Lecture.19-Celestial-Mechanics.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Celestial Mechanics\n",
    "## Lecture 19"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Material taken from Chapter 4: The Solar System of Giordano*\n",
    "\n",
    "Consider a hypothetical solar system.  There is one planet (call it *Earth*) in orbit around the Sun and the only force in the problem is gravity.  Newton's Law of graviation gives us the magnitude of the force as\n",
    "\n",
    "$$ F_G = \\frac{G M_S M_E} {r^2},$$ \n",
    "where $M_S$ and $M_E$ are the masses of the Sun and Earth, $r$ is the distance between them, and $G$ is the gravitational constant.  \n",
    "\n",
    "Assume that the Sun's mass is sufficiently large that its motion can be neglected.  Our goal is to calculate the position of Earth as a function of time.\n",
    "\n",
    "From Newton's second law of motion we have\n",
    "\n",
    "\\begin{align}\n",
    "\\frac{d^2x}{dt^2} &= \\frac{F_{G, x}}{M_E} \\\\\n",
    "\\frac{d^2y}{dt^2} &= \\frac{F_{G, y}}{M_E} \n",
    "\\end{align}\n",
    "\n",
    "where $F_{G,x}$ and $F_{G,y}$ are the $x$ and $y$ components of gravitational force. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each component of the gravity force can be written as\n",
    "\n",
    "$$F_{G,x} = - \\frac{G M_S M_E}{r^2} \\cos\\theta = - \\frac{G M_S M_E x}{r^3}, $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to rewrite each of these second order differential equations as two\n",
    "first-order differential equations.\n",
    "\n",
    "\\begin{align}\n",
    "\\frac{d v_x}{dt} &= - \\frac{G M_S x}{r^3} \\\\\n",
    "\\frac{d x}{dt} &= v_x \\\\\n",
    "\\frac{d v_y}{dt} &= - \\frac{G M_S y}{r^3} \\\\\n",
    "\\frac{d y}{dt} &= v_y \\\\\n",
    "\\,\n",
    "\\end{align}\n",
    "\n",
    "We can then solve these equations numerically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "π = np.pi\n",
    "\n",
    "def orbit(tmax = 1.0, dt = 0.002, v0 = 2*π, x0 = 1):\n",
    "    \"\"\"\n",
    "    Calculate the orbit of planet\n",
    "    \"\"\"\n",
    "\n",
    "    # number of timesteps\n",
    "    N = round(tmax/dt)\n",
    "\n",
    "    # allocate arrays\n",
    "    x = np.zeros(N)\n",
    "    y = np.zeros(N)\n",
    "    vx = np.zeros(N)\n",
    "    vy = np.zeros(N)\n",
    "    t = np.zeros(N)\n",
    "    \n",
    "    # initialise position of planet in AU\n",
    "    x[0] = x0\n",
    "    y[0] = 0\n",
    "\n",
    "    # initialise velocity of planet in AU/yr\n",
    "    vx[0] = 0\n",
    "    vy[0] = v0\n",
    "\n",
    "    # loop over the timesteps\n",
    "    for i in range(N-1):\n",
    "        t[i+1] = t[i] + dt\n",
    "        \n",
    "        r = np.sqrt(x[i]**2+y[i]**2)\n",
    "        \n",
    "        # Compute new velocities in the x and y directions\n",
    "        vx[i+1] = vx[i] - (4*π**2*x[i]*dt)/(r**3)\n",
    "        vy[i+1] = vy[i] - (4*π**2*y[i]*dt)/(r**3)\n",
    "        \n",
    "        # Euler-Cromer Step - update positions using newly calculated velocities\n",
    "        x[i+1] = x[i] + vx[i+1]*dt\n",
    "        y[i+1] = y[i] + vy[i+1]*dt\n",
    "        # if Euler's method, then update x using the *old* value for vx\n",
    "        #x[i+1] = x[i] + vx[i]*dt\n",
    "        #y[i+1] = y[i] + vy[i]*dt\n",
    "        \n",
    "    return x, y, vx, vy, t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x, y, vx, vy, t = orbit(tmax=1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_orbit(x, y):\n",
    "\n",
    "    plt.plot(x, y, '--', linewidth=2)\n",
    "\n",
    "    # Plot the Sun at the origin\n",
    "    plt.plot(0, 0, '.',color=\"yellow\", markersize=40, markeredgecolor='black')\n",
    "    # Plot the Earth at the final position\n",
    "    plt.plot(x[-1], y[-1], '.', color= 'k', markersize=15)\n",
