animate.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from astropy.time import Time\n",
    "import astropy.units as u\n",
    "import astropy.coordinates as coord\n",
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "%matplotlib inline\n",
    "\n",
    "from twobody import KeplerOrbit, Barycenter\n",
    "# from thejoker import RVData"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make some fake data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "t0 = Time(58425.134, format='mjd')\n",
    "K = 13.013 * u.km/u.s\n",
    "orbit = KeplerOrbit(P=110*u.day, e=0.4, M0=0.52*u.radian, omega=1.6*u.radian, \n",
    "                    Omega=0*u.deg, i=90*u.deg, t0=t0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "rnd = np.random.RandomState(seed=1234)\n",
    "t = t0 + rnd.uniform(0, 3, size=8) * u.year\n",
    "t = t.sort()\n",
    "\n",
    "rv = K * orbit.unscaled_radial_velocity(t)\n",
    "rv_err = np.ones(len(rv)) * 0.5 * u.km/u.s\n",
    "rv = rnd.normal(rv, rv_err.to(rv.unit)) * rv.unit\n",
    "\n",
    "# data = RVData(t=t, rv=rv, stddev=rv_err)\n",
    "# _ = data.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'unscaled radial velocity')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1069a0e80>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# If we don't specify K or a, then the absolute RV variation is unknown\n",
    "\n",
    "t = t0 + np.linspace(0,2,1024) * u.year\n",
    "\n",
    "unscaled_rv = orbit.unscaled_radial_velocity(t)\n",
    "\n",
    "fig,ax = plt.subplots(1,1,figsize=(10,4))\n",
    "ax.plot(t.datetime, unscaled_rv, marker='')\n",
    "ax.set_xlabel('time [{0:latex_inline}]'.format(u.year)) \n",
    "ax.set_ylabel('unscaled radial velocity') \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'radial velocity [$\\\\mathrm{km\\\\,s^{-1}}$]')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115ba0588>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We have to specify the semi-major axis to produce a real velocity amplitude\n",
    "# But these are still computed relative to the barycenter/reference point of the orbit\n",
    "\n",
    "orb = KeplerOrbit(P=1.5*u.year, e=0.67, a=1.77*u.au,\n",
    "                  omega=17.14*u.deg, i=65*u.deg, Omega=0*u.deg,\n",
    "                  M0=35.824*u.deg, t0=Time('J2015.0'))\n",
    "rv = orb.radial_velocity(t)\n",
    "\n",
    "fig,ax = plt.subplots(1, 1,figsize=(10,4)) \n",
    "ax.plot(t.datetime, rv.to(u.km/u.s).value, marker='') \n",
    "ax.set_xlabel('time [{0:latex_inline}]'.format(u.year)) \n",
    "ax.set_ylabel('radial velocity [{0:latex_inline}]'.format(u.km/u.s)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'radial velocity [$\\\\mathrm{km\\\\,s^{-1}}$]')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11651d550>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Need to also add the barycentric or systematic velocity of the system \n",
    "# to get real line-of-sight velocities\n",
    "\n",
    "v0 = 100 * u.km/u.s\n",
    "fig,ax = plt.subplots(1, 1,figsize=(10,4)) \n",
    "ax.plot(t.datetime, (rv + v0).to(u.km/u.s).value, marker='') \n",
    "ax.set_xlabel('time [{0:latex_inline}]'.format(u.year)) \n",
    "ax.set_ylabel('radial velocity [{0:latex_inline}]'.format(u.km/u.s)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# For sources with appreciable tangential motion over the timescale of observations, \n",
