notebooks/proper-motion.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:a710d0b33d829b1a65d8c07d455fd9d14995ae425cf592fc497d7f9c3b9d01df"
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In my [asterisms](https://github.com/digitalvapor/asterisms) project I want to see what the night sky used to look like for ancient civilizations as well as what it is going to look like in the future. This notebook was inspired by a paper I found by Matt Jones and took some unexpected turns. I documented the whole process, even my mental wrangling of celestial concepts, because hopefully it helps some amateur astronomers to understand by the following examples.\n",
      "\n",
      "My initial goal is to view the stars in the far-flung future, and in the ancient past. To roll back time for constellations, we'll need to consider the proper motion of the stars. I found a recent [paper](http://www.unc.edu/~marzuola/Math547_S14/Projects/M_Jones.pdf) by Matt Jones (2014) on the subject and wanted to try it out for myself."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "%matplotlib inline\n",
      "import numpy as np\n",
      "from mpl_toolkits.mplot3d import Axes3D"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def alphaUM(time):\n",
      "    originalX = -61.3\n",
      "    velocityX = -12.9\n",
      "    originalY = 46.7\n",
      "    velocityY = -20.5\n",
      "    originalZ = 96.7\n",
      "    velocityZ = -9.65\n",
      "    KMtoLY = 1.05702341*10**-13\n",
      "    newX = originalX + velocityX*KMtoLY*time\n",
      "    newY = originalY + velocityY*KMtoLY*time\n",
      "    newZ = originalZ + velocityZ*KMtoLY*time\n",
      "    fig = pylab.figure()\n",
      "    ax = Axes3D(fig)\n",
      "    ax.plot([originalX], [originalY], [originalZ], 'd')\n",
      "    ax.plot([newX], [newY], [newZ], 'd')\n",
      "    pylab.axis('equal')\n",
      "    #fig.savefig('alphaUM.png')\n",
      "    return newX, newY, newZ"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alphaUM(100000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "(-61.30000013635602, 46.699999783310204, 96.69999989799724)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Px6RJk9DQ0ID6+npdbk5CEAT069cP7777rlQs/oMPPgCAJrXPcOErIHoEz+l0wu/3IxwO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\ntU9tAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f5760a5e1d0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Sweet! Pretty simple. Let's do this for all of the Ursa Major stars now. All of the stars happen to be in the PyEphem [stars database](https://github.com/brandon-rhodes/pyephem/blob/master/ephem/stars.py) so we'll leverage that. Although [Alcor](https://en.wikipedia.org/wiki/Mizar_and_Alcor) isn't listed as part of the Ursa Major constellation, I wanted to include it because it is a binary with the Mizar system. It is crazy, their combined system is actually a sextuple system."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import ephem\n",
      "\n",
      "UMa = {\n",
      "'dubhe': '\u03b1UMa', #HIP 54061\n",
      "'merak': '\u03b2UMa', #HIP 53910\n",
      "'phecda':'\u03b3UMa', #HIP 58001\n",
      "'megrez':'\u03b4UMa', #HIP 59774\n",
      "'alioth':'\u03b5UMa', #HIP 62956\n",
      "'mizar': '\u03b6UMa', #HIP 65378\n",
      "'alcor': '80UMa',#HIP 65477\n",
      "'alcaid':'\u03b7UMa', #HIP 67301\n",
      "}\n",
      "\n",
      "def const(const,year=None,epoch='2000',title=None):\n",
      "    s = []\n",
      "    \n",
      "    for star in const.keys():\n",
      "        s.append(ephem.star(star.capitalize()))\n",
      "        \n",
      "    for i in range(len(s)):\n",
      "        if(year!=None):\n",
      "            s[i].compute(year,epoch=epoch)\n",
      "        else:\n",
      "            s[i].compute(epoch=epoch)\n",
      "        \n",
      "    tau = 2.0 * pi\n",
      "    degree = tau / 360.0\n",
      "    hour = tau / 24.0\n",
      "    \n",
      "    ra_list = [star.a_ra / hour for star in s]\n",
      "    dec_list = [star.a_dec / degree for star in s]\n",
      "    \n",
      "    mag_array = np.array([star.mag for star in s])\n",
      "    size_array = (5 - mag_array) ** 1.5 * 4\n",
      "    \n",
      "    scatter(ra_list,dec_list,size_array)\n",
      "    if(title!=None):\n",
      "        pyplot.title(title)\n",
      "    gca().xaxis.grid(True)\n",
      "    gca().yaxis.grid(True)\n",
      "    gca().invert_xaxis()\n",
