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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# The Big Dipper, Then and Now"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "import ephem\n",
      "from mpl_toolkits.basemap import Basemap"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This notebook demonstrates how the date and epoch arguments\n",
      "to PyEphem\u2019s `compute()` call change the appearance of a constellation\n",
      "over very long periods of thousands of years.\n",
      "It was inspired by the question posed by this GitHub issue:\n",
      "\n",
      "https://github.com/brandon-rhodes/pyephem/issues/61\n",
      "\n",
      "The Big Dipper is made up of eight principle stars:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "names = ['Dubhe', 'Merak', 'Phecda', 'Megrez',\n",
      "         'Alioth', 'Mizar', 'Alcor', 'Alcaid',]\n",
      "stars = [ephem.star(name) for name in names]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plotting their position in the sky is simple\n",
      "thanks to the Basemap extension for Matplotlib,\n",
      "which is particularly easy to install if you are using\n",
      "the [Anaconda](http://continuum.io/downloads) distribution:\n",
      "\n",
      "    $ conda install basemap\n",
      "    \n",
      "Computing where the stars are located at any particular moment\n",
      "and then displaying them can be described in two simple functions,\n",
      "the first dealing only with numbers\n",
      "and the second plugging those numbers into a plot:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def dipper_radec(*args):\n",
      "    for star in stars:\n",
      "        star.compute(*args)\n",
      "    ra = [-degrees(star.a_ra) for star in stars]\n",
      "    dec = [degrees(star.a_dec) for star in stars]\n",
      "    return ra, dec\n",
      "    \n",
      "def plot_dipper(*args):\n",
      "    ra, dec = dipper_radec(*args)\n",
      "    width = 4000000\n",
      "    m = Basemap(width=width, height=width, projection='aeqd',\n",
      "                lat_0=dec[3], lon_0=ra[3])\n",
      "    m.drawparallels(np.arange(-80,81,10))\n",
      "    m.drawmeridians(np.arange(-180,180,10))\n",
      "    x, y = m(ra, dec)\n",
      "    m.plot(x, y, marker='o', linestyle='--', color='b')\n",
      "    plt.title('date={} epoch={}'.format(*args))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## What difference does the epoch make?\n",
      "\n",
      "The epoch makes no difference to the shape of the constellation.\n",
      "Indeed, the epoch also has no effect on almost any of a star\u2019s\n",
      "properties or coordinates \u2014 both `ra` and `dec`\n",
      "as well as `alt` and `az` are completely unaffected!\n",
      "\n",
      "The only coordinates that pay attention to the epoch\n",
      "are the astronometric `a_ra` and `a_dec`\n",
      "because they, and they alone, express coordinates\n",
      "in a fixed coordinate system tied to a specific date.\n",
      "That is why the code above is careful to use `a_ra` and `a_dec` \u2014\n",
      "because otherwise it would not pay attention to epoch at all.\n",
      "\n",
      "The reason that the epoch makes no difference to the shape\n",
      "of the Big Dipper is that the epoch merely choses *how we name*\n",
      "different positions in the sky.\n",
      "It chooses one naming scheme over another.\n",
      "This is clear if we plot the Big Dipper\u2019s current coordinates\n",
      "using the sky coordinate systems of three different dates:\n",
      "8,000 years ago, today (well, the year 2000), and 8,000 years in the future.\n",
      "\n",
      "While the celestial north and south pole\n",
      "were at a different location on each of these three dates,\n",
      "giving all of the points in the sky a different right ascension and declination,\n",
      "that merely tips the Big Dipper in different directions\n",