    "\n",
    "    plt.xlabel('x (AU)')\n",
    "    plt.ylabel('y (AU)')\n",
    "    plt.axis('equal')\n",
    "    \n",
    "    \n",
    "plot_orbit(x, y)\n",
    "plt.title('Simulation of Earth orbit around the Sun')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall that the Euler algoritm is not a good choice for oscillatory problems such as planetary motion.  Energy with the Euler method is not conserved and we would find the energy of the planet would grow with time.  The Euler-Cromer method, which conserves energy, avoids this difficulty."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise\n",
    "> Comment out the Euler-Cromer step and uncomment the Euler step in the above routine and rerun with `tmax = 2.0`\n",
    ">\n",
    "> Notice that the solution is unstable.  The solution would also be unstable if `dt` was too large.\n",
    ">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Choice of units\n",
    "\n",
    "Distance: Astronomical Units (AU)\n",
    "\n",
    "Time: Year (yr)\n",
    "\n",
    "Mass: ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Elliptical orbits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The choice of initial velocity was critical to acheive a circular orbit. \n",
    "\n",
    "Notice that we chose\n",
    "\n",
    "$$ v_0 = 2\\pi $$\n",
    "\n",
    "which may seem like a slightly strange looking speed. \n",
    "\n",
    "But, if you recall the units for this speed is in units of AU/yr perhaps, hopefully you'll see why this has to be the correct speed.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we change the initial speed to being different from $2\\pi$, we get different shaped orbits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y, vx, vy, t = orbit(v0 = 2*π, tmax = 1.0)\n",
    "plot_orbit(x, y)\n",
    "\n",
    "x, y, vx, vy, t = orbit(v0 = 4, tmax = 1.0)\n",
    "plot_orbit(x, y)\n",
    "\n",
    "x, y, vx, vy, t = orbit(v0 = 8, tmax = 4.2)\n",
    "plot_orbit(x, y)\n",
    "plt.title('Comparison of different orbits')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise\n",
    "> Adjust `tmax` so that the faster planet completes its orbit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Making animations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes animations are better at vizualization what is happening in a system.  Orbital mechnics is one of those cases.  Wouldn't it be better to to *see* the planet orbiting the sun?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import animation, rc\n",
    "from IPython.display import HTML, display\n",
    "rc('animation', html='html5')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example\n",
    "Example taken from http://louistiao.me/posts/notebooks/embedding-matplotlib-animations-in-jupyter-notebooks/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# First set up the figure, the axis, and the plot element we want to animate\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.set_xlim(( 0, 2))\n",
    "ax.set_ylim((-2, 2))\n",
    "\n",
    "line, = ax.plot([], [], lw=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialization function: plot the background of each frame\n",
    "def init():\n",
    "    line.set_data([], [])\n",
    "    return (line,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# animation function. This is called sequentially\n",
    "def animate(i):\n",
    "    x = np.linspace(0, 2, 1000)\n",
    "    y = np.sin(2 * np.pi * (x - 0.01 * i))\n",
    "    line.set_data(x, y)\n",
    "    return (line,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# call the animator. blit=True means only re-draw the parts that have changed.\n",
    "anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