    "# There are additional effects due to spherical projection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot the orbit from various perspectives"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1144ec2b0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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73elIEHvf8qteR3vXQmAb/d/MB6MV5pD29rbNkvv17z+m4GNHDftF3rPqqdVllI6sX6Iho2bgGG5w9snzK/rm0qTX+Q8FjgD+4b9+E15BvKrCL4KNAIcdsluRB0vws729clYrMnmGzc8PPLaoY48aHUag3bngpagkOee+RUcDvXMTbmz0jCHbPDDiIJ1Oo7aCYzjG6SdPRGpEZCawHJgOzAZaVDXn9bgQGLeVY88TkRkiMmPFihWlEVwCLrq4b+nM6+vC+N/f3fFUFJKSgYYbVCfvskdRh35zrzDvS6tWkNFHO1k8A2eXfpcUfbxs8dMwouKJedeRESGj3sMwXODUwFHVjKpOAcYD04Cu8u53eYOqqtep6lRVnTpixIg4ZZaUF19aHLR33aXwLYcc++8RVhu/7/FXItHkmq8+fI/X6OUW1YjmAWyeJagy8ALtvCRqu4w+o+jjzcAx4mKZ/t3bnrIVHMMhifjkqWoL8CiwHzBYRGr9X40HFm/tuIpEw0JLv/rpx4s+/IsfOTRor25tj0yWS/4+OywcObl5QK/HEamci/mspTcCuRINvR8n935sbK/sAq1GacmwnqyaD47hFpdRVCNEZLDfbgKOAl4DHgFO97udDdzlRmHpWbqsJXyivbtqjRs1uPLWKvL+Mf/+yHm9GkIqbLnitfW/Ct6WFIXlvnk3E4PW6pYfRiHLMAAvgiq3epNNxn20UYW4/OSNAR4RkVnAc8B0Vb0HuAT4soi8DQwDfu9QY0k5+xO/iXbACriYd3R0hE8UUqm+f2TXtm/s8xiu8YwbL/fNieN7Vz2+f/NZQbsz/WQ0wgwDv4K4mg+O4RaXUVSzVHUvVd1DVXdX1e/4r7+jqtNUdXtV/aCqdvQ0VqXQmQ6jp7777T4Ej1VQVfFD//q7SMYZXNsQtP/wVuU4XyvQ2Ni7/EeDBnwayH1U1nXX1TCKIpcDJ2srOIZD7JOXJPIKSR500M5OpSSFpe0bQT2L7Qt77tPrcQ4esX3QfmDhqxEoc8f9cz/rZYklvw5V8dTVNZEiLNlgGFGRxfO9yZgPjuEQ++QlhOeemx1ZoE9DXfhnfeHV+X0bzDV5Rt/F+x3W62HO3/mgoL1gY0s3PZPP6vQLQWmGETUH9GmsXCFSqyxuRElGBwQJKK1Ug+EKM3ASwiWX/j1wLO6rm8k2Y4cF7b9Pn9m3wRyyqjW6DLs7DBkVtNNl7n6di5pShaO3+ZlbMYbRBdtxGml/9SZrKziGI+yTlxQ0vGrd8PtP9WmoEw7eNWjPeqt8o+wP/0u0/uWV4JqUTqeDRb6+bE8ZRpwcueM5pDVF2gwcwyH2yUsgEwusHr41Tjg0LO+wel1bX+U4Y10mHWzZ/ejgo13LSQT/mvcZQNDIzLXQQXlj+5sRjGcYIOJtTdkWleESM3ASwHPPzc6rk913+jU2BgNVyl3+6bvt6VpCIlidfTnYYBtff0wEI24TtNav/2ME4xmGR9ZWcAzH2CcvAVx6ya3BSkVtbY/dC6eMb5zWbYw3V002W96mXxY4fNJ3+jxOU9NRgWHd2fGfPo+XJESkUUSeFZEXReQVEbnCf30bEXlGRN4Skb+JSL1rrZVI2k/2l9Ya11KMKsUMnCSQ5/P662s/6U5HgjjmlhsiT8fcPxVex15cvTC6gUtKKkjwFwUD+n2UFOLbwuXrr7UVOoAjVHVPYApwnIjsB1wNXKOqOwBrgHMcaqxYMtSQpcZqURnOsE9ewthuu9GuJSSCpR3hCs7Xpx0cyZg7DBxOzmq6e+5LkYxZSh6e902g11U8uqShwSvX4Jk4G6IbOAGox3r/aZ3/UOAI4B/+6zcBfciqaWyNXBbjrGUyNhxhBo5jli5Zs1mBzajIP6WU+3bMp9+7byTjHDJqh6A9Y/XcSMYsJfM6Hg4+JkNlL7diygQRqRGRmcByYDowG2hR1bTfZSEwzpW+SqZTU6SzlujPcId98hzzmfOiKUWwJYP6h6UJ3pi7LJY54iKbzcZSKfSkiXsECe0WbyzH0gSpIHna+7b5uWsxZYGqZlR1CjAemAbs0lW3LV8QkfNEZIaIzFixYkXcMiuStHrbUxlN8b1Zn3Utx6hCzMBxTGtrZ9D++jdOjGzcSaOHBi4sDz1bXuG/n7r7Nq8RsZEzbsAQwMva25bdFO3gJSIXHl5TY46bxaCqLcCjwH7AYBHJufOPpwvnI1W9TlWnqurUESNGlE5oBZHWFOlsDWmtYb2W102WURmYgZMgjjhy98jGmrbHxKD9wuvl5VD76MKwvMQx47eNZY5yy2X85soHy06za0RkhIgM9ttNwFHAa8AjwOl+t7OBu9worGwy1JD28+CkbZvKcIB96hySyWQijxTKceTUnYLEOotXrI1+gtjxxP/m/eb/CfD46u8GHxVhcMSjh9uZmUxnN/3KjjHAIyIyC3gOmK6q9wCXAF8WkbeBYUC0KbMNIOdkXENGa+g0R2PDAVFmXTGK5Ipv/SN8ErGRM3lcWI+qta0j2sHjJvdeCKT6WpirovAuEqeOvz7icYcDiwBo3ziDfv33j3h8N6jqLOBd3tiq+g6eP44RI6IDSeMFsWXMwDEcYFcPhzz1RJjBeL/9o92Kkbzy0Ols+WxuPPR2nr9Q+ciOnfwgu8HNYyIdu7Zmp+Bz2NExPdKxjerlgkFfJ5P1Mhlns2bgGKXHDJyE8J3vf9C1hETwufvvDi62g2uiX2CsLcOPfEdHmJ8mDlu1sfGgMJtx5/+in8CoSrbddlvSpLxwccwp3ig95Xe2ryRy+W9ULSrGJ98D5NbTzox8/EG1jeQcn5asLw/fpDvnXegVLdRcFFW0NDSFhUw1My/y8Y3q5OLnLvby4GRTpG0Fx3CAGTiOePPNikuLHw0aPnYc2beq6l0xof+goP348vIIn2/Rt/DWV1K8p98ZkY9fX5+/PdoS+fhGdbI8u5qMX4+q0+pRGQ4wA8cRX7nwz0G7LqZSf6kyu2lKp9M9d+ojewydgIiXC+e5VXNjny8K8mw+Dhj/ucjHz/fXgvbIxzeqk86sV028M5sia1tUhgPMwHFE24bO4Kr1nSvj8b9pagh9WNLpTCxzRMkX7r879jn2Gz45aL+9tjwy1OYKbZjPtVFOqHqVxNNaw+f6WSZjo/SYgeOKvPJQ+0zbMZYphg/uH7Rfm7s0ljmi5P457wTtoyZuE8sc+wwPt2OWtye/XMOCtS/ilWjIVRE3jORz6pOf8/LgZFN0ZlIcuPtU15KMKsTZGVNEJojIIyLymoi8IiIX+q9fLiKLRGSm/3ifK41xIhBbkr8ck8YMCZL9Pffq/B77J4lrTzgplnH7N4RJ7Takk1+u4Z6lXwvaKZodKjGMwslkIIu3emMRVIYrXN4SpoGLVXUXvPownxeRXf3fXaOqU/zHfe4kxsPfbvkPENgesbHH9mGR5FfnlFctmNra+HNQdpL8KusZ3RgE25005gcxzlRmDltGYjn+8S+ACFkV0lnhjgOvdS3JqFKcZTJW1SXAEr/dKiKvAeO6P6oy+N2vHw8yt42bODS2ed67y4SgvWDpmtjmiYKVra2uJSQaBcYOfE9s44s0IdoW2/hGdXDsYxeR8iveZ1XMbDackohNfRGZjJdS/Rn/pQtEZJaI3CAiQ7ZyzHkiMkNEZqxYUR7OogF5aWl/8suPxzbNjhPDMOvV65J98frInbcGW3aJ+FAmBgkqiMdJiqGAICJ0di6PdS6jMvnSIz8lm/W+xhn1EvzdfcgvXcsyqhjn1xIR6Q/cBlykquuAa4HtgCl4Kzw/7uo4Vb1OVaeq6tQRI0aUTG/UDB3Wv+dOvaSuLtz73tiRbH+Tt9aE+Ve+um9l1ELqKy8s+0fPnSJCasaSixbf1DGjZPMalcFdbzzKizofhWBr6oFDf+5allHlODVwRKQOz7i5WVVvB1DVZaqaUdUscD0VVhQvm3Xj97Epnewg4/z1ic9MOyDWuWrKZN38qTW/DfzQ+8W8e1tXu0vQTpuBYxTBawvm8ZOFd6OaM25SXL/Nl1zLMgynUVQC/B54TVV/kvd6fiXBU4GXS60tTq796f1eI9n2hhPi34jxaE55mRUl4YZOhmxg4Jw++ZpY56qpf284b+b1WOcyKoeVK1dy3hu/QPDKiGRVOHvUUUyePNm1NMNw52QMHAh8DHhJRGb6r10GnCkiU/DO63OB893Ii4c7b3shMG52f894t2ISwvzVq0KDrwRGx+D6Zta3e1t2K9taGd48IP5Je4UEtacGNA6Pdab6hn3Y6Pt5ZzILYp3LqBxO/t8PSYmQVe+ru1/j9py92wmuZRkG4DaK6gm6vpxVXFj4ZuSt3Fx5zUdKOV1iOfv224N2Qzf9omJM00AWtns+Py+tXsDhzbv2cIRDlJIYfbW1YcQdujr+CY2yZ/8HLyEl+MaNsG1qCFcfZBmLjeTg3Mm4mmlqiqkIVR61ZVCQat6GMET82wcfEft82w8MndJnrUlm0dNnlv7Ny39TovlSqfxTQbIj7gz37PfApd62lIKqMFia+OORl7mWZRibYQZOCclmswRZ20pEY0Nt6Zxb+oQn8oy99op9pt0GhVuDb29IZkj0U2tuDPxvBhFP2Yqtk+yIO8Mt0+73smtnfeMmJcI9R33HsSrDeDdm4JSQ63/5YMnnHNivMWiv27Cx5PMXTAn30vYYEkYkLdrQ0k1Pl2Twvp4pTpsUZwZjwyicafdfttnKDSI8cfTVrmUZRpeYgVNCbvvLc8Fiyu67lyZp84ihYZ6dN+clb7VicUtLaNyUyMiZPDB02F3Vsb40k/aBAU3DSjZX4hf6DGdM+9dledumgiA8fYwZ30ZyKcjAEZGhBTwGxy22krj8/z5cknkmjwlLQbw6N3kGzjl33RG060o0Z02ev8mGdEeJZi2OEtt8gHfJyv9pGDmueO5vZPGTjasXDv7f465yLcswuqXQKKrF/qO7M18NMLHPiiqZnO+NCIMGlaYy9I7jQ4fatxeuLMmcxfDGmrBG1lcOiDfBX1ds0kzJ5+yJWSunk8W7+yhlWkihFq8GrmGErFu3jrtWzPLuhsX7TD5//JWOVRlGzxRq4Lymqt16f4rI/yLQUx2U0Ml4121GBe1FKxLqb+KHQn962n4lnzp55g08vOKXgJAFBjCqp+4R0gysK+F8Rjlw2H9+GBg2KPzn0K+7lmQYBVGoD04hxYGsgFA33HP7s07m3TZvBWfV2g1ONHSLi70Yf0IJ4pSSRYb2oH3qxFJGpwwKWul0gh3SjZIx5d5v+ttSgAqfn3QY/fr1cy3LMAqiIANHVduj6FPN/PbnYQTVuIlDu+kZLc2NYa6d1g3J8jdp3+QuHDmXHiiJaYJymQRUYWS/ySWbV2rC1aJM51slmzcORGSCiDwiIq+JyCsicqH/+uUiskhEZvqP97nWmlS+8tSfNnMqRoRzdjvGsSrDKJyio6hE5JI4hFQ6He3ZYLHgOz86w4mGjQ4Niq740n33Ops7RXJrUbla1KqpDV3oMulXSjx75KSBi1V1F2A/4PMikktZfY2qTvEflZ05vQ88uOpNwHMqVoQX3vc9x4oMozh69MERkVvznwJTAEt8UCxZ8CvSMWFivHWFtkY6YRXFH5gzJ2ifsuOOJZ27MVVHW7azpHMWwooNc4CUk42zVO3O4C/ypTvfdKAgOlR1CbDEb7eKyGsQc0n2CmKPu78FeKuIAsx8/3fdCjKMXlDICs46Vf2Q//gg8FDcoioWxy4fyTJvCN8PhauPObakU/erC7futIRO3z1x27zwLrmWppLOXVsb1uTKZOZ007O8EJHJwF7AM/5LF4jILBG5QUSGbOWY80RkhojMWLFiRYmUJoMvPXHzZnEQBwwqdSZtw4iGQgyc7wOISG7ZwVzoi2Tu7KVuBcgWPxNIXV2psuB4DK4LHSVXtbd207O0rGNxYIgeOfIzJZ27tn7noJ3NJLNGV7GISH/gNuAiVV0HXAtsh7cSvQT4cVfHqep1qjpVVaeOGDGiqy4Vy/S8rSlUuPaQTzlWZBi9o0cDR1Vzt3I3+M+t1HCRfOeSvwft5mZHBdwTaNxI3qPUjG4aGLRnr0tOAsRc2LoCew4vrUNnTc3I8El2zdY7lgkiUodn3NysqrcDqOoyVc2oahaXw+3iAAAgAElEQVS4HpjmUmPS2O2uywHf70aFWSdZjSmjfCnGyTiBl8jyYOH8NUHum898qfRRCHU1yfvT3frii07nn9QvLH/wVmuStiC8/DelTPCXY/OK4glMKVAEIiLA7/FyeP0k7/Uxed1OBV4utbak0traimquiCYMkfqeDzKMBFPMckJyHBXKjdyGtirHnTy15NM3NtTT2ZasEPErH300+ERtM3hQt33jYPsB4WrFnIQYOOl0LouwW4PUy6Bc9nlwDgQ+BrwkIjP91y4DzhSRKXifvrnA+W7kJY9pD3m7dSJehqj/nGTeCEZ5U4yBk7xlgDLB9Rs3oLmeVt/AyWazW9ypu6E1HeYQ/vVJJ5V8/u0HhgbOoo3JyPD84OJfu5ZAyg/1qynzkg2q+gRdf/UsLLwLnl8cOpWrwvd3PcGhGsOIhmKudF+LTUUFE96Vu2NI/zAaZ+mq5KXi39GBE+e2A8I5V7Qno6L4i+sfDBL8bduwrxMNnk+Ua5PcKDVn/fePwWcP4AM77eNWkGFEQMEGjqraXnUv+MO1D7HZmcMBI4eGDrXzlpS/82gUDKgPjb6WzjaHSkKy6nneKHDy+IvdijGqhucWvhNmK0Z48JAvuBVkGBFR1F6FiHxQRAb47W+IyO0isnc80iqDO295JmhP2dtNsfWJowcH7bcXu68ovrYtGQZFLgnPhs6k+CelUFJAisaG/s40GNXFR5/9M/jZikGYMGxYj8cYRjlQ7Nnsm35W0IOAY4Gb8PJKGFsh3Rmu3Hztqg850bDN2PCEtWCZe3+Ti+69L0jwV9rsN5uT24jp1ORlNHZHo2sBRglZv369t7gs3iLzg4d+zrUkw4iMYg2cnGfoCcC1qnoXYLGEBTJ4qJsqvNvmGThJ8MF5fN78oH3Ge97jTohXP5BOJ0HZm7NswxzXO5k+za4FGCVk7/uvgbzP3cRhbsrIGEYcFGvgLBKR3wIfAu4TkYZejAF0W+13qIhMF5G3/J9dplI3CmfiyPAtXNWSlO0hj28ccbhrCYngH/PChLq1Lo0MCUP2Mxn3DvJGvHjVwr2MxRdvf5BrOYYRKcUaJx8CHgCOU9UWYCjw1V7OvbVqv5cCD6vqDsDD/vOyZPmyFucOxgD9mhuCsk9rNyQrv0ltraPMzgljVXZ+kODvyOHnOtMhqXC1L5tZ5EyHET/73/YjwK8BrHD+nke4FWQYEVOUgaOqbap6u6q+5T9foqoP9mZi/9gX/HYrkKv2ezKebw/+z1N6M34SuPqysERDfUMynDfXtyfAodZx0dEcqcSFQ3sOxlNHlT7bdaCgNiy4nUm/40yHET8rMu3B/VfSvgmGEQWJuOpuUe13lKouAc8IAkZu5ZjEV/t9eebCoP3hsw90qISg6FNHp9tth5kLk7Mq0CA1riUkjlRNGOmXTc92qMSIk3Q67S8sezWn3vzgN11LMozIKTZMfKqI3CEiL4jILBF5SURm9UVAF9V+C6Lcqv2eec5hriUAkM64XTr5yr1hItnh9W7905vrGpzOn09CFrVI1e4QtLOZue6EGLGy020/ABKxg24YsVGsA8TNeD43LxFBPcCuqv0Cy0RkjKou8QvjJafUcx+oqUnGaoHrc9ncda3Bcvi3jjrSqZYBtQ2s2uQVlXRZwuLFVY/hR+o6j+eqrduG3CZmNr3YqRYjRtQryQEwpTn5N4iG0RuKPaOvUNV/quocVZ2Xe/Rm4q1V+wX+CZztt88G7urN+IlASc6teQI5YdddnM4/JC+Z3or2Vmc6HlhyA+AlWhsiY53pAJCaSd5PgExF3FsYXRBETyHcdpLVGzUqk2JXcL4tIr/Di24KvFXzVl+KYWvVfn8A3Coi5wDzgQ/2YmznvPbi/EQZNimBbBL05JYqEsDIxrwSFutXMaq59FXNAdoIky+eOuHLTjTkqK0d5NeiUlD3SSGN6Nn2L1fiZfZL1CnKMCKnWAPnk8DOeAloc6vpChRt4HRT7RfA7d5FBPz48juC9tDh7pOn1dfW0N6Z6bljKUjIWXVCc1jCYl7bKqaxrTMtql7SwYkDd3SmIYfk/q/JKEJqREze9682ITcbhhEHxRo4e6qqw9Sz5cOCuauD9vlfPtahEo/mxnraO93mwLn/9TdJzPINMKF/mPNl4YbV3fSMl5yTZ/KcPZOVM8mIhlxpBhTe/MhlruUYRmwU64PzXz8Zn1EI/hXrsOOnOBYC/ZrCiCV1dCX93kOPBO3JAwc40ZDP5H7DyTlJLd641okGVSXrq3DtYPxuNrkWYETMklWrzC/QqBqKNXAOAmaKyBtRhYlXLAm7LR/crylor9vgplzD0rwq4t8/7ignGvIZ3xRuUa1sd2PgPL3sXvKriCeLhGxpGpFxwL+uQ/3cN14klWFULsVuUR0XiwojdoYPDgt9LlrRyqD+Dgp/5tl6+06eXPr5t2BY4wDEP8e3bHKzHfPvFX8N2mNqt3Oiwage8u+3Bpl9Y1Q4xd4yDs8PD/dDxPeIQ1g5M/PZ2bnEwYnxOBkzLAyJXrDcomOAzfLetKbdGDgdbAguOqdO+KITDe8maStJRmTkpa6Y+dGvuVZjGLFS7JnsehEJnIxF5EzgG9FKKn9++f0wdc/wMe59TQDGDg+3YxatWONQSTJpS7vxN8nm7WSO6T+x+84lw22GaSNOknbrZRjxUewW1enAP0TkLDx/nI8D7ioDJpSF81qCuN/PfuV9ruUAMGHUkKC9eGXpk9o98PqbJZ+zGDrVnb9JMry08mkC2l2LMCJm0cqV4YfN7BujCijKwFHVd0TkDOBOYAFwjKpaLOmW5DkYH3jkbm61+IwfEa7gLG8pvYFz5cOPBe3tBg/spqcb0s4MnCReaZoBd6t8IjK0gG5ZVctEWAwH3vt7gs9b8qxqw4icggwcEXmJzb8SQ4Ea4BkRQVXNDyfhjBo6MDi3tbSW3iZdtH59kMX48mOOKPn8PeEiRPu55f92MGsB1AyGjFf1PZPppKamrtQKFvuP7qy/GiApe3rlQf4ZPIl2tWFETKErOO+PVYURO40N4Z963QYH/iYa/tx/m21KP/9WCEsOlp7pS/8cVK4YWZug9yQ1lNyCVjazhJqaktsRr6nqXt11EJH/9fD7CcAfgdF49ut1qvozf3Xob8BkYC7wIVWtDqc0DSulfHKS2zpwhlEKCjJweltQsxqZ/eYS1xJ6pK2jo+dOEZPUG8YaUqQdpdhb79egUuCU8ec50dAVqdTYIANONr0Q6ktu4OwfQZ80cLGqviAiA4DnRWQ68AngYVX9gYhcClwKXNIntWVCsHMOfPvwk5xqMYxSUFAUlYi8EEWfauBnV9zul+pVhiSgBlVXtLVbhtocDali/eyjI4sEGYwnDdzJmY4tkZpxQZyNZuaXfH5V7dHDuac+qrpEVV/w263Aa8A44GTgJr/bTcApfVNbRqj/V7UEf0aVUOjZfZceMhYL4KYUc8J48+WlQfujnz3coZKt05kprUPtiwsXl3S+YmiubWDDJlcGn6AJXNuqqZ0QVtLNLHSmQ0Q+CNyvqq0i8g1gb+B7OcOliHEmA3sBzwCjVHUJeEaQiIzcyjHnAecBTJxYIa4+usVPw6hwCjVwdi6gj+V1h81Shb7vtH0dCtk62RLvyHz7/oeCk+qY/sla1epXW88K375RVUSSZ3CUmlTtpOB90Owil1K+qap/F5GDgGOBHwHXAgV/sUSkP3AbcJGqriv076uq1wHXAUydOrUyTAIzcIwqw3xwYiSpF8tSn99eWbEqaF90UCHuFaVjcEM/aPP0bUi307+uqYcjomF2y6slmadX1EwImppZ4VBIcNN0AnCtqt4lIpcXerCI1OEZNzer6u3+y8tEZIy/ejMGWB6p4kQjVmjTqCosJ3sVUZMAg+sDeyUro8Cw+rAm19K2dSWb946F1+dctRggw0s2byHU1OTp0dXuhMAiEfkt8CHgPhFpoHC/QQF+jxeR9ZO8X/0TONtvnw3cteWxlYpo+DCMasAMnAhZu2Z94GCcRGpr7M+9JaObwqSDi9pKdzFfnlkY3EwfO+qMks1bCKlUTfgk66bKus+HgAeA4/ykfkOBrxZ47IHAx4AjRGSm/3gf8APgaBF5Czjaf14d5NWhMoxqoKgQEhG5AG+5tzryRhTJr39wd9BubHIXnbM1Ghvr6FhvrlL5jG70fOMFWNRe6sS43ora1JGHlXjeItA2d1OrtonII8AOInKI/3JBNSRU9Qm2np3gyCj0lR2BD477lVzDKAXFXoVHA8/5IeE3AA+oJnS5wgFPPxz6VRzx/j0dKuma5vpaSn0/vmbDhkTXvxnfbyi5nbslbZb5/924q0klIucCFwLjgZnAfsDTQPJSYZcDOcPGzthGlVDUnoWqfgPYAW9v+xPAWyJypYhsF4O2smNTRxiedO7FxzlU0jUD+jUG7WyJQqm+N/2RoN2vpqabnm4Y3xyWPVq6sXQ+OOWD05xJFwL7APNU9XC8UG+nXs9ljW1RGVVG0U4Z/orNUv+RBobgVRj/YcTayprm5tJE4xTDoP6hppb1palHNf312UHSuJN3LyTbQGnJbVEBrOlcX5I513esL6PrTNrl5O25hH4i0qCqrwPJyYhYbpiBY1QZxfrgfBEv8mAl8Dvgq6raKSIp4C3g/0UvsczIFXtJIMMH9gvObcvXtDJ0YL9u+0dBe95K0VePOKSbnm4YUB8afWs3lcbf5K5FNwQfkxoae+ruCJdVugIWishg4E5guoiswSvCafQG88ExqoxifXCGAx/YMi+OqmZFpKiCnCJyA14Rz+Wqurv/2uXApwmXoS9T1fuK1OgEVU3A9aB7Rg7xDRoRFq5Yx86TRpd0/v6NybuY5+cqau0sTY2ul1pnACkUmDLwwJLMWTw1OF69QVVP9ZuX+87GA4H7HUoqa0QlyfdfhhE5xW5RNWxp3IjI1QCq+lqRY90IdOWoco2qTvEfZWHcADx8z/8Sv/w7Ztggch61i1eV0N04we9JPhszpfE3SRMaUieO+3hJ5iyeBtcCEJGpInKHH9TwC+BK4HnHssqXXA6cMvk+GkZfKdbAObqL147vzcSq+jjgNItYlPz5Fw8F7W13Lu3KSKGMHR76myxbs6E0k5ZReviOEhk4+TTXJ6t0RUgiVttuBv4AnAaciLfie6JTReVMGX0XDSMKCtqiEpHPAp8Dtt2i6OYA4MmINV0gIh8HZgAXby3nTtKK4S1dFK6IfOb/9crmi50xw8OkdivWxO9Qe9/LxS7quaVTS5MjSDVYSEsu0g90Vc/94mWFqv7TtYhKQczAMaqMQn1wbgH+BVwFXJr3eqtqpLncrwW+i/cV/C7wY+BTXXVMcjG8PfbZ3rWELhk5uH/QXt0av0PtTx8Lbd+dhw+Lfb6+UqoapOr/r8Q1T4tDBvo+G0o2myWVcpIF+9si8jvgYQj39fLqShnFYHlwjCqj0GKba4G1wJlxilHVZbm2iFwP3BPnfJES3JYn9+zR3FgftNe1xR8mPrelNWhfcuTBsc/XV0rxl3tl9QsokuBPiUcqNQzNgpAim11NKuWkXtYngZ2BOkJ7UAEzcHpDFvMwNqqKQreonlDVg0Sklc2vA4KXGmfgVg4tilyVX//pqcDLUYxbMhKe1Dk/YmjDxs6Szn3g9tuUdL5iqCNFZ4nWU+5ZfEvQHpkaW5I5e0XNCCTtfV40vQRqnRg4e6rqe1xMXImIH+hpxTaNaqGgdWdVPcj/OUBVB+Y9BvTWuBGRv+ClXd9JRBaKyDnAD0XkJd/P53DgS70Zu9Ssa1kfJLMrlxukto0lCIkuk8Ri9am6ks21NL0waL9v7IdLNm/RpEYFTc0s7KZjrPxXRHZ1NXnFkQ2jqD71+xtcqzGM2Ck20d9NwIV+ZV9EZAjwY1Xt0k+mO1S1q+2u3xc7ThL4/Y/D1BxNzaW7WPaFTWkrupmjqaaWDdnS5MCBcDdzz+H7lmzOYqmpGU/uE6LZRa5kHAScLSJz8HxwcivGe7gSVNYowUbf4yut7ppR+RSb6G+PnHEDoKprRGSviDWVHU9MD3fSDjq2PFbUOzPxGjhtHaUzGPpKc10D0rm+JAtNWc1dpUswWR+Q2nFBWzPOkgcnr6BbGSOa5yNo2YyNKqBYAyclIkNyodsiMrQXY1Qcbes2Bbfl5361PM7JmZhdTn7+6NNBu6nGSQROwQys9ZLapYB0Jk1tTbwf6YTbNh6pfAPHTX3LLZOKGn1EsUgqo6oo9srzY+ApEfmuiHwXeAqwIpu523FVBuaFYieRUt233T4rXNU6bIfkOhgDDKlv9gLgBNZuii+6rLOzE8rEW0tq8pJVZleWdm4vc3Gf+xibc+m09yJ+NmNJdI4Cw4iGom5VVfWPIjIDOMJ/6QOq+mr0soy4qKtJsSnu5RugpaMzuEv82jGHxT5fXxjWGPrJL2lfw7CmAbHM8/CyMOtBippY5oiK2tr+BHF22ZL7a+yyRULRLRFgUDe/N7rg3CMP4YdPP5+QOqqGET+9WYuvI/yKlIdHrRFQV1tTEgMn/wQ6emAkWQRiY1SegbNs4zp2HxLPPE+ueDBob99YRsFB2dae+0TLzgX0MS/53lAmkY2GEQXFRlFdiFft+zY8I+fPInKdqv4iDnHlwPzZS11LKIrmxjo2dMSfAyfZGzCbMzrPwFncFt9qxTpagt3MUyd8LLZ5oif+rNf5mO9NfFi5BqOaKHYF5xxgX1XdAEEl8afxKv1WJddffW/QHjoqnq2NKGluqoe1beVlgcTMmKahQXtZe3xV1nMRVABj+0+IbZ7oKZ+IOKMHctmMzQfHqAKKdTIWNl8azlDll8qZz77jORmrcuKZ01zL6ZH+TfXBXywdUy6cZS3llWNjdFNeEdKOOLdjUqj/KC9KX2XdiIecg7E5GRvVQLErOH8AnhGRO/znp1CmyfmiIr0xE3gknX7OYa7l9Mig/k1Bu2V9G8MHR7/q9H8PPRG0h+TVv0oqIxtDf9XVm+Kvsl5+mLtLJbDLN64JA/hsi8qoAoq6lVTVn+BV914NrAE+qao/jUNYWeGfLGprk58SaMTAfkF7eUs8F/N/vzUnaJ+8eyH+om5pqs0rQtoZT5h426bS+rFEQ25xtrRXQxH5lIg0+O2TReR8ETmgpCIqEMmEqzdWj8qoBopeK1fV51X156r6M1X9XxyijPgYMSTM07N4VTz+JhvS6aB9wWHJvy7lFyFd3xmPv8l9i28PzIR6GmOZI3qchbJfqKodInI58GVgG+DbIvKUiIzu/tAQEblBRJaLyMt5r10uIotEZKb/eF/08hNKXg6cz+23g2s1hhE7hVYTz68iLlu2o6ombsTP6CF5OV9Wxr8dM6CpqedOCWJjJh5/k+dWPwl4X5xdB0yJZY7oaUJoxYGbXe6P8D5gf1XNAIjICcCvgQ8UOM6NwC+BP27x+jWq+qMIdJYNu/2/a0LnYoUvnPh+15IMI3YKrSY+YMsK4n2tJl4JvPnSPECTX1goj7HD83K+rCl5fpPE05GNJ4S+lVayeNeXU8Z3VWc2eaRoBMRFFMECEbkRGAkEFrKq3ou3mlMQqvo43nZ6VbNmzZqgkrhkqzwqxKgqitqiEo+Pisg3/ecTRCT5