407415087e-24\n",
      "t=0.0411, r=29999999999.97945, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407417557e-24\n",
      "t=0.09110000000000001, r=29999999999.954453, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407429901e-24\n",
      "t=0.09998888888888889, r=29999999999.95001, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407432095e-24\n",
      "t=0.1111, r=29999999999.944454, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407434838e-24\n",
      "t=0.1111, r=29999999999.944454, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407434838e-24\n",
      "t=0.31110000000000004, r=29999999999.844463, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407484216e-24\n",
      "t=0.4111, r=29999999999.794468, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407508906e-24\n",
      "t=0.9111, r=29999999999.544495, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407632349e-24\n",
      "t=0.9999888888888888, r=29999999999.500053, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407654295e-24\n",
      "t=1.1111, r=29999999999.444504, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407681727e-24\n",
      "t=1.1111, r=29999999999.444504, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407407681727e-24\n",
      "t=3.1111, r=29999999998.444603, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407408175505e-24\n",
      "t=4.1111, r=29999999997.944653, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407408422394e-24\n",
      "t=9.1111, r=29999999995.444904, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407409656838e-24\n",
      "t=9.99998888888889, r=29999999995.000504, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407409876296e-24\n",
      "t=11.1111, r=29999999994.445004, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407410150616e-24\n",
      "t=11.1111, r=29999999994.445004, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407410150616e-24\n",
      "t=31.1111, r=29999999984.446003, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407415088395e-24\n",
      "t=41.1111, r=29999999979.446503, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407417557283e-24\n",
      "t=91.1111, r=29999999954.449005, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407429901726e-24\n",
      "t=99.99998888888888, r=29999999950.005005, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407432096295e-24\n",
      "t=111.1111, r=29999999944.450005, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407434839505e-24\n",
      "t=111.1111, r=29999999944.450005, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407434839505e-24\n",
      "t=311.1111, r=29999999844.460003, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407484217284e-24\n",
      "t=411.11109999999996, r=29999999794.465004, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407508906173e-24\n",
      "t=911.1111000000001, r=29999999544.490005, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.40740763235062e-24\n",
      "t=999.9999888888889, r=29999999500.050003, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407654296301e-24\n",
      "t=1111.1111, r=29999999444.500004, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407681728401e-24\n",
      "t=1111.1111, r=29999999444.500004, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407407681728401e-24\n",
      "t=2888.8888800000004, r=29999998555.700005, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407408120642024e-24\n",
      "t=3777.77777, r=29999998111.300003, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407408340098853e-24\n",
      "t=8222.22222, r=29999995889.3, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407409437383134e-24\n",
      "t=9012.345677777777, r=29999995494.277775, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.40740963245592e-24\n",
      "t=10000.0, r=29999995000.5, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407409876296914e-24\n",
      "t=10000.0, r=29999995000.5, θ=1.5707963267948966, φ=3.5\n",
      "result of step r=-0.49995, θ=0.0, φ=7.407409876296914e-24\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.constants import pi\n",
    "from scipy.integrate import solve_ivp\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "r_0 = 3e10\n",
    "theta_0 = pi/2\n",
    "phi_0 = 3.5\n",
    "\n",
    "initial_pos = [r_0, theta_0, phi_0]\n",
    "\n",
    "def d_dt(t, X, E=1.5, L=1, M=1.2e9, m=150, G=6.67e-11, c=3e8):\n",
    "    print (\"t={}, r={}, θ={}, φ={}\".format(t, *X))\n",
    "    r, theta, phi = X\n",
    "    dr_dt = ((E / m) ** 2 - (1 - (2 * G * M) / (c ** 2 * r)) * (1 + (L ** 2) / (m ** 2 * r ** 2))) ** 1/2\n",
    "    dtheta_dt = 0 # orbits are planar, so dtheta/dt doesn't change\n",
    "    dphi_dt = L / m * 1 / (r ** 2 * np.sin(theta_0) ** 2)\n",
    "    result = np.array([dr_dt, dtheta_dt, dphi_dt])\n",
    "    print (\"result of step r={}, θ={}, φ={}\".format(*result))\n",
    "\n",
    "    return result\n",
    "\n",
    "tmax = 10000\n",
    "samples = 5000\n",
    "t = np.linspace(0, tmax, samples)\n",
    "geodesic = solve_ivp(d_dt, (0, tmax), y0=initial_pos, dense_output=True)\n",
    "r, theta, phi = geodesic.sol(t)\n",
    "\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = plt.axes(projection='3d')\n",
    "\n",
    "# Convert from spherical to cartesian\n",
    "x = r * np.sin(theta) * np.cos(phi)\n",
    "y = r * np.sin(theta) * np.sin(phi)\n",
    "z = r * np.cos(theta)\n",
    "\n",
    "ax.plot3D(x, y, z)\n",
    "ax.set_title('Plot of Schwarzschild Geodesic')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "91103f75",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}