    "                               frames=100, interval=20, blit=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Installation of ffmpeg..\n",
    "\n",
    "     conda install -y ffmpeg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x10e434320>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "anim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Animation of a an orbiting planet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def animate_orbit(x, y, t):\n",
    "    \n",
    "    # First set up the figure, the axis, and the plot element we want to animate\n",
    "    fig, ax = plt.subplots(figsize=(8,4))\n",
    "    \n",
    "    # Plot the orbit\n",
    "    orbit, = ax.plot([], [], '--', linewidth=2)\n",
    "    # Plot the planet at the current position\n",
    "    position, = ax.plot([], [], '.', color= 'k', markersize=15)\n",
    "\n",
    "    label = ax.text(-3, 1, '', fontsize=14)\n",
    "    \n",
    "    plt.xlabel('x (AU)')\n",
    "    plt.ylabel('y (AU)')\n",
    "    \n",
    "    ax.set_xlim(( -4, 2))\n",
    "    ax.set_ylim((-2, 2))\n",
    "    \n",
    "    dt = t[1] - t[0]\n",
    "    animate_dt = 0.02\n",
    "    skip_frames = int(animate_dt // dt)\n",
    "    nframes = int(len(t) // skip_frames)\n",
    "\n",
    "    # initialization function: plot the background of each frame\n",
    "    def init():\n",
    "         # Plot the Sun at the origin\n",
    "        plt.plot(0, 0, '.',color=\"yellow\", markersize=40, markeredgecolor='black')\n",
    "        orbit.set_data([], [])\n",
    "        position.set_data([], [])\n",
    "        label.set_text('')\n",
    "        \n",
    "        return (orbit, position, label)\n",
    "    \n",
    "    # animation function. This is called sequentially\n",
    "    def animate(i):\n",
    "        i = i*skip_frames\n",
    "        orbit.set_data(x[:i], y[:i])\n",
    "        position.set_data(x[i], y[i])\n",
    "        label.set_text('t = {:.2f} yr'.format(t[i]))\n",
    "        \n",
    "        return (orbit, position, label)\n",
    "\n",
    "    \n",
    "    # call the animator. blit=True means only re-draw the parts that have changed.\n",
    "    anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
    "                                   frames=nframes, interval=20*skip_frames, blit=True)\n",
    "    \n",
    "    return anim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y, vx, vy, t = orbit(v0 = 4, tmax = 1.0)\n",
    "anim = animate_orbit(x, y, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "AAgAAAAAAgAAEAAAAAABAAAYAAAAAAEAAAgAAAAAAQAAKAAAAAABAAAQAAAAAAEAAAAAAAAAAQAA\n",
       "CAAAAAABAAAoAAAAAAEAABAAAAAAAQAAAAAAAAABAAAIAAAAAAEAACgAAAAAAQAAEAAAAAABAAAA\n",
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       "AAAAHHN0c2MAAAAAAAAAAQAAAAEAAAAyAAAAAQAAANxzdHN6AAAAAAAAAAAAAAAyAAASNwAAAZsA\n",
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       "ALcAAADRAAAAlwAAAa8AAACDAAABDQAAAIIAAACFAAABpAAAAJIAAADCAAAAyQAAAMgAAAHaAAAA\n",
       "hwAAAXIAAACZAAAAjAAAALAAAAKpAAAA6wAAAL8AAADpAAAB9QAAAOwAAADSAAAAnQAAAPEAAACA\n",
       "AAABSQAAALIAAAChAAAAaQAAAJwAAAAUc3RjbwAAAAAAAAABAAAALAAAAGJ1ZHRhAAAAWm1ldGEA\n",
       "AAAAAAAAIWhkbHIAAAAAAAAAAG1kaXJhcHBsAAAAAAAAAAAAAAAALWlsc3QAAAAlqXRvbwAAAB1k\n",
       "YXRhAAAAAQAAAABMYXZmNTguMjAuMTAw\n",