      "as we name its position according to these different celestial poles:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_dipper('2000', '-6000')\n",
      "show()\n",
      "plot_dipper('2000', '2000')\n",
      "show()\n",
      "plot_dipper('2000', '10000')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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MrkekHeZastCmY/fu3fTHH39YXF+HTCYjb29vXoazCQkJ1LdvX6tXqrOzs2nv3r0m72+X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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb076a26c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mRPbGjRtrLLhsLOnp6diwYQMnsjWUlJRUmfWBK9atW4eRI0eyWu/JGDh32rt3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\nNNpOOhEY/wOu2TD3AzR9kwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb07741cc>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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sPpP2tPPnz8ebb77Zap7t28//y2ABICNjM3bsuKBPaVpjKl6pgaeeesokdvoA\ngJOTE1599VWUl5cbpD6TNtolS17HmTPRSEgA/vwTKCr6b57CQlGz1xYUGNcuFIVCYTKeFlAHDDSF\nnT4N/PTTT+jUqZNB6uJt91gkAiwsgOaioq5ZAxw+DBQV/YRTp4CuXQFfX+DDD4EuXf6dt6g5SwZQ\nVFSsB9Xtx1RmjhsYO3asyazwAoBDhw6hZ8+eeOmll/Rel96NNjQ0Atu3n4dUagVbWwVWrJio9Vjx\n8GEgNBQoLFR/CgoAhQLYuxdoboXiwoXqz7Rpw3H+/B/w8/NrsWwfH1eUl68D0LSLvBY+PoZ5amqK\nKY1pASA5ORlubm4ICAjgWgorLFmyBE5OTgapS69G29IkT2YmYGsb3GiADca4fDnw6qv/LadzZ2D8\neLXHbPCanToBLTmehiAV169fbvPAKl9fLyQlTQTwPgBLAEoAk9G1q3GNaU2NESNGmMRCkQbS09Px\nzTff4PDhw3qvS6+t1tIkz+7d7+Phh4PRtSswfPg/xthSRJgnntC+7qKiIowZMwb37t1rNd+KFROR\nkfHvB0vPnmuxcuVk7SvVI6bmabOzs+Hi4oJBgwZxLYUVhg4dim+++cYgdenVaKXS5ot3d7fEnj36\nrBnw8fHRKGxqQ1d9x473IZFYws5OieXLJxvV6x7A9GaPBw4caLDZVkNgb2+P/v37IzExEY6Ojnqt\nS69Ga2uraPZ7Ozv9h005ceIEfv/9d/z8889t5p0yJbhNIxUKgStXgOnT2VKoHaY2eywQCJCTk4PH\nHnuMaymswDAMYmJiDHJelF5f+axYMRE9e67713c9e67F8uUT9FktAGDGjBn4/vvvWSuvqAhYvRp4\n4QWAKwdhSrPHQUFB8PDw4FoGq2zYsAGHDh3Sez169bRcdj3XrFmDrl27YuXKlayU98ADQFwcsG4d\nMGgQ8N13wLRprBStETKZzKQmbmpqanD37l1MmTKFaymssXXrVr13jQGox0otfdTJ/EQul5NEItFL\n2eHhRD16EL3yCpFCoZcq/kNaWhodOHDAMJUZgOrqavrll1+4lsEqp06doueff56Vsuptr1m7NNkV\nUePGjdPbMZ3BwcDt28C4cYClpV6q+A+mNnusUChw+/ZtrmWwysSJE7F//36912M6/a37uHDhAiz1\naFFOTkBIiN6KN3nc3NzQvXt3k1rpxTAMfHx8UFpaqtehjEl6WpVKBQ8PD5MJ7g2ox7Sm5GkZhkFS\nUhInp84VPj96AAAgAElEQVTpCxsbGxQWFuq9HpM0WgAoKyvj5FjIuDjg7bcBtjewMAxjMh6pgVGj\nRqG2tpZrGawSEhKCc+fO6bUOk+wex8XFYdmyZYiOjjZ43f7+6qWZQ4YAixZF4Px53dZdN2Bqs8cA\nkJGRgbq6Ori5uXEthTWOHDkCmUym1zpM6y6oZ9CgQbh69SondXt4qDc4vPdeBFavPgeVir3N9abm\naYcOHQqpVMq1DFY5dOgQoqKi8N133+mtDpPsHu/Zswdvv/02pxri4s7/y2AB3TbXm9rsMQDk5eUZ\nNPSoIQgJCcHWrVv1WkebRpuRkYH9+/ejoqICAoGAF2tg58+fjy+//JJTDS2tu5ZIDPSOiAcMGDDA\npPbUAoBIJEL//v21shOVSoXExETIZDJ89NFHEImaD8zQQJtG6+vri6ysLDAMg4kTJ6KoqAjTp09H\nRUUF9u7di7q6OlRVVWks0BC8/vrrBtki1Rpsr7s2RU8rEAhQUVHBtQxWcXFxQXJycovj2pSUFKhU\nKnz88ceQyWQYMmQIxGIxXnnlFahUKlhbW7d9OFlLqy6olRVR4eHhpFQq6Y033iCJREI+Pj5UW1tL\nEyZMIJlMRtu3byelUklZWVmkUqlYWSGiDbW1tZzU25QzZ8KpZ8+1BFDjp2fPNXTmTDgRESmVRHv2\nEGm6aCs8PJwuXbqkR8WGJyEhgS5fvsy1DNZ5+umn6cCBAyQWi+mrr76i8vJyGjduHOXl5dHo0aOp\nuLiYtm3bRkKhkFJTU0nRzLI6tLIiipVljCqVihQKBYWHh1NdXR298847JBQKqX///lRVVUWjRo2i\n2tpa2rRpE8lkMrp586buLdMK/fr1o4yMDL3WoQlnzoTTpEnrafToDTRp0vpGgyUiqqwkmj6dqHt3\noqNHidp6xly4cIHCw8Nbz8QzIiMj6fDhw1zLaBcKhYLkcjlFRERQWVkZbd68mTIyMmjixIkUFRVF\nzzzzDKWmptLOnTupuLiY7t27R1KpVOPy9W60rSGXyyklJYWqqqpox44dVFBQQNOnT6f09HQaMmQI\n5efn0/Lly6miooKOHDlCEomE8vPz212fSqUioVDIuafVlMuXiQYPJnrkEaLo6JbzXbx4kSIiIgwn\nzADk5OTQiRMnuJbRIiqVitLT06m8vJyOHz9OqamptHbtWoqOjqbJkyfTpUuXaM2aNZSQkECnTp2i\noqIiEggEtGvXLtqwYYNOdXNqtC2hUqmosrKSqqqq6Ny5c5Sbm0sfffQRJSYm0pQpU+jWrVs0Y8YM\nSk9Ppy1btlBJSQn9+eefVFtbS4WFhS2WKxAIKDAwUG+69YFCQbR3L1HXrkQXLzaf5+zZsxQVFWVQ\nXfrm7t27tGPHDs7qV6lUlJeXR6WlpXThwgVKTk6mL774gq5cuUKvvvoqHT58mFatWkWXLl2iffv2\nUWJiIt28eZNKS0ub7dI2IJfLKTc3VydtrRktQ63McjEMQ62l6xOZTAaBQABLS0vExsaid+/eOHHi\nBJ544gns2LEDixYtwvfff4/Vq1cjNDQUL774Im7fvo2RI0eitLQUffv2hYWFhV7XH7NNbS1gZ9f8\nJoS//voLrq6uGDlypOGF6Ynq6mqcOHEC8+fPZ71sqVQKhUKBnJwc2NnZITk5GR4eHoiNjUVAQACu\nXLmCfv36obCwEIMHD0ZtbS2CgoJgaWkJHx8fuLq6wtHRsV3HsGRnZ2PevHkIDw9vt36GYUBEzb6Y\nN1qjbQu