      "    return s"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that we are using `a_ra` and `a_dec` instead of just `ra` and `dec`. If you swapped out `a_ra` with `ra` you wouldnt see a difference in the values between the epochs. Why is this? `a_ra`/`a_dec` are the **astronomical geocentric position** for the star atlas epoch you've specified, while `ra`/`dec` are the **apparent topocentric position** for the epoch-of-date. Additionally, there is a third `g_ra` and `g_dec` which are the **apparent geocentric positions** for the epoch-of-date. See the full explanation on [how these three positions differ](http://rhodesmill.org/pyephem/radec.html).\n",
      "\n",
      "Below are different combinations of varying the year and epoch for the Big Dipper constellation. In the examples that keep the epoch as the default `J2000`, we are able to reproduce the results seen by many sky plotting programs. Specifically, we see the same result as documented by Ian Ridpath and Rick Pogge. I recommend watching their animations, because it makes the transitions between depictions easier to see."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ancient_uma = const(UMa,year='-100000',epoch='-100000')\n",
      "#savefig('uma_ancient_epoch.png')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f5745d80dd0>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ancient_uma = const(UMa,year='-100000',title='Butterfly Net')\n",
      "#savefig('uma_ancient.png')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f5745f37c90>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "present_uma = const(UMa,year='2014',epoch='2014',title='Current Big Dipper (Epoch 2014)')\n",
      "#savefig('uma_present_epoch.png')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7/HEee7+5wKN5lsV5/FPy5Xdl/IO4MP65xHnsR2DtGbx/R+RZr6CxL1ZhrwK+\nByz0zcv17hLn7/C9GvvAVSP2adtcTsYOpc4Gvo0dWsVFd/njPPYpVwMfA/fkWR7n8Yfg/C6Mf3fi\nPv75uDL2neTPWtDYF6uwj8f6V6uxXtARwH8Dh2Wt9w6ZJ/bGYO+ecXIP+b+tcqP37xZgCXaIFzf5\n8sd97Buw7yT6WsA6cR7/BoLzx338w4jz+AeJ89hvBkZ69w/HPumfS0FjX6zCvgY7hBjn3TZgJzKy\nQ64EjsLeBAYCfwU8VKQMvXGU7/4s7MxztirSJymrgbPIfVVQFMLkj+vYg12xcAWWfU+edeI8/mHy\nx3n8/fL1ceM8/in5ssd57B/C2qd4/z6YY52Sjf29QBuwF+tdzcla/j+kz+COAv7Lt+xs4HXsZMaC\nvgjXjVT2j7Hsc4H7sIFKAveTPtLwZz/SW54EXiGa7NDz/BD92EPu/H8E1mFvSKuAn3vrujL+YfJD\nfMf/y9793cAm4HfeunEb/55mh3iO/RysTi6j6+WOcRt7ERERERERERERERERERERERERERERERER\nETlQ/C/UUJqWROFCnAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f5745ee8150>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "present_uma = const(UMa,year='2014',title='Big Dipper (Epoch 2000)')\n",
      "#savefig('uma_present.png')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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zZzJlylr27fsDhYWjmTnzLK655pqgY4kcQj12EZ+6d+9O69bLgZdo0WIl3bt3DzqSSFao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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f5745d438d0>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "future_uma = const(UMa,year='100000',epoch='100000')\n",
      "#savefig('uma_future_epoch.png')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f5745d5c2d0>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "future_uma = const(UMa,year='100000',title='Dustpan')\n",
      "#savefig('uma_future.png')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f5760a5e410>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![pm](https://raw.githubusercontent.com/digitalvapor/asterisms/master/notebooks/images/uma_proper_motion.png 'proper motion of ursa major in m.jones paper')\n",
      "\n",
      "Ian Ridpath gives a talk, *Pictures in the sky: the origin and history of the constellations*, that displays an animation of the same transition. See the [video at t=2563](https://www.youtube.com/watch?v=nZm-QaKqS-Y#t=2563). Jones got his images from Rick Pogge's [video](http://www.astronomy.ohio-state.edu/~pogge/Ast162/Movies/proper.html) and lecture which was output from his Fortran code.\n",
      "\n",
      "I read the PyEphem tutorial section on [fixed objects, precession, and epochs](http://rhodesmill.org/pyephem/tutorial.html#fixed-objects-precession-and-epochs). This computes the position of [Halley's Comet](https://en.wikipedia.org/wiki/Halley's_Comet) in 1066.\n",
      "\n",
      "> **halley.compute(epoch='1066')** <br>\n",
      "> This is probably useless: it computes the current position of halley, but returns coordinates relative to the direction the earth\u2019s axis was pointing in the year 1066. Unless you use a Conquest-era star atlas, this is not useful.\n",