       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x10e583550>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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8JCKei4idEXH7+HY/MhGxOCKej4jdEbGyxfHJEfFAdfypiOhuOnZLNf58RFw2nn23Y7RzjoiFEbEtInqr94vHu/fRaOdnXB2fFRFvRMRN49XzmMhMXzW9gDuAldX2SmBNi5rpQF/1Pq3antZ0/FPAfwM7Oj2fsZ4zMAW4qKo5BvgfYEmn53SYeU4CXgDmVL3+HJg7qOaLwH3V9tXAA9X23Kp+MjC7Os+kTs9pjOf8UeAD1fbZwG86PZ+xnG/T8R8CDwE3dXo+7by8YqjXUmB9tb0euKJFzWXApszcm5mvAZuAxQARcTxwI/D1cei1LqOec2buy8wnADJzP/AzYOY49Dwa84HdmdlX9Xo/A3Nv1vzf4mHgkoiIavz+zHwzM/cAu6vzHelGPefMfCYzX67GdwLviYjJ49L16LXzMyYirmDgl56d49TvmDEY6vW+zHwFoHo/pUXNacBLTfv91RjA14BvAPvGssmatTtnACJiKvAJYPMY9dmuIefQXJOZB4DXgZOG+dkjUTtzbvZp4JnMfHOM+qzLqOcbEccBNwOrx6HPMdfV6QYmmoh4DHh/i0O3DvcULcYyIs4FzsjMFYPvW3baWM256fxdwA+Ab2Zm38g7HBdvO4chaobz2SNRO3MeOBhxFrAGWFRjX2OlnfmuBu7KzDeqC4gJzWAYocy89HDHIuK3EXFqZr4SEacCv2tR1g9c2LQ/E9gCLAA+FhEvMvBzOSUitmTmhXTYGM75kLXArsy8u4Z2x0o/cHrT/kzg5cPU9FdhdyKwd5ifPRK1M2ciYibwI+BzmfnC2Lfbtnbmex5wZUTcAUwF/hYRf83Mb41922Og04sc76QXcCflQuwdLWqmA3sYWHydVm1PH1TTzcRZfG5rzgysp/wQOKrTcxlinl0M3D+ezf8vTJ41qOZLlAuTD1bbZ1EuPvcxMRaf25nz1Kr+052ex3jMd1DNV5ngi88db+Cd9GLg3upmYFf1fuh/fg3gO011/8LAAuRu4AstzjORgmHUc2bgN7IEfglsr17XdnpObzPXy4FfMfDkyq3V2G3AJ6vt9zDwRMpu4GlgTtNnb60+9zxH6JNXdc4Z+Ffgz00/1+3AKZ2ez1j+jJvOMeGDwb98liQVfCpJklQwGCRJBYNBklQwGCRJBYNBklQwGCRJBYNBklQwGCRJhf8FOE0EisNjF6YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "anim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y, vx, vy, t = orbit(v0 = 7.5, tmax = 4.0)\n",
    "anim = animate_orbit(x, y, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x115d31208>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "anim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kepler's Laws"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. All planets move in elliptical orbits, with the Sun at one focus.\n",
    "2. The line joining a planent to the Sun sweeps out equal areas in equal times.\n",
    "3. If $T$ is the period and $a$ is the semimajor axis of the orbit, then $T^2/a^3$ is a constant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Planetary data\n",
    "\n",
    "planet\n",
    "- Mass, `m` in kg\n",
    "- Semimajor axis, `a` in AU\n",
    "- Eccentricity, `e` (non-dimensional)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = { 'Mercury' : {'m':2.4e23, 'a':0.39,  'e':0.206},\n",
    "         'Venus'   : {'m':4.9e24, 'a':0.72,  'e':0.007},   \n",
    "         'Earth'   : {'m':6.0e24, 'a':1.00,  'e':0.017},  \n",
    "         'Mars'    : {'m':6.6e23, 'a':1.52,  'e':0.093},\n",
    "         'Jupiter' : {'m':1.9e27, 'a':5.20,  'e':0.048},\n",
    "         'Saturn'  : {'m':5.7e26, 'a':9.54,  'e':0.056},\n",
    "         'Uranus'  : {'m':8.8e25, 'a':19.19, 'e':0.046},\n",
    "         'Neptune' : {'m':1.03e26,'a':30.06, 'e':0.010},\n",
    "         'Pluto'   : {'m':6.0e24, 'a':39.53, 'e':0.248},\n",
    "        }"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data above is presented as a Python dictionary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'a': 1.0, 'e': 0.017, 'm': 6e+24}"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['Earth']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6e+24"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "planet = data['Earth']\n",
    "planet['m']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.2"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['Jupiter']['a']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Period"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to determine the period, $T$. This is time before the $x$ and $y$ positions repeat."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109479198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n",
    "\n",
    "x, y, vx, vy, t = orbit(v0 = 4, tmax = 2.0)\n",
    "\n",
    "plt.sca(axes[0])\n",
    "plot_orbit(x, y)\n",
    "\n",
    "plt.sca(axes[1])\n",
    "plt.plot(t, x)\n",
    "plt.plot(t, y)\n",
    "plt.xlabel('t (yr)')\n",
    "plt.ylabel('x or y (AU)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109479f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = np.sqrt((x - x[0])**2 + (y - y[0])**2)\n",
    "plt.plot(t, r)\n",
    "plt.xlabel('t (yr)')\n",
    "plt.ylabel('r (AU)')\n",
    "plt.title('Distance from initial position to planet')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_period(x, y, t, tolerance=0.01):\n",