5XA6hUAi5XI6MjAy4urri+vXrqKqqwu7du/HZZ5/h4MGDWLBgAc6fP49Zs2bh77//xoQJ\nE5Ceno7hw4ejoqICPXr0gFKpNMw+SB34448/4Ovri+HDh3MthTUqKyvx9ddft3oCxP1UVVVBqVSi\npKQEDMOgsLAQVlZWyM3Nhb29PTIyMuDs7Iz8/Hz4+fnB0tIS3t7esLOzg7u7O1xcXODs7Ax3d3fY\n2trq7WykzMxM+Pn5tXsprUkabUuIRCJYW1vD1tYWRASRSITKykqoVCrk5eXB0dERycnJ8PHxQUxM\nDHr16oVLly5h9OjRiI6OxsSJE5GQkIDg4GCkpaVh2LBhKCwsRN++fVFVVYVu3bpBJpPB3d0dDMMY\n5DXM0aNAcnI0nn7aBkOHDtV7fYZAJpNBLpdj27ZtmDdvHkQi0b8exDU1NZBKpRCJRJDJZKipqYFE\nIoGTkxOsrKzg6ekJa2truLu7w9raGh4eHrCxsWn8t4uLC6e/b/Lkydi1axd69OjRruvNymg/++wz\nKBQKrc9WkUqlkEgkkEgkqK6uBhGhpKQEtra2yM3NhYuLC9LS0tC5c2ckJiYiICAAcXFxGDJkCFJS\nUvDQQw8hIyMDDz74IHJzc9GvXz+UlJSgR48eKC8vh6+vL6qrq+Hj4wORSARPT09IJBK4urpCLpfD\nxcUFKpWq8VjOpt36v/4CXn21Bt27A99/74wBA1htslZRKBRQKBSQy+WQy+VQKpWQSqUgosZjPcRi\nMSwsLCASiUBEEAqFsLCwQGVlJaysrFBeXg4bGxsIBALY2dlBIBDA09MTVVVViImJwVNPPYWAgADU\n1dXB19cXMpkM3t7eUCqV8PT0BMMwcHNzg7W1NW/WXwsEAgBA586d23W9WRltRUUFnJ2dDbYQQSqV\nQiaTQSqVQiwWQ6lUQigUgmEYVFZWwsbGBqWlpXByckJxcTFcXV1RUFAAd3d35ObmwsvLC9nZ2fD2\n9kZmZiZ8fX2RkZGB7t27IysrC71790Z2djYqK0VISnocd+5MxwMPJOOVV7IgEmXA39+/sStYUFAA\nPz+/Vv/t4+OD/Pz8f/2Zm5sLX19fZGdnw8/PD1lZWejWrRuysrLQo0cP5OXloVevXsjPz0dQUBCK\niorQvXt3CAQC+Pv7o7S0FN26dUNFRQW6deuGmpoadO3aFbW1tfD29oZUKm3cKtmpUydYWFg0dhv3\n7NmDWbNmGexIDUPxf//3f/D29sa8efPadX1rRsuPx5YWrFixAiEhIZg82TBxi21tbWFra9tmUHRt\nUalUUKlUUCqVUCqVOHLkCBYt6gkvLxm2bu2LP/4YiL171ZutZTIZbGxsIJVKYWtrC4lEAltb22b/\n7eDgAJlMBgcHB8jlctjZ2UGpVMLW1hYqlQo2NjYgosaHnr4n8gQCgd53xXDB0qVLUVBQoJeyTc5o\nv/jiC3h6enItQ2caDpBu6A7a29vD2dkZgYGd8O23gFIJWFr6cqxSd4KCgiAWi7mWwTopKSn44Ycf\nsHv3btbLNjmjHT9+PC5dugQvLy+upbCKVCr913iuNQfIxvlJhqKiosLktucBwPDhw6FSqfQSTsek\njFapVOL8+fMmZ7CA2vO29Z8vEABz5kQgI+MccnON+5DsBgIDAyGRSLiWoRfWrFmDU6dOsX4wl0nt\npxUIBCYVR7cpEomkzck1Z2cgL+/8vwwWMM5DshsQCoWsdo9DQyMwadJ6jBmzEZMmrUdoaARrZWsD\nwzDYtWuXXrr+JuVpXVxc9B6fhyssLS3b9LT29oCvrxXS0/+bZqz7eBvee7NBS6c0Atz0Mg4dOoQx\nY8bgifacINcKJuVpr127htWrV3MtQy/cP6ZtCS7PT2oPYrGYteBuLZ3SyFUvY+nSpe1+T9saJmW0\nw4cPx1dffcW1DL2gyZgW4Pb8pPbQpUsXKBTNP2i0xdiihdy5cwdnzpxhvVyT6h7v27cPVlZWWLFi\nBddSWEcqlWr0zpQvR3c2IJVKUVNTw0pZxtbLCA4O1st7bpMy2tmzZ8Pd3Z1rGXpBU08LaHZ0p7Hg\n5eWFxMREVspasWIi7t1bh5ycfx8Qvnw5NweEK5VK7NixA2PHjmX1tY9JGe369evxyiuvYPTo0VxL\nYR1Nx7R8Q6VSsRaRccqUYJw6BZw58z569eK+l+Hg4IC33noLVVVVrMZ2Nqm7YP369QgICOBahl7g\n075gbXBzc2M1wmdSUjB++CEYxvLmLzQ0FJ6enqwarUlNRM2ZM6fN8JN8xVQ9LcMwrEXzrK0FqquB\nCUY05zZ//nzWz5QyGaOVy+X49ddf4erqyrUUvaDJe9r7qawEcnL0JIglnJycYG1tzcqN7egI3LkD\ncHCEU4skJyfjzp07rJZpMkZbUlKCxYsXcy1Db0gkEq27yKdPA2vX6kkQi4jFYtZe+xgbo0ePhoeH\nB6tlmozROjs7G+RAX66wsrLS2tMGBaHZ1VHGRpcuXUx2WFNTU4OwsDBWyzQZo42NjcVnn33GtQy9\n0R5P26sXkJamJ0EsIpFITNbTBgYGYuDAgaz+PpMx2v79++P999/nWobesLKy0joImacnoFIB5eV6\nEsUS3t7erC2wMEaioqJYPYfXZIz22LFjOHnyJNcy9IJKpYJcLtfaaBmGH962IfZUe8nNBX78kUVB\nLPPcc8+hrKyMtfJMxminTJmCOXPmcC1DLzQN/6ItEycCxr7H3MvLSydPe+QIEBPDoiCWSU1N7TDa\n5vjss89YWw5nbCiVynYvQNi8GTD2BWIKhUInT3v0KDB7NouCWGbMmDGsdo9N5m39smXL0LdvX65l\n6AVdPC0f8PDwaPdSxsxM9btoY34wlZeXIzc3l7XyTMbTrly50iQDhAEw2ZnVBhoiT7aHo0eB554D\njHmx2ACWA1WbhNHK5XJ8+eWXJhc7tymmuISxAXd393Z72qNHgeefZ1kQy1hYWCAlJYW98lgriUMq\nKiqwbt26tjPyFFP3tADaPabdtQsINvJdiE5OTujTpw9rp96bhNHa2Njgiy++4FqG3tB1TBsbCxQV\nsSiIZTp16tRuTztyZOvhZI2F8vLyxmNUdMUkjDY5ORnffvst1zL0hkKh0Gn72vbtwPnzLApiGQsL\ni3aPafnC0KFDWTtxwCQGSgEBAXj77be5lqFXdPG0xr7AwsXFBdXV1VzL0CtisZi1PdEm4WkvXbqk\nlwBaxoKuY1pjN1pLS0tWN8IbI3379kVhYSErZZmEpx0xYoRJnN/TGrrMHhu70drZ2TWeV6tpjyIv\nD+jWTc/CWKZjTNuEX375Bbdv3+Zaht6Qy+U6XZ+ZGYHbt9dj9Ghuo+63ho2NjcYzyMnJwKhRAJ+c\nc0BAAAoKCljpUZiEp50+fTr69evHtQy9ocuJ86GhEVi37hxUqs2IqLdVYzzbx97eHjU1NbCzs2sz\n77FjwMyZ6g0RfKEh8ohSqdT5nbtJeNpt27ah3Nj3n+mALp7W2KLut4SNFjFijH2tcXMwDIOuXbsi\nOztb57J472mJCIsXL4afnx/XUvQGwzDtfjq3FnX/rbeAq1eBgIB/f0aNAvRwmkWr2Nvbo7q6us0T\nD5OSgJoaYMQIAwljEXt7e1biH/PeaCUSCbZs2YIxY8ZwLUVv6HJAVWtR99euBTIy1Avuc3KAe/fU\n73NdXZs32lOngLq6f4zb2xvQcotvi1hbW2t0Qx89CsyaxV69hqRr165ISUlBz549dSqH90Yrk8nw\n8ccfcy1DrzQ9EV5bVqyYiIyMdf/qIjdE3ffyAry81KuKNCEnB4iI+MfIq6sBPz/1ftZhw/6bX6XS\n3LgcHBxQWVnZZj53d+CZZzQr09iws7NjZREJ7402Pz8fe/fuxfDhw7mWojekUmm7u1Vsnu2zfLn6\n00BdnTpqhK9v8/lHjFAvnwwIAPz9//HQc+YA98futra2bnXxQdPT7c+eNe7T7VuiS5cuOHHiBMaO\nHatTObw3WhcXFyxveieZIBYWFjqtptHX2T729sADD7Scfv06UFj4j2fOyQHi4oBnn22uLHts3+6C\ngQP/Pb729ATOnjWuc2fbi52dHSvhVHlvtPHx8UhPT0efPn24lqI3ZDIZqwc4GQorK7WH9fcHHn+8\n9bzW1tZwdVX9pwsulQIjRrQ0A/4+r4zWy8sLcXFxmDNnjk7LUnlvtD179sTgwYO5lqFXdBnT8gUH\nBwc89lgCnnuu17++FwqBadOM69zZ9sIwDPr06QOFQqGT0fJwDu7fXLx4EfHx8VzL0Cu6zB7zBWtr\na9ja2v7nexcXwM7OuM6d1QWFQoF0HSPI895oH3roITz22GNcy9Ar5uJpS0pKmk3j2+n2rREYGAgn\nJyedyuD9nXDkyBEsXryY1aMEjQ1dZo/5gpWVFRwcHJpN49vp9q1hbW2N2NhYdO/evd1l8N5on3zy\nSQQFBXEtQ69YWlqahactaiW8Bp9Ot28NHx8fnT0tr7vHRISdO3dyLUPvSI092jgLWFtbw9HRkWsZ\nesfZ2Rnnzp3TqQxeG21dXR1Wrlxp0jGBAfPxtGyFYzFmOnXqhEGDBulUBq+NtrKyEkePHuVaht6R\nSCRcS9A7VlZWcHZ25lqG3nFzc8Off/6p0/8pr43WwsICr776Ktcy9I45eForKyuIRCLWojsYMxMn\nTtRpMzyvjTYnJweXLl3iWobeMYfZYwDw9PQ0+VhRAJCXl4c7d+60+3peG62bmxue4euWDy2wtLRk\nLZKfMaNQKEw+KiOgXlvQpUuXdl/Pa6NNSEjArVu3uJahd8zF07q5uWl9Bi8fEYlEOs0g83qgFBAQ\noNMTiy+Yi6dVqVQoLy+Ht7c311L0SlBQEHx8fNp9Pa8fa9euXUNWVhbXMvSORCIxCw/k6uqqVawo\nvmJjY4N9+/a1+/o274R79+5h1apVKCgowMmTJyEUClFWVmYUEwYDBw7U+Z0XH7CysjILT0tELa4/\nNiXc3d0xdepUAOogDgKBAGfPnkV8fDw+/vhjnD17ttXr2zTanj174rHHHkOnTp1w+fJlyOVyPPHE\nEygqKsL48eNRVlaGzZs3o6amBlFRUZDL5Tqd6q0NZ8+eNYuJi7q6OrMY07q4uLS4/pivCIVCVFRU\nIDY2Frdv38aBAwcQFhaGlStX4osvvsD+/fsREREBiUQCmUyGWbNm4aGHHmq1zDbHtFZWVo0ztNu3\nbwegngACgM8//xxubm6wtraGnZ0dNmzYgNOnT8PLywtFRUWYPn06Tp8+ja1bt2Lt2rWIjIzE6NGj\noVAoWOkGPfroo/BtKdaJCWEuntbCwgKFhYUYMmQI11I0pqamBlKpFCUlJZBKpSguLoZcLkdeXl7j\nqQlOTk7w9vaGo6MjBg4cCAcHB3z66acYN25cu9Yh6zQR1bD5fPXq1QCACxfUsXRLS0thaWmJdevW\nwdLSsvFUtC1btmDUqFHw9vZGSUkJnnzySZw/fx4bN27Ehx9+iNOnT2P69OkoLCxsMyQqEeHYsWOY\nMWOGLj+BF5jLmNbJycmoxrQqlQpVVVUQCoWoqalBWVkZpFIpCgsLQUTIysqCn58fqqqq0L9/f9TW\n1qJ3795QKBR45JFHYGVl1eLusyNHjsDT0xOPPvqo1rr0MnvcsBZ49OjRAID169cDQOM0d2VlZaMR\nKxQK+Pj4QCwW49SpUwgODsaUKVNw8eJFjB07FlevXsWKFSuwa9cu7NmzB6+//jqio6MxaNAgTJ06\n1SxuZisrK7P4nZaWlsjNzdV7PSqVCkKhEJWVlVAqlcjLy4O9vT3u3r0LT09P3Lx5EwEBAbh27Rom\nTZqEe/fuITg4GAKBAEOGDEHnzp0RFBQEhmHavfRyypQp7Y/VTUQtftTJ3KBUKqmkpIRqa2vp/Pnz\nVFFRQZ999hkVFRVRSEgIxcTEkLe3N2VkZNDw4cMpPz+fXnzxRRIIBPTRRx9RVVUVHTlyhMRiMd2+\nfZvkcjmJRCLOfo8uHDx4kJKTk7mWoXeSkpIoNDRU6+tUKhWJRCLKz8+nwsJCio6Oprt379Lx48cp\nNjaWvvrqK7pw4QKtWrWKjh07RrNnz6bQ0FB677336Pr16/TDDz/Q3bt36eLFiyQQCCgzM5Pkcjmp\nVCo9/Eo1x44do2+//bbF9Hrba94uW0ogjo22LXJzcykiIoKUSiWVlZWRSCSi69evU1lZGe3fv5/y\n8/Np/fr1lJ6eTrNnz6akpCR6+OGH6c6dOzR69GhKTU2ll19+mXJycmj9+vVUVFREP/zwA1VUVNBf\nf/1FIpGIkpOTSSqVUllZGalUKr3+J7bG4cOH6e7du5zUbShUKhUlJyfTtm3bKCcnh0pLSykmJoZy\ncnLojz/+oJSUFPrhhx/o5s2b9NFHH1FkZCQtXbqU/vzzT5o2bRpduHCBXnvtNYqOjqaPP/6YkpKS\n6MCBA5STk0NXrlyh8vLyRmNUKpVc/1zKysqie/futZhukkYbExND27Zt0/o6uVxOpaWlJBKJKC4u\njsrKyujUqVOUn59PO3fupPT0dFqzZg0lJiZSSEgIxcXF0cSJEyk6OppGjRpFt27doqeffpoSExNp\n0aJFlJqaSmvXrqWsrCz66quvKD8/nw4cOEDFxcX0xx9/UFlZGYWFhVFVVRXFxcVRbW0tZWZmNj4M\nlEolyWSyVjX/9NNPlJaW1t6mYgWVSkVyuZxkMhlVVlaSWCymvLw8EgqFlJKSQhUVFXTjxg0SCAQU\nFhZGeXl59Ntvv1FGRgbt3r2bkpOTacuWLRQfH0+rV6+m2NhYWrhwIUVGRtKMGTPo4sWLNGbMGPrw\nww/plVdeoZs3b9KaNWsoOTmZtm/fTllZWXTs2DEqKiqiyMhIqqqqooyMDJLL5aRQKDhtm/aQlJRE\nS5cubTHdJI02ISGB4uPjDVqnTCYjiURCBQUFJBQK6fbt21RaWkoXLlyg/Px8OnToEGVlZdHOnTsp\nLS2NPvnkE0pOTqb33nuPEhIS6PXXX6dbt27Riy++SDExMTR16lS6du0aBQcH09WrVyk4OJiioqJo\nwoQJFB0dTU8//TTFxsbSiBEj6OTJk/Tyyy9TXFwcLVq0iOLj4+n111+n27dv07Jly/715/Llyykh\nIYFWrFhBCQkJtHLlSkpISKA333yTbt++TUuXLm0s5+bNmzRv3jy6ceMGzZ07l2JjY2nmzJkUHR1N\n06dPp2vXrtGECRMoPDycRo8eTdeuXaMpU6ZQdHQ0zZ49m27evEkLFiyg+Ph4WrlyJSUlJdH69esp\nNTWVvvzyS8rOzqYDBw5QYWEhhYaGUllZGUVHR5NQKKS0tDSSSCRUXl5OKpWKSkpKaPPmzQb9P+WK\n6upqio2NbTG9NaNlqJVFEgzDUGvpXPL7779DoVBg1qxZXEthBSJqfL8tkUhgY2MDoVAIR0dH7Nix\nA1OnToWtrS28vLyQl5cHPz8/ZGdnIzAwEFlZWY1/du/eHZmZmejRowcyMjLQo0cPpKenIygoCOnp\n6ejduzeys7PRo0cP5OXlwd/fH8XFxejatStKS0vRuXNnVFVVwd3dHTU1NXB1dYVMJmPt8KjWqKqq\nwm+//YYFCxbotR5jQKVSYfz48bhw4UKzr/MYhgERNdvgvDXaiIgI+Pv7IzAwkGspemf//v0YO3Ys\n/P39uZaiVyQSCTZu3IgtW7ZwLcUgXL16FaNGjdLaaHn7HuHOnTsoLi7mWoZBEIvFZvHKx8rKyiwW\nyzRw+PDhxoVK2sDbO6Fbt27o3bs31zIMgrW1tdkYbV5enlkEsgOAxYsXo0ePHlpfx9s74fr16xCL\nxVzLMAh1dXVmYbQA0L17d6PYjGIIoqKicPz4ca2v4+1+2r59+5rFXlpAvZXLXIy2oqIC1dXVsLOz\n41qK3nnyySfbFfuLl3eCSqVCWFiY2dzI5rLLB1APe0w9iF0D+fn5+PTTT7W+jpd3fU1NDZ566imz\nuZHNydNWV1ejoqKCaxkGoV+/flixYoXW1/HyThCJRCZ/Ul5TzGX2GAB8fX3NomsMqDdIzJ8/X+vr\neHknyOXyxh1E5oA5eVqRSGQW0SsA9VbEb775RuuJN17eCRUVFUhNTeVahsEwpzGtt7e3zgdU8QWG\nYbBp0yat72VeGq2FhUWbITlMCRsbG7Mx2rq6OrM406eBTz/9FAEBAVpdw0ujLSoqQl5eHtcyDIZY\nLDaLcDOA+pQBUz5r+H6OHDmC3377TatreDm3bm9vr9OhvHzD1tbWbDytTCaDQCDA0KFDuZZiEBYs\nWKB1MDteetqcnByUl5dzLcNg1NbWms1ElJubG7y8vLiWYTD+/vtvbNq0SatreOlpO3Xq1K41m3zF\nzs7ObDytSqVCeno6Hn/8ca6lGITg4GA8/PDDWl3Dy8d3amqq2aw7BtSe1lzGtC4uLujatSvXMgxG\nRUUFQkJCtLqGl0br5eVlNuuOAfPytACQnJzMtQSD4efnhx9//FGra3hptElJSWazE4SIzGpFlKOj\no9avQPiMjY0Npk6dipqaGo2v4d2dIJPJ0Lt3bzg6OnItxSAQEezt7bmWYTAsLS11OnCZj5w5c0ar\nGWTeGa1UKkVGRgbXMgyGUqmEXC7nWobBsLOzQ8+ePbmWYVDWrVuHyMhIjfPzzmhra2sxbNgwrmUY\nFHNZQA+o30mbw0HhTdm2bRtGjRqlcX7eGW1dXZ1ZrYYyN09rZWWFBx54gGsZBuXgwYPYtWuXxvl5\n955WIpFg4MCBXMswKObkaa2srJCSkgKJRGI2v3vhwoWN519pAu88rVAohEAg4FqGwVAqlVAoFFzL\nMCjm9lC+ceMGFi9erHF+3nlahUJhNlEYGzAXj9NAbm6u2cSJAoDHHntMq1VRvPO0lZWVqKqq4lqG\nwVAoFGY1pgXUQfuM6ZxafVNTU4ORI0dqnJ93RgvALE4VaIq5eJwGCgsLzWoI5OnpadqvfEpLS1FX\nV8e1DIOhUCjMbkwbFBRkNotnAHVQh3Hjxml8oDbvjNbS0tKs1h0zDANbW1uuZRgUgUCAwsJCrmUY\nlCtXrmh8MjzvjLa4uLjxdDlzwBzHtIGBgWYVvQIA3n77bfz+++8a5eXd7LGNjQ08PDy4lmEwGIYx\nq7XHgHq7GsMw6NWrF9dSDMb27ds1Xn/MK09LRCgsLDSbCPSAOlysuXlaX19fdO7cmWsZBmXfvn1Y\nu3atRnl5dfeLRCJ0797dbLapAepJCnObPRYKhSgtLTWrRRYLFy7U2Bnx6u6Xy+Vm9Y4WME9P6+Pj\nYw3Os1kAAAL+SURBVFbRKwDg1q1bmDx5skZ5eWW0IpHIrDZIA+bpaUUiEe7evcu1DIMyYsQInD17\nVqO8vOoey2QyrXb4mwIymczs3tN6enqaTWSSBurq6tC9e3eUlZW1mZdXnlYsFmv8LstUMEdPK5VK\nzS56hZOTE/Lz8zV6WPHKaKVSqVlFYQTMc0zr5uaGoKAgrmUYFIZhMGTIEGRlZbWZl1dGKxaLzW6C\nwhw9rUKhMLvoFQAQHx+v0bp6XhmtVCqFVCrlWoZBMccxrZOTE/r27cu1DIMzb948nDx5ss18vDLa\nuro6eHt7cy3DoFhaWprd2mOGYRAbG8u1DINz8OBBTJ8+vc18vDNac/M65uhp7e3tMWjQIK5lGJzP\nP/8cGzdubDMfr175SCQSs1p3DJinp7WyssK1a9cwZ84crqUYlHfeeUejfLzztOaGVCo1q11NAGBt\nbW02R1025cKFC3j22WfbzMcro5VKpXB1deVahkGxtLQ0q9ArgNrTxsTEmN2rrkmTJuH48eNt5uOV\n0ZrTmTYNyGQyqFQqrmUYHG2Cd5sKJSUlGm1H5I0FKBQKMAyj9anZfMccPS0AJCYmQigUci3DoPj4\n+CA1NbXNVVG8Mlpz9DjmOKYFgOHDh5vdw4phGAQFBaG0tLTVfLwxWqFQCHd3d65lGBwrKyuzu3kB\n9cHhmiyeNzUyMjLaDLXDG6NVqVRmt/MDUHtac+xhPPjgg3BycuJahsF59tlnER4e3moe3rynraqq\nMrtgX4Da02pzzoupkJmZiYCAAHh5eXEtxaCcPHmyzcU0vDFaIgLDMFzLMDgSicQsPW2/fv3M8iG9\nYcOGNhcQ8aZ7XFlZaXbvaAHz9bR5eXnIycnhWobB2bRpU5uHcbXpaQUCAfLy8hrPV+EqEiLDMGbp\nac11TNurVy+z2RxCRCAiZGVlISwsDIcOHWo1P9Pa5A7DMOY389NBB0YCETXrpVo12g466MD44M2Y\ntoMOOlDTYbQddMAzOoy2gw54RofRdtABz+gw2g464Bn/D82vK4ojn1wGAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb06ec82c>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# What difference does the date make?\n",
      "\n",
      "The date \u2014 the first argument to `compute()` \u2014\n",
      "is what can change the shape of a constellation,\n",
      "because the stars of our galaxy gradually change\n",
      "their relative orientation to each other\n",
      "as we all swing slowly around the galactic center\n",
      "in our different orbits.\n",
      "\n",
      "When checking out the way a constellation shape changes,\n",
      "there are two approaches.\n",
      "\n",
      "The first approach is to use the modern J2000 coordinate system\n",
      "for each of the plots.\n",
      "This means that the \u201cright side up\u201d direction\n",
      "of all of the plots stays the same,\n",
      "so all of the motion between one plot to the next\n",
      "is really truly the motion of the stars themselves.\n",
      "\n",
      "To see much motion, we will need to go much farther\n",
      "back in time and ahead in time than we did before.\n",
      "We can try 50,000 years in each direction:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_dipper('-50000', '2000')\n",
      "show()\n",
      "plot_dipper('2000', '2000')\n",
      "show()\n",