      "\n",
      "> **halley.compute('1066', epoch='1066')** <br>\n",
      "> This is slightly more promising: it computes the position of halley in 1066 and returns coordinates for the orientation of the earth in that year. This might help you visualize how the object was positioned above contemporary observers, who considered it an ill omen in the imminent conflict between King Harold of England and William the Bastard. But to plot this position against a background of stars, you would first have to recompute each star\u2019s position in 1066 coordinates.\n",
      "\n",
      "> **halley.compute('1066')** <br>\n",
      "> This is what you will probably use most often; you get the position of halley in the year 1066 but expressed in the 2000 coordinates that your star atlas probably uses.\n",
      "\n",
      "I am a little confused by Jones and Ridpath's results. Although I am happy that we can get the stellar dustpan and butterfly net they talk about, why are they using coordinates relative to our current position? Wouldnt using the ancient epoch and far flung future epoch *and* year give results for how ancient or future man would see these stars instead? Based on the second Halley's Comet example Brandon Rhodes gives, I am going to go with the following as what I think the depictions of the precession of the Big Dipper are.\n",
      "\n",
      "![transition](https://raw.githubusercontent.com/digitalvapor/asterisms/master/notebooks/images/uma_transition.png '200000 years transition for Ursa Major')"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Some additional food for thought:\n",
      "\n",
      "> The first assumption is that the brightness of each star will remain constant so that the predominant stars in the night sky will remain the predominant ones in the future (and would have been similar in the past). The second assumption is that no star will reach the end of its life and thus completely disappear and that no new bright stars will form (and thus create an added point in the constellation). These combine to also assume that the gravitational tug among and between stars will also remain constant.\n",
      "\n",
      "Matt notes some assumptions; and although discovering stars that have ceased to exist or predicting star formation is probably just a fantasy, we do know of some observed changes in the stars such as [Betelguese](https://en.wikipedia.org/wiki/Betelgeuse). Betelgeuse was described as red by Ptolemy, but described as [yellow by the ancient Chinese](http://books.google.com/books?id=L4NTyHivbV8C&pg=PA238#v=onepage&q&f=false). This suggests that before it was a red super giant it was a yellow super giant. \n",
      "\n",
      "Hopefully we will find an Atlantian library with ancient star charts, but until then we can calculate the change in apparent magnitude using distance calculations."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To update you on this subject, the [big-dipper.ipynb](https://github.com/digitalvapor/asterisms/blob/master/notebooks/big-dipper.ipynb) ([nbviewer](http://nbviewer.ipython.org/github/digitalvapor/asterisms/blob/master/notebooks/big-dipper.ipynb)) notebook shows the different iterations of varying epochs and years. It also shows how to display constellation line segments, and can handle wrapping constellations like the [iau-bounds.ipynb](https://github.com/digitalvapor/asterisms/blob/master/notebooks/iau-bounds.ipynb) ([nbviewer](http://nbviewer.ipython.org/github/digitalvapor/asterisms/blob/master/notebooks/iau-bounds.ipynb)) notebook. What we find out in subsequent notebooks is that the above method of varying date *and* epoch together is correct. However, the depiction is broken due to the precession model being implemented. In [far-flung-proper-motion.ipynb](https://github.com/digitalvapor/asterisms/blob/master/notebooks/far-flung-proper-motion.ipynb) ([nbviewer](http://nbviewer.ipython.org/github/digitalvapor/asterisms/blob/master/notebooks/far-flung-proper-motion.ipynb)) I find out why this happens, and in [vondrak.ipynb](https://github.com/digitalvapor/asterisms/blob/master/notebooks/vondrak.ipynb) ([nbviewer](http://nbviewer.ipython.org/github/digitalvapor/asterisms/blob/master/notebooks/vondrak.ipynb)) I implement a long-term precession model that works for hundreds of thousands of years."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}