    "\n",
    "    # calculate distance from planet to sun\n",
    "    r = np.sqrt((x - x[0])**2 + (y - y[0])**2)\n",
    "    i = 0\n",
    "    # get beyond starting position\n",
    "    while i < len(r)-1:\n",
    "        if r[i] > tolerance:\n",
    "            break\n",
    "        i += 1\n",
    "            \n",
    "    # determine when planet returns to starting position\n",
    "    while i < len(r)-1:\n",
    "        if r[i] < tolerance:\n",
    "            break\n",
    "        i += 1\n",
    "        \n",
    "    # the period is when the orbit returns to its starting position\n",
    "    T = t[i]\n",
    "    # check to make sure we have actually made a complete orbit\n",
    "    if r[i] > tolerance:\n",
    "        print('Warning! Complete orbit not completed')\n",
    "\n",
    "    return T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "x, y, vx, vy, t = orbit(v0 = 2*π, tmax = 2.0)\n",
    "T = calc_period(x, y, t)\n",
    "print(T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.496\n"
     ]
    }
   ],
   "source": [
    "x, y, vx, vy, t = orbit(v0 = 4, tmax = 2.0)\n",
    "T = calc_period(x, y, t)\n",
    "print(T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning! Complete orbit not completed\n",
      "1.998\n"
     ]
    }
   ],
   "source": [
    "x, y, vx, vy, t = orbit(v0 = 8, tmax = 2.0)\n",
    "T = calc_period(x, y, t)\n",
    "print(T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.29\n"
     ]
    }
   ],
   "source": [
    "x, y, vx, vy, t = orbit(v0 = 8, tmax = 6.0)\n",
    "T = calc_period(x, y, t)\n",
    "print(T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Eccentricity\n",
    "\n",
    "*Show geometry on board*\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_eccentricity(x, y, t):\n",
    "\n",
    "    # major semiaxis\n",
    "    a = (max(x)-min(x))/2\n",
    "    # minor semiaxis\n",
    "    b = (max(y)-min(y))/2\n",
    "    \n",
    "    if b > a:\n",
    "        a, b = b, a\n",
    "\n",
    "    # compute eccentricity\n",
    "    e = np.sqrt(1 - b**2/a**2)\n",
    "    \n",
    "    return e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00823106669062\n"
     ]
    }
   ],
   "source": [
    "x, y, vx, vy, t = orbit(v0 = 2*π, tmax = 2.0)\n",
    "e = calc_eccentricity(x, y, t)\n",
    "print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.588331486911\n"
     ]
    }
   ],
   "source": [
    "x, y, vx, vy, t = orbit(v0 = 4, tmax = 2.0)\n",
    "e = calc_eccentricity(x, y, t)\n",
    "print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.621124249856\n"
     ]
    }
   ],
   "source": [
    "x, y, vx, vy, t = orbit(v0 = 8, tmax = 6.0)\n",
    "e = calc_eccentricity(x, y, t)\n",
    "print(e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Trial and Error\n",
    "Determine the period of Jupiter around the Sun.  We need to determine **`v0`**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "e = 0.047, T = 12.752\n",
      "e =  0.048\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1094796d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "planet = data['Jupiter']\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n",
    "\n",
    "x, y, vx, vy, t = orbit(v0=2.82, tmax = 20, x0 = planet['a'])\n",
    "T = calc_period(x, y, t)\n",
    "e = calc_eccentricity(x, y, t)\n",
    "print ('e = {:.3f}, T = {:.3f}'.format(e, T))\n",
    "\n",
    "plt.sca(axes[0])\n",
    "plot_orbit(x, y)\n",
    "\n",
    "plt.sca(axes[1])\n",
    "plt.plot(t, x)\n",
    "plt.plot(t, y)\n",
    "plt.xlabel('t (yr)')\n",
    "plt.ylabel('x or y (AU)')\n",
    "\n",
    "print('e = ', planet['e'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to adjust `v0` so that the eccentricity matches that of Jupiter.\n",
    "\n",
    "#### Exercise:\n",