      "plot_dipper('50000', '2000')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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4Om8mPWra9PR0GjZsGOtZBvQhNDSUlTWs+iAWizlb5kdEdOrUKfr00085kZ2X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\nx2Y10hYUFEClUvGmvnFjzp8/j8zMTLZlGATf1rQAEBISgn/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       "text": [
        "<matplotlib.figure.Figure at 0xb0885ecc>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mRPbGjRtrLLhsLOnp6diwYQMnsjWUlJRUmfWBK9atW4eRI0eyWu/JGDh32rt3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\nNNpOOhEY/wOu2TD3AzR9kwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb07689ac>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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CQkpMTLRYjkajoT/++IO1B97ly5epuLiYFVlE2iipffv2WfRQEYlEJBQKaciQIZScnPyc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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb080deec>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "But if we want to imagine how the constellation\n",
      "looked in the sky of its time,\n",
      "we probably want to switch to the coordinate system\n",
      "of that distant (or far-future) era.\n",
      "(If, indeed, the constellation would still have\n",
      "been recognized as such \u2014 eventually the motion\n",
      "will carry these stars into groupings with\n",
      "stars that today belong to other constellations!)\n",
      "\n",
      "Switching to the coordinate system of the other era\n",
      "will rotate the Dipper left or right in our diagram,\n",
      "making it more difficult to see which stars have moved\n",
      "and in which direction.\n",
      "\n",
      "But the other era\u2019s coordinate system\n",
      "will give us an idea of whether the Dipper\u2019s\n",
      "stars were up closer to the pole,\n",
      "or down closer to the equator,\n",
      "in the sky in which they appeared.\n",
      "\n",
      "If only PyEphem could compute in far-past\n",
      "and far-future coordinate systems correctly!\n",
      "\n",
      "## Far-past and far-future epochs are broken\n",
      "\n",
      "If we try computing the location of the Big Dipper\n",
      "in the skies of the far past or future, we get nonsense:\n",
      "50,000 years ago PyEphem thinks the Dipper was in the southern sky (!),\n",
      "and 50,000 years in the future it places it up at the north celestial pole:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_dipper('-50000', '-50000')\n",
      "show()\n",
      "plot_dipper('2000', '2000')\n",
      "show()\n",
      "plot_dipper('50000', '50000')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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EmZHdu3cjMzNTahkWYc6cOYWmy85ob9++bTdG++GHH+LNN98sNE9SEtCwoYUE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\nIf4hCa0QhpHQCmEYCa0QhpHQCmGYDwLh+mqRpvxaAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb0734e6c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mRPbGjRtrLLhsLOnp6diwYQMnsjWUlJRUmfWBK9atW4eRI0eyWu/JGDh32rt3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\nNNpOOhEY/wOu2TD3AzR9kwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb0be368c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7QywWw8PDA3w+v2o3PANYtmwk7OwyAKx/6XizZiuxdOlHllHKANq1a4f69etb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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb0734e2c>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What could be causing such chaos?\n",
      "\n",
      "Let us plot the position of Polaris,\n",
      "which is currently quite near to the north celestial pole.\n",
      "Its path over 26,000 years should be the smooth circle\n",
      "caused by the precession of the Earth\u2019s axis:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "polaris = ephem.star('Polaris')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "width = 9000000\n",
      "\n",
      "m = Basemap(width=width, height=width, projection='aeqd',\n",
      "            lat_0=70.0, lon_0=280.0)\n",
      "m.drawparallels(np.arange(-80,81,10))\n",
      "m.drawmeridians(np.arange(-180,180,10))\n",
