brandon-rhodes/VenusFromJupiter.ipynb

## VenusFromJupiter.ipynb
{
 "metadata": {
  "name": "",
  "signature": "sha256:ce9ee21ba6aa7a4d4e447579ac5fdc418ce0a0618ba773d8a6caff240d58ad43"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "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": [
      "# Compute ICRS position of Venus in Jupiter's sky\n",
      "\n",
      "from skyfield.api import JulianDate, jupiter, venus\n",
      "jd = JulianDate(utc=(2009, 1, range(1, 366 * 6 , 5)))\n",
      "astrometric = jupiter(jd).observe(venus)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# How to build a rotation matrix for another\n",
      "# plantary pole.\n",
      "\n",
      "from skyfield.functions import rot_x, rot_z, rot_y\n",
      "from skyfield.positionlib import to_polar\n",
      "from skyfield.units import Angle\n",
      "\n",
      "def rotate_to(pole_ra_degrees, pole_dec_degrees):\n",
      "    ra = Angle(degrees=pole_ra_degrees).radians\n",
      "    zenith = Angle(degrees=90.0 - pole_dec_degrees).radians\n",
      "    W = (rot_y(zenith)).dot(rot_z(-ra))\n",
      "    return W"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Rotate the observation for Jupiter's poles\n",
      "# and equator.\n",
      "\n",
      "W = rotate_to(268.06, 64.50)\n",
      "xyz = astrometric.position.AU\n",
      "xyz = (W).dot(xyz)\n",
      "d, dec, ra = to_polar(xyz)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# How did we do?  Compute this new declination\n",
      "# number against where SPICE found zero crossings:\n",
      "\n",
      "d, leapsecond = jd.utc_datetime()\n",
      "plot(d, dec)\n",
      "for spice_crossing in [\n",
      "      (2009, 3, 11, 2, 57, 39.814),\n",
      "      (2009, 5, 20, 2, 22, 53.815),\n",
      "      (2014, 12, 23, 5, 55, 39.816),\n",
      "      ]:\n",
      "    plot(JulianDate(utc=spice_crossing).toordinal(), 0.0, 'ro')\n",
      "    \n",
      "# Success!"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pJlbEoyDvk9NUTUTVqtC1K4wd6/yc2bNttl3lyu7vT0SCFdSyw9OnF794YYUK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\nxoI3wG4sDROtGrAr6ufIMZH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       "text": [
        "<matplotlib.figure.Figure at 0xb0e3662c>"
       ]
      }
     ],
     "prompt_number": 5
    }
   ],
   "metadata": {}
  }
 ]
}
	{
	"metadata": {
	"name": "",
	"signature": "sha256:ce9ee21ba6aa7a4d4e447579ac5fdc418ce0a0618ba773d8a6caff240d58ad43"
	},
	"nbformat": 3,
	"nbformat_minor": 0,
	"worksheets": [
	{
	"cells": [
	{
	"cell_type": "code",
	"collapsed": false,
	"input": [
	"%pylab inline"
	],
	"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": [
	"# Compute ICRS position of Venus in Jupiter's sky\n",
	"\n",
	"from skyfield.api import JulianDate, jupiter, venus\n",
	"jd = JulianDate(utc=(2009, 1, range(1, 366 * 6 , 5)))\n",
	"astrometric = jupiter(jd).observe(venus)"
	],
	"language": "python",
	"metadata": {},
	"outputs": [],
	"prompt_number": 2
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": [
	"# How to build a rotation matrix for another\n",
	"# plantary pole.\n",
	"\n",
	"from skyfield.functions import rot_x, rot_z, rot_y\n",
	"from skyfield.positionlib import to_polar\n",
	"from skyfield.units import Angle\n",
	"\n",
	"def rotate_to(pole_ra_degrees, pole_dec_degrees):\n",
	" ra = Angle(degrees=pole_ra_degrees).radians\n",
	" zenith = Angle(degrees=90.0 - pole_dec_degrees).radians\n",
	" W = (rot_y(zenith)).dot(rot_z(-ra))\n",
	" return W"
	],
	"language": "python",
	"metadata": {},
	"outputs": [],
	"prompt_number": 3
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": [
	"# Rotate the observation for Jupiter's poles\n",
	"# and equator.\n",
	"\n",
	"W = rotate_to(268.06, 64.50)\n",
	"xyz = astrometric.position.AU\n",
	"xyz = (W).dot(xyz)\n",
	"d, dec, ra = to_polar(xyz)"
	],
	"language": "python",
	"metadata": {},
	"outputs": [],
	"prompt_number": 4
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": [
	"# How did we do? Compute this new declination\n",
	"# number against where SPICE found zero crossings:\n",
	"\n",
	"d, leapsecond = jd.utc_datetime()\n",
	"plot(d, dec)\n",
	"for spice_crossing in [\n",
	" (2009, 3, 11, 2, 57, 39.814),\n",
	" (2009, 5, 20, 2, 22, 53.815),\n",
	" (2014, 12, 23, 5, 55, 39.816),\n",
	" ]:\n",
	" plot(JulianDate(utc=spice_crossing).toordinal(), 0.0, 'ro')\n",
	" \n",
	"# Success!"
	],
	"language": "python",
	"metadata": {},
	"outputs": [
	{
	"metadata": {},
	"output_type": "display_data",
	"png": 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	"text": [
	"<matplotlib.figure.Figure at 0xb0e3662c>"
	]
	}
	],
	"prompt_number": 5
	}
	],
	"metadata": {}
	}
	]
	}