    "> Adjust `v0` in the above code and rerun.  Try to get `e` to match 0.048."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wouldn't it be better if we had a more *interactive* way of dealing with this?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ipywidgets import interact"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "78611e20738a4d448006bc20a883dfdc",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(Dropdown(description='planetname', index=4, options=('Mercury', 'Venus', 'Earth', 'Mars', 'Jupiter', 'Saturn', 'Uranus', 'Neptune', 'Pluto'), value='Jupiter'), FloatSlider(value=1.0, description='v0', max=5.0, min=1.0, step=0.01), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@interact(planetname=list(data.keys()),\n",
    "          v0=(1, 5, 0.01))\n",
    "def investigate_orbit(planetname='Jupiter', v0=1):\n",
    "    planet = data[planetname]\n",
    "    \n",
    "    fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n",
    "\n",
    "    x, y, vx, vy, t = orbit(v0=v0, tmax = 15, x0 = planet['a'])\n",
    "    T = calc_period(x, y, t)\n",
    "    e = calc_eccentricity(x, y, t)\n",
    "\n",
    "    plt.sca(axes[0])\n",
    "    plot_orbit(x, y)\n",
    "\n",
    "    plt.sca(axes[1])\n",
    "    plt.plot(t, x)\n",
    "    plt.plot(t, y)\n",
    "    plt.xlabel('t (yr)')\n",
    "    plt.ylabel('x or y (AU)')\n",
    "    \n",
    "    plt.suptitle('{}: v0 = {:.2f}, e = {:.3f}, T = {:.3f}'.format(planetname, v0, e, T), fontsize=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimization problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def eccentricity_error(v0, planetname='Jupiter'):\n",
    "    planet = data[planetname]\n",
    "    \n",
    "    x, y, vx, vy, t = orbit(v0=v0,dt=0.001, tmax = 14, x0 = planet['a'])\n",
    "    e = calc_eccentricity(x, y, t)\n",
    "    \n",
    "    return abs(e-planet['e'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00029395911434870747"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eccentricity_error(2.688)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import optimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.6884162092357462"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimize.brent(eccentricity_error, args = ('Jupiter',))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0011009255709062"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimize.brent(eccentricity_error, args = ('Earth',))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Demonstrate Kepler's third law by estimating period of each planet."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Need to determine the velocity v such that we get the correct eccentricity and then\n",
    "$T$, period....\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Earth {'m': 6e+24, 'a': 1.0, 'e': 0.017}\n",
      "==> 0.0150309179528 6.33836025681 1.026\n",
      "\n",
      "Mars {'m': 6.6e+23, 'a': 1.52, 'e': 0.093}\n",
      "==> 0.0925039997167 4.8533070551 1.638\n",
      "\n",
      "Jupiter {'m': 1.9e+27, 'a': 5.2, 'e': 0.048}\n",
      "==> 0.0479967442824 2.8207137533 12.764\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for planetname in ['Earth', 'Mars', 'Jupiter']:\n",
    "    planet = data[planetname]\n",
    "    print(planetname, planet)\n",
    "    \n",
    "    v0 = optimize.brent(eccentricity_error, brack=(2,6), args = (planetname,))\n",
    "    \n",
    "    x, y, vx, vy, t = orbit(v0=v0, tmax = 20, x0 = planet['a'])\n",
    "    \n",
    "    e = calc_eccentricity(x, y, t)\n",
    "    T = calc_period(x, y, t)\n",
    "    \n",
    "    print('==>', e, v0, T)\n",
    "    print()"
   ]
  }
 ],
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  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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