      "\n",
      "for year in range(-13001, 13000, 500):\n",
      "    polaris.compute(str(year), epoch=str(year))\n",
      "    x, y = m(degrees(polaris.a_ra), degrees(polaris.a_dec))\n",
      "    m.plot(x, y, marker='o', linestyle='--', color='b')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2uC4QCMDj8XD58mUkJSVh1apVCAsLw/3799HQ0GCznS4lJQWenp4m22g0Gmg0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\nT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       "text": [
        "<matplotlib.figure.Figure at 0xb06ecd0c>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So far, so good!\n",
      "\n",
      "The path of Polaris in the above diagram\n",
      "is exactly what we would expect from precession,\n",
      "and matches other diagrams that show the phenomenon.\n",
      "\n",
      "But everything goes haywire\n",
      "if we step out to many tens of thousands of years\n",
      "in the past and future:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "width = 18000000\n",
      "\n",
      "m = Basemap(width=width, height=width, projection='aeqd',\n",
      "            lat_0=70.0, lon_0=280.0)\n",
      "m.drawparallels(np.arange(-80,81,10))\n",
      "m.drawmeridians(np.arange(-180,180,10))\n",
      "\n",
      "for year in range(-50001, 50000, 500):\n",
      "    polaris.compute(str(year), epoch=str(year))\n",
      "    x, y = m(degrees(polaris.a_ra), degrees(polaris.a_dec))\n",
      "    m.plot(x, y, marker='o', linestyle='--', color='b')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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NoaGhuHv3bhspS6FQ4NKlSw6LkdbacHbqNMrp7DC1Wg2xWGxVAmJZFgEBAZDJ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\n4v8Y3hrtW7zF/zH8PySf4Mcg9mtRAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb07644cc>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Even though the calculations inside PyEphem\n",
      "seems to be stable over what look like two complete precessions\n",
      "of the Earth\u2019s axis, outside of that safe range it goes crazy\n",
      "and stops returning stable results.\n",
      "\n",
      "Well, drat.\n",
      "Which `libastro` routine is at fault?\n",
      "    \n",
      "This was going to be such a simple notebook,\n",
      "involving only Python code.\n",
      "But now it appears we have a bug on our hands,\n",
      "and need to dive down into the lower layers\n",
      "to see whether it is the precession or nutation\n",
      "algorithm that is dying.\n",
      "\n",
      "Thank goodness for `ctypes`!\n",
      "\n",
      "Here goes:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from ctypes import *\n",
      "cdll.LoadLibrary('../ephem/_libastro.so')\n",
      "lib = CDLL('../ephem/_libastro.so', use_errno=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lib.precess.argtypes = [\n",
      "    c_double, c_double, POINTER(c_double), POINTER(c_double)\n",
      "    ]\n",
      "\n",
      "ra = []\n",
      "dec = []\n",
      "\n",
      "ra_double = c_double()\n",
      "dec_double = c_double()\n",
      "\n",
      "epoch1 = ephem.J2000\n",
      "year = arange(-50001.0, 50000.0, 100)\n",
      "for y in year:\n",
      "    epoch2 = epoch1 + 365.25 * y\n",
      "    ra_double.value = 0.0\n",
      "    dec_double.value = 0.0\n",
      "    lib.precess(epoch1, epoch2,\n",
      "                byref(ra_double), byref(dec_double))\n",
      "    ra.append(ra_double.value)\n",
      "    dec.append(dec_double.value)\n",
      "\n",
      "plot(year, ra)\n",
      "show()\n",
      "plot(year, dec)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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V+F97Lc8VcD+51tdb2ycJjBV/v5MX1vZpa+O7fpDsgJ49OxeT9iOq+APAhAns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\ncds+YR7Zsiz+QVi+3Fo+Dq+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       "text": [
