code/orbitalHW.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modeling and Simulation in Python\n",
    "\n",
    "David Tarazi\n",
    "\n",
    "Earth's Orbit\n",
    "\n",
    "Copyright 2017 Allen Downey\n",
    "\n",
    "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Configure Jupyter so figures appear in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "# Configure Jupyter to display the assigned value after an assignment\n",
    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
    "\n",
    "# import functions from the modsim.py module\n",
    "from modsim import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Earth falling into the sun\n",
    "\n",
    "Here's a question from the web site [Ask an Astronomer](http://curious.astro.cornell.edu/about-us/39-our-solar-system/the-earth/other-catastrophes/57-how-long-would-it-take-the-earth-to-fall-into-the-sun-intermediate):\n",
    "\n",
    "\"If the Earth suddenly stopped orbiting the Sun, I know eventually it would be pulled in by the Sun's gravity and hit it. How long would it take the Earth to hit the Sun? I imagine it would go slowly at first and then pick up speed.\"\n",
    "\n",
    "Here's a solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>x</th>\n",
       "      <td>1.470000e+11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>vx</th>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>vy</th>\n",
       "      <td>-3.033000e+04</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "x     1.470000e+11\n",
       "y     0.000000e+00\n",
       "vx    0.000000e+00\n",
       "vy   -3.033000e+04\n",
       "dtype: float64"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# And an inition condition (with everything in SI units)\n",
    "\n",
    "r_0 = 147e9\n",
    "\n",
    "init = State(x = r_0, # m\n",
    "             y = 0, # radians\n",
    "             vx = 0, # m/s\n",
    "             vy = -30330) # m/s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>init</th>\n",
       "      <td>x     1.470000e+11\n",
       "y     0.000000e+00\n",
       "vx    0....</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>G</th>\n",
       "      <td>6.674e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>m1</th>\n",
       "      <td>1.989e+30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>r_final</th>\n",
       "      <td>7.01879e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>m2</th>\n",
       "      <td>5.972e+24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t_0</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t_end</th>\n",
       "      <td>3.154e+07</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "init       x     1.470000e+11\n",
       "y     0.000000e+00\n",
       "vx    0....\n",
       "G                                                  6.674e-11\n",
       "m1                                                 1.989e+30\n",
       "r_final                                          7.01879e+08\n",
       "m2                                                 5.972e+24\n",
       "t_0                                                        0\n",
       "t_end                                              3.154e+07\n",
       "dtype: object"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Making a system object\n",
    "\n",
    "r_earth = 6.371e6 # m \n",
    "r_sun = 695.508e6 # m\n",
    "\n",
    "system = System(init=init,\n",
    "                G = 6.674e-11, # N / kg**2 * m**2\n",
    "                m1 = 1.989e30, # kg\n",
    "                r_final=r_sun + r_earth,\n",
    "                m2=5.972e24, # kg\n",
    "                t_0=0, # s\n",
    "                t_end= 3.154e7) # s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Here's a function that computes the force of gravity\n",
    "\n",
    "def universal_gravitation(vector, system):\n",
    "    \"\"\"Computes gravitational force.\n",
    "    \n",
    "    state: State object with distance r\n",
    "    system: System object with m1, m2, and G\n",
    "    \"\"\"\n",
    "    unpack(system)\n",
    "    \n",
    "    mag = G * m1 * m2 / vector.mag**2\n",
    "    direction = -vector.hat()\n",
    "    force = direction * mag\n",
    "    \n",
    "    return force"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "[-3.6686486e+22 -0.0000000e+00] dimensionless"
      ],
      "text/latex": [
       "$[-3.6686486e+22 -0.0000000e+00] dimensionless$"
      ],
      "text/plain": [
       "<Quantity([-3.6686486e+22 -0.0000000e+00], 'dimensionless')>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "testXY = Vector(init.x, init.y)\n",
    "universal_gravitation(testXY, system)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The slope function\n",
    "\n",
    "def slope_func(state, t, system):\n",
    "    \"\"\"Compute derivatives of the state.\n",
    "    \n",
    "    state: position, velocity\n",
    "    t: time\n",
    "    system: System object containing `g`\n",
    "    \n",
    "    returns: derivatives of y and v\n",
    "    \"\"\"\n",
    "    x, y, vx, vy = state\n",
    "    unpack(system)    \n",
    "    \n",
    "    r = Vector(x, y)\n",
    "    force = universal_gravitation(r, system)\n",
    "    a = force / m2\n",
    "    #print(dxdt, dydt)\n",
    "    \n",
    "    return vx, vy, a.x, a.y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0,\n",
       " -30330.0,\n",
       " <Quantity(-0.006143082049146188, 'dimensionless')>,\n",
       " <Quantity(-0.0, 'dimensionless')>)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Always test the slope function!\n",
    "\n",
    "slope_func(init, 0, system)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\ndef event_func(state, t, system):\\n    x, y, vx, vy = state\\n    return r - system.r_final'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Here's an event function that stops the simulation\n",
    "# before the collision\n",
    "\"\"\"\n",
    "def event_func(state, t, system):\n",
    "    x, y, vx, vy = state\n",
    "    return r - system.r_final\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Always test the event function!\n",
    "\n",
    "#event_func(init, 0, system)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>sol</th>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t_events</th>\n",
       "      <td>[]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nfev</th>\n",
       "      <td>464</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>njev</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nlu</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>status</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>message</th>\n",
       "      <td>The solver successfully reached the end of the...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>success</th>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "sol                                                      None\n",
       "t_events                                                   []\n",
       "nfev                                                      464\n",
       "njev                                                        0\n",
       "nlu                                                         0\n",
       "status                                                      0\n",
       "message     The solver successfully reached the end of the...\n",
       "success                                                  True\n",
       "dtype: object"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Finally we can run the simulation\n",
    "\n",
    "results, details = run_ode_solver(system, slope_func, max_step = 500000)#, events=event_func)\n",
    "details"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11e47b50c18>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(results.x)\n",
    "plt.figure()\n",
    "plot(results.y)\n",
    "plt.figure()\n",
    "plot(results.x,results.y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "31540000.0 second"
      ],
      "text/latex": [
       "$31540000.0 second$"
      ],
      "text/plain": [
       "<Quantity(31540000.0, 'second')>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Here's how long it takes...\n",
    "\n",
    "t_final = get_last_label(results) * UNITS.seconds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "365.04629629629625 day"
      ],
      "text/latex": [
       "$365.04629629629625 day$"
      ],
      "text/plain": [
       "<Quantity(365.04629629629625, 'day')>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ... expressed in units we understand\n",
    "\n",
    "t_final.to(UNITS.day)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}