oUMx8Ycf3x+sZY0eP9itmAIZPTTcolq1boNDJclkUzbdc6de43l4DmsaHuMcESL9XF0MPwE8BpwM3CYiXxKRY0TkEqKJWb9ARGb5W1hdpnUUkfNEZIaIzFixwk0trqg45Ls3en9Hv5r4K1d/ybEiwygNxfrg/BrYH/iI/3w98KtIFZURr8yYG7RP/vj+7oQUwfBBoYGzujV6x9clLS1lnSk1W67C4yAVRthls6WLK1bVdar6B1V9Efgg3lb62cAxwKo+Dn8tsB0wBViCV1+vKw3XqepUVZ06YsSIPk7pjvd86Rqv4a/ejLHc80YVUayBs6+qfh5oB/Criic/DjgmOjeFJ/33n3WgQyWF05wXtr1uQ/QOtT9++MmgPbypXJxpc8v2ipqBEyJhAsRs6etR5dgWGAEcBPT3f/YaVV2mqhlVzQLXAxW7Ar3HRdcE7Vzk1ENX2eqNUT0Ua+B0ikgN/v25iIzAcmIC5REiDltEDLVFb+A89mYYIv7+3XaKfPy4qPXflzi2ZNo2teVyQZYXNcOCpmaWlGxaEdlRRL4lIq8Dv8NbtTlUVfeljz41IjIm7+mpwMtb61vO7HnhNUHUVM5mf+knZtwY1UWxV+WfA3cAI0Xk+8DpwDciV2WUhI0x1KRa1xmOecFh5bFtB9CYqiWdjSeC6l+L/hm06ymfqDKpGROsZ2lmMbBbqaZ+HXgOOF1VtzRACjYTReQvwGHAcBFZCHwbOExEpvjjzAXOj0Jwktg/Z9yIZ1QLMOunZtwY1UdRBo6q3iwizwNH4n1vTlHV12JRVg7kbsmlPOMS2jvjdKgtrxDxhpo61sdk4Dyz5j/BVXn3sgkRB1J5ix3pxaWc+TTgDGC6iDwE3Arcr6pFWeSq2lW4WkVnXj/tiutpyyugI8CLPzPjxqhOiq0m/iXg76patY7FOea+Ubol+7jYFLOBU0401zawqjOeqLJ1uo7cFefksR+MZY44kJqx4QpOtnQGjqreAdwhIv3wysGcD/xORO4DqjYtRU9c9vt/Mnv5+s0SUL/4CzNujOqlWB+cgcADIvIfEfm8iIyKQ1Q5cOM19wXtEaOTX0W8K7Jx+ISUaQRV/9pwtSnOiKER/UbGNnbk1IwL25llJZ9eVTeo6s2q+n5gF+C/wEslF1IG3PnoTO57fjbgJyNQeOSKs92KMgzHFFuL6gpV3Q34PDAWeMxfQq46Xnzq7aB9/Bn7OlRSPCJ+SoyId9bWtJVjvSWPQXVhxFdc9ajKDanJu3/JrnQnBFDV1ar6W1U93KmQBLJgwXKu+Nsj4QsKd371TIYOHbr1gwyjCii6FpXPcmApXnRDr25Jt1InZqiITBeRt/yfXSbhSgLtG8MKy6d+6mCHSoonVROPz9AvHnkyKFY8pL68sgcMawhX4Za1r4t07LKMoAJSeXlwyMZTt8zoOyddeTMQrtz87NxjmTyp4JJdhlGxFJvJ+LMi8ijwMDAc+LSq7tHLuW8EjtvitUuBh1V1B3+OS3s5dklpbCyffC8ADbW1scRDP/ByuKp15E7bRT9BjAzPM3CWtEWX3X9T56Zgxy6WLcEYSaXyTw/RGn1GNOz9mTDXDQpnHbwbh+61qztBhpEgig0TnwRcpKoz+zqxqj4uIpO3ePlkvLBOgJuAR4FL+jpXLKiWbfRUQ30tG2IIEV/V3h60Lzwy+VXE8xnTOChoL2uPbrXiseX/BlIoUEcZp5HNlu/2Y6Wy9/mecZM7C00a3p+vnHmMO0GGkTCK9cG5NArjphtGqeoSf64ldLP9lYhaMWW699DcGP+FduTA8gp2Gd0c7oYujXCL6pHloYvats07RjZu6TEDJ0nsff41oTO///OO733amR7DSCK99cFxjstaMatXlPdyff/GhqAdacRQmUZQAYzOW8FZHuEKzspMaHyfMu4DkY1bSlIIkOmxn1Earv7Tg2H+eP/79sJvLBzcMLYkaQbOslwqdf/ncsd6uuTmXzwYtAcNaXaopHcM7h+GRK/d0N5Nz15ShkbOqKZwxWl15/pY5thu0PaxjBsnKUn5P83ASQq3Pv6K18gZN78148YwuiJpBs4/8aoG4/+8y6GWrfLUA2EqjoOOe49DJb1j6MDQKFu+pjWSMTd1Ru/TU0ry8+Cs7YhuO0Yp64UthBQigpTtv6CyeO+5PwFAUAR44qcVV2nCMCKjIANHRFpFZF0Xj1YR6dV+jV8n5mlgJxFZKCLnAD8AjhaRt4Cj/eeJo2VVeAH8yBeOdqikd4wc3C9oL1kdzXbMrTNmBe2mmqTZzT2THzHUmo5uVWsLN4kypPz+lpXK1HN/4lvLCgrv33cHmpvLbwXZMEpFQVFUqhp5qt6t1IkBr85V8vGdi4eOHNRDx+Qxemi4HbNkVTTbMTc/92LQfu+k8ZGM6YqN6ShXo8p97aMesJIernlr7hKvgCb+qUfginPf71qWYSSaYsPE8ZPv7QAEyV9U9fEoRSWebO5M41pI7xg7NDTKlqyOxmF6bt5K0OcPLa/MziHesn97piOS0V5dExbCljgSD5WEJiyCyj1nfucvXkO8U8+M333ZqR7DKAeKLbZ5LnAhMB6YCeyHt810RPTSEk6ZGjcAo4f2D9orW6IpMKnB/2CvMl3BSeH9EzIajUPt3Yv/GbTH1o2NZMzSUz4V4SuVA3NbU/5N1Q2XneZakmGUBcVusF8I7APM82vC7AU4SkLjhkym/KNJRuYZOKtaI7o7L2ODLx8vIDqa0Pk5G98J2keOKj9fLQBqwu3MOIuQGl2jqmzK+Mn8/O/YHttPcinJMMqGYg2cdlVtBxCRBlV9HdgpelnJ5YG//TdoNzQXvcOXCPLz4LSst8KSOXKbSFHZamnSQS7IA0eUV72yAAm3M7NWj6rkTPtkWIpBgBk32NaUYRRKsVfohSIyGLgTmC4ia4DF0ctKLnf/6emgvfOeEx0q6T35EUPr26PxN6kEahDSES5FZTQ0mmpqaiIbt6SkhoftzHKoTWz924rjP/97azNr+8NH7uZOjGGUIUUZOKp6qt+8XEQeAQYB90euKsEsmL00qEN1xgVluu2QR9vGvkcMzZy/KGiX6WUcgLpULemsRVBtRu1o2OS3M/OpsgVbp1z807vDrSmBr3zsWMeKDKO86PUei6o+FqWQciHTmQUENMuU/XdwLaf3+A6LmzJ9DwH+9aNPBe3JQwf3eTxXNKTq2BipgVMBeInFPTKLtt7PiJSf3/xwuHojcP9PPuVUj2GUI4Um+nvC/9man+CvL4n+ypuyvy/3ENjU2Xen6efnLQ7S9X5o6h591+WIfrUNPXcqkHWbKuRrUTsubGeXuNNRZdx8f5hXCoWhZXzjYBiuKEbhd1cAACAASURBVDTR30H+z8gT/hluyURgq23oDKNrzpy2Z98HdES/2iC1E5lshppU7zfc7l54d9AeIGX8tUnlhfynl7rTUUXccNsTAIj/3Xz6poscqjGM8qUgA0dEunXdV9WfRCPHKBVR5inMT2FXX1eekWUAg+vDnC/rNrUxpLH3hsmzq2fkkl0zZfCUvkpzR83osJ2tqowQzvjtHc+GT2TzoADDMAqn0KtR7ky/E14enFwGsxOBqsliPG/2svBJuSam9ampEdJRLN9UEMMaQoNm8caWPhk4a7MtQfvU8ad20zPZpFIDwqxA2tJdVyMC5s9fGQQxADx63WcdKzKM8qWgWwNVvUJVrwCGA3ur6sWqejHwXrysxlXBLT/7F7nEJqPGl18NqnzqyzVsOUZGNoZ/06Ub+3YxV1LBY0hT+YZWp1IpxP+PbDRZr0uFiNwgIstF5OW814aKyHQRecv/mag/zoe+dhMCiCqC0tRkmaQNo7cUu/Y5kTBoFL89OTI1Cef5x94I2oefvI9DJX2nsaEuknE2VFAenTFNoSPnorZVDpUkC6+OlpCivAwc4EbguC1euxR4WFV3AB72nycHDR//9yUrpmkYfaFYh4k/Ac+KyB14X8NTgT9GriqhbFjbHrRPO/9wh0r6TnNDPatb+57F+KYnXwiceQY1RmM0uWJc09CgvaSPKziVhrdhsqmHXslCVR8XkclbvHwycJjfvgl4FLikZKK64bCP/zisOQUc/F7LOWQYfaHYRH/fF5F/Abm8859U1f9FLyv59O9f3kvHA5rDkOjOzgx1db3bsrpr5qtBe/9tyjOzc44xzaGBs7y9tdfjVG7NpvIycLbCKFVdAqCqS0RkZFedROQ84DyAiRNL87nu6GSzxH6GYfSN3rjnz8GrIP4/YICIHBKtJKMUDBkQGmir1vV+62FhS5jv5bOH7dcnTa4ZmedkvKaz9+/Ji6tnAZ67Vk1Z53bekko13N6Nql6nqlNVdeqIESNin6+jo2Oz7amnb7k49jkNo9IpagVHRM7Fqyg+HpgJ7Idn7BwRvTQjTkYMDCuKL1q5jtHDBnbTe+vkX/J2HNvlzXDZ0FQXrmqt7YOBc8/iB4IQ8fH1leCDH2VSAecsE5Ex/urNGGC5a0EAh3/8l95bnKKC3mrDcEuxKzgX4oWJz1PVw4G9gKpIjpHJZIIIqkpg5NB+QXvxKvM3ySHiPdrSvXeenrNxLl4MjHDsmEqoH1RJq1D8Ezjbb58N3OVQS0jWMyMlC7tvO8y1GsOoCIo1cNpVtR1ARBpU9XWqpPreQ/8Ik281lLkzLcD44WHE0MKVFVJWIEI29sHA6SSsZ7Xf8KlRyHFMY89dEoiI/AVvhXknEVkoIucAPwCOFpG3gKP95wlAg+2p66/6hGsxhlERFBtFtVBEBgN3AtNFZA2wOHpZyePuG/8TLB3vNKW8nWkBJgwPc74sWbW29wPlFQSsJDZp34uQAtRURL6hJmC9axFFo6pnbuVXR5ZUSA8c9qEf4xXwDRP8GYbRdwo2cEREgC+qagtwuYg8AgwC7o9LXJKY90ZYh+fDFyTq/Ngrxg4PfW5WrO2dv8krC8P3pBIu4/lkzBEiRPqBejvRqorYRThSOjPq3R/Y22oYkVKwgaOqKiJ34mUvRlUfi01VAkmnQ3favQ/axaGSaBg6oF/gO7p6fVuvxvjNI/8NzskThpR3Zuct6Yt5U3GLWqlB4Bed10wbUtuv+/5GceTCwhWe/IdFTxlGVBTrg/NfEYk9ha+IzBWRl0RkpojMiHu+aqS21l9zEVjX1t59563w3JyFQfvUvXaLQlbZs2FT2WX77ZlUntNrZok7HRXIpk2bQkPYFg0NI1KK9cE5HDhfROYBG/DvO1R1j8iVweGqujKGcY0taGvv7LlTF6zbFB730QPKuGJ2HvWk2NSHfC/3Lp6Ov+FAMxWy0pEaFbaz84HtnUmpNI444+egIGbcGEbkFGvgHB+LihKQyWTIdGaob6zv3QAVEh7eFZs6++5Q29zQ0HOnMqC+pp5Nmd6taAE8sfLpoL374F2jkOSemrxcPul57nRUIJJVb+HGnHAMI3KK2qJS1XldPWLQpcCDIvK8nzL9XYjIeSIyQ0RmrFjRfSqebDbLaSPO4YTms3jlqTe67dsVK5ZUduHFzkwfMtRWmN3XVNO3FACrMquD9mnjTuirnGRQOylsZ5duvZ9RPOrnv1G498ZPu1ZjGBVFb0o1lIIDVXVvvBWjz3dVDqKYVOqbOjrZ0OL5Rvz+spuLFvPXn08P2kNGDeimZ3mS7a2Rolv8rAAG1IYlLNKZvq1sjes/rq9ykkH9e8N2w4HudFQieeUZBg2qLEd9w3BNIg0cVV3s/1wO3AFM68t4jU3h9smKhcWvxjw1/eWgfcBxcbgblR/pdDR5YpLGkIbQb2Z1R+9yv1Tabmaqdhgy/D5k6F9JNVrpuSgxB2PDiI/EGTgi0k9EBuTawDHAy90fVTht64oPiW5ZFlaWPuOCo6KS4pzaVO/3/O94IfyTNNVWThac4fXhCt38tuKN4ZxxU2lGjtRuj9Tv7VpGRfGtK//ubVFl1ZyMDSMGEmfgAKOAJ0TkReBZ4F5VjSyZYMeGXqbg969Yw0cPjUqKc+r6YJj85elZQXvPCaOjkJMIxjYNIbdnMH/DsqKPz9txMIxueezJOX59O9dKDKMyKTaKKnZU9R1gz7jG37SpFyHRFXpb3lhfy8ZNvdtqmr0iXN04/5A+7SAmivHNw4Jtg/kbVnfbd0tmr5uLRcIYBZNfmaHXjnCGYWyNJK7gxIpmXCtIDv2bwpB5LdJ468xbpth3x8nRiXLMpH7Dg4riSzauKerY2xbcE7RH147qpqdh4H1/st7jqm+/z7Uaw6g4qs7AKZZstg8h1AlnUL+wSvSa1iIz8FZgBBXAuP5h1t6VHcVVWX+tNUxBcOhIizYyekA1eBwwbXfXagyj4qgaA0dqerd18MJ/Xg/atfWV9XaNGBQ61M5bVtxqRaUypC6MolrTWZzR105HsIt5/JjDo5RlVCDir4Kag7FhxENlXbG7oba+d+5Gt/7ywaA9eacxUclJBGOHDQocYucsbXEtJxGkUuFXYkO6uIzG2TxXrYa6ysjsbMSIhkaOYRjRUzUGTn4unGJ448X55M5AJ3/qsMj0JIGJowYH7XeWFl72a0nL2qBdyS617elNRR4hFkFlFEFlBi8YRlKoGgOnaWDob1KMQ+2mtrQf96sc/oGpMShzx7ajh/p54mHRyrU99s9x7cNhvaVRA5pjUJYMNlGsR7rgfaWq5mtl9AGxHDiGEStVcyYeOLR/0G5ZWcR2TJ4xVFNTOQntACaNHhK0l60t3N/kkVffCdrH7rZjpJqSRDHXnU1Fr/YYVU+ek7FhGNFTNQbO8PFhdMz815Y4VJIchvYPV1/WrN9Y8HGrNnYE2ezOPbxycuD0hQeXPBa0G+hlxXqjqpCs/7DUFYYRC1Vj4IzZdjS5/Zg5L8VRAL38yHeoXb+xCIfavBvOYQP6bb1fmdIbv6J/L3syaO/cf/voxBiVi63gGEasJC6TcVxM3HlckDZ0/quLCjqmdW3vii2WI+0dhWd4rmTHYoBaUnRSXP6jRZ3Lg+vUaeMtaZvRM4Hvjdk3hhELVbOCs+2eE4P2orcL26L6668eCNoDhjZ207P8SVduPsOiaUwVv8WU1WwQQbXTEFvBMQrAVnAMI1aqxsCZsNO4oL1qUWFOxo/d/nxwApp2xHviklZWZDKV7zDQv66BnJNRJlvov1fyHoZRAFaZ1TBipWoMnAGD86KoVhUWEr1q8drAwDnry8fGJa2suPeF14J2Q6oyL+aD68PPysL1q7rpaZQrIjJXRF4SkZkiMsOJBvVCxMVWcAwjFqrGwMmnfX2BDrV5550xkyqzeGKxJsqNTz4f3HXuPm5kHJKcM6ZpcFBw8631i13LMeLjcFWdoqpuElxlgKwitj1sGLFQlQZOR3vhDrWVTn1tcbl9Zi9bHbQ/fcT+UctJBJOaRwTtN9f17K81e+2cOOUYFUpuBcd8cAwjHqrSwCkyQKaiaWooLpAunXcuPnjnbSJWkwy2HzA6aM9tW95j/1vm3xO4UoyuHdFTdyMZKPCgiDwvIue5UWBOxoYRJ9Vp4BRANTjTAgxsDmt0taxvc6gkOew4cGzQXtK2upueHq+3vh0YOEePOTg+YUaUHKiqewPHA58XkUPyfyki54nIDBGZsWLFilgEeGUa1HxwDCMmzMDZCo/987ng7qq2sbJKNOQzYnD/IPjnjYXxnMjLjXHNYdbrVZt6LmHRTie5N/G4MYfGJ8yIDFVd7P9cDtwBTNvi99ep6lRVnTpiREyrclmFjEIWrrzsj/HMYRhVTFUZODV1hf9zb/vFw0F7u93GxyEnEUwaEVYUf2mOOdTC5hme29KFl7AAqK+1Mg1JR0T6iciAXBs4Bni55Drytqgee2B2qac3jIqnqgyc+sa6glOVzHkzzHZ81pePj0+UY3aaEEaHvd7DCs6suUuCCKpq+eB0FF1R3CgDRgFPiMiLwLPAvap6f8lVZAm3qMwv0DAip2pKNQD0G9yPjes7EBE2trXT1Lz17MSaDtv7VHCSv90nhwbO/GXdJ0D8+YNPBO3xQwbGpskw4kRV3wH2/P/t3XmYHVWZx/HvL92dPYEkBIQkGhNADBAiNBFEAVnDJsvgkEAEx3EyKgzqPMowriPPiCOgjKM+gjowiCigI8swgRAQ8RlByEJWQpImBMgiWcTsJHTfd/6o03WrO73c7tzuurfq/TzPpc+tOrfuOUWl7lunTp2TdjnAiONn74fjXNnl5UIcgOEH74/CfFQr5/ujvQCHHlLsX7B5a8f9TeavLrZqTf9ABfw+VICNOzb5gzCuW/7hiyfHt6hU8CYc58qtIgMcSVMkLZfUIOn6cm131PiD4/Ti/1vWQc786FtXbMTb/taeDvPubir+ik/9wPt6rEyVobRx9O9+9aE41xAGd5jXuaTzLz8DFQqhL07apXEueyouwJFUA/yQ6PHNCcA0SRPKse3D68fH6RVzO+nUl8PL8j1NpV9F1tRk98kygBqV1l1r7ptLaM55ysjJneR2rhUzKBSiJ6qcc2VVcQEO0eOaDWa2ysz2APcCF5Zjw0effEScXrui/SeG/vDoC8U32Zxuqftych7uT208XUNHdlFs9bps7Hk9XCqXOeEx8bxdTDnXGyoxwBkFvJ54vyYsa6E7A3GNn/iuOL15ffsTbv7s2/8Tp8cdeUi7+bKi5EmNrdXfDBtcNyBOb9j5ZkmfGZj4jHOlUKEQv5xz5VWJAU5b18x7/aR2ZyCu2tpif5Nd29sf3+S1l4rzD02/LgdX5SW0Us1reK3ny1FBDupfHB9o3pur2s+YvzuZrpwKVnw558qqEgOcNcCYxPvRQNlHoCs0dnBCSaw68aysd6YN8U0nHU5ufuTpOMvY4UN6pVxpOnRIseVu3uaV7eZrPlT898l1S6FQfDnnyqoSA5w5wGGS3i2pLzAVeLhXS5CzS/J+dcUOw42NbQ9s9+K6TXF6xmkn9HiZ0nbc8ESH9G1r28zTsOVVDIUgxztruW5oKhRfzrmyqrgAx8wagWuAWcAy4H4zW1reb+mkucIITzfkI9AZMbjYd2Txq+vbzJM8/V5QX5aH2ira8cMOjdNvvNV2f63bGn4VUmJEjQ986LpmxrnfACtAoQmaGjv/gHOuSyouwAEws5lmdriZjTezb5Z14wpVbufxmF27Qt+cfMQ2AIw5aFicfmpBQ9uZEj2Rk3M1ZdWQ/oPi9I7C7jbzNOxaHacvOeTsni6Sy5jXX9gQtdwUfBwc53pC9n+pWulT2/Gzv3fc8ECcru2X7bFemk0+7J1xet7La1IsSaWJIjpr59enuaEP4JzRH+y1UrmMaB5rq1Dg1KkT0y6Nc5mTuwBn8H4D4/RrL+39ZNDsXz4bp0+ckt05qJLOnFS8HfPahr3no9qxs+0WjLxoLxxuDm7Msj/woSuvKQfMiA6cpiZobOSfbvlk2kVyLnNyF+C8Y1xxcsnZ9zyz1/rdO97GzDAzPnPTtN4sWmrGHDQ8Tm9/6+291t/40G/jdN8cHTHxQH/tRDgljx/kXMLXrrwlDC9gmD895VyPydHPVeSYDx8Zp+fOWrjXerPiCWf/4fv1SpkqSVs/1o8ueClOn3X0e3qvMBXsL29todhZ3Z+gcqV7/uFlRDOJF6CxiUff+FHaRXIuk3IX4Jx+ebGvxJqVbT8xlMvrcrX6m7CnQLxLvnzxh3uxUOnqk9gZO99+q8W6W1+6O073pRbnSnH24KuiRCHqe/PDOWWbS9g510ruApxxE4pjCO7e2XL27PgJqrxqt7NJMTlkUH6mIxhWW3yS6vE181usm79tedxHdMqBJ/V20VwVOnvQlSBhhUJ0a6oGxo8f3/kHnXPdkrsAB4jvKqjV01S3XntXMYtflMfyeiPmvUOLwfDM9XNarEsOkfTxcWWZC9Zl2NkDPhYlQlQsMx7b9NN0C+VcxuUywJG0V3AD8PsH5scnoFMuOj6FkqWnJrE7Xl5XnLx09Z82tZE7Hy4afSLN9+YadrW+nan4RmZdXV2vl81Vj7P7X9HikXAKBR7bemfaxXIu83IZ4LQrcVn++e9dmWJBet87hhVH4r3t0eKj8lff8WDc/2ZAbb4Ol8kHHB63XDXS1hQWeWzXcl1xVt/LsebxBMKAfrN2/CzdQjmXE/n6xWrDtq07Wi4IP+b9+vVLpTxpOb/+PXGLxDMvro6Xv7Z5W5y+7oIP9Xq50tSnT5/io+IJv37liXQK5KrKWXVT48GSoqczjVm77u74Q865ssllgDNwaP84ffsXfw5AU1Pbk0zmxVVnFm/JbX+77X1x6UnH9lZxKtqdrz8cB4Oj6w5MuziuAp3Z97J4PC0rGFiBWW/dk3axnMuVXAY4J10ymebbC0/dFw32d8P07xfvk+fQwP79/I5LJwphULZCov/NjZOuTrVMrvJcfcJ10Nh8Lon63Ty+5960i+Vc7uQywJlx0/Q43bg7+tF67rEl8bLJ5x3V62WqRL95ZmEuhwTaW7QT7lw5K7EsigZHDBjWzmdcXq14/hWioYqBQoHZTfelXSTncimXAc7QoYNos3NF8