        "<matplotlib.figure.Figure at 0xb08cb06c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "[<matplotlib.lines.Line2D at 0xb05eeccc>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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EwHHHATff7M2qcWMxOM3h7iQMYjFklCA+QnPus9liANzHGYwWA8DuJDdzOXiN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\ngiAIQhtEGARBEIQ2iDAIgiAIbfj/6r2CXoQZ0XgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb0630fec>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lib.nutation.argtypes = [\n",
      "    c_double, POINTER(c_double), POINTER(c_double)\n",
      "    ]\n",
      "\n",
      "deps = []\n",
      "dpsi = []\n",
      "\n",
      "deps_double = c_double()\n",
      "dpsi_double = c_double()\n",
      "\n",
      "epoch1 = ephem.J2000\n",
      "year = arange(-50001.0, 50000.0, 100)\n",
      "for y in year:\n",
      "    epoch2 = epoch1 + 365.25 * y\n",
      "    deps_double.value = 0.0\n",
      "    dpsi_double.value = 0.0\n",
      "    lib.nutation(epoch2, byref(deps_double), byref(dpsi_double))\n",
      "    deps.append(deps_double.value)\n",
      "    dpsi.append(dpsi_double.value)\n",
      "\n",
      "plot(year, deps)\n",
      "show()\n",
      "plot(year, dpsi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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O9c/9+jVu/Y10yCHw0Y9ms+wNNoBvfSubZTejTTaBI47Ieytay7bbFqZ7ctO8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\nLVw798ADrXt/oKyoCU5EpEb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       "text": [
        "<matplotlib.figure.Figure at 0xb05fc22c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "[<matplotlib.lines.Line2D at 0xb056154c>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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W2M7MeuA7F8wqUn4WcKyZ9TCz7YHBwBPOuTeA98xseNAp4WthGTOLttIOB+an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\nEZFMKACJiEgm/j/MdVk4s+7u+QAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb05b122c>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And that settles it!\n",
      "\n",
      "Nutation looks quite stable over long periods:\n",
      "it stays within its own defined little range\n",
      "of tiny numbers, without going wild.\n",
      "\n",
      "But precession, once it gets out past 10,000 years\n",
      "and 20,000 years ahead or behind the present,\n",
      "goes completely wild and cannot be trusted.\n",
      "\n",
      "I supposed I should add some sort of guard statements\n",
      "to PyEphem so it will not try computing out that far,\n",
      "so that other users do not run into problems.\n",
      "\n",
      "What about PyEphem\u2019s replacement, Skyfield?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from skyfield.api import JulianDate\n",
      "from skyfield import precessionlib"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "years = arange(-50000, 50000)\n",
      "jd = JulianDate(tai=(years,))\n",
      "plot(years, precessionlib.compute_precession(jd.tdb)[0][0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "[<matplotlib.lines.Line2D at 0xb07643cc>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Un9w6HjAnhjxiDNx2Ro0xqFZQ3ESPIBuJ9+F1r6M5VqoORwwJYwy6dr1h6aq6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\nrFkztCn82AAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb0a0552c>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Wow!\n",
      "\n",
      "Skyfield, I believe, uses very modern precession formulae\n",
      "derived from more recent IAU resolutions\n",
      "than those that power PyEphem.\n",
      "Yet we see the same limitation:\n",
      "once we are out past 20,000 years before or after the present,\n",
      "the formula goes unstable and ceases to predict accurately.\n",
      "\n",
      "So maybe Skyfield needs a similar sanity check\n",
      "to protect users who might want to look too far out!\n",
      "\n",
      "I will update the issue with a link to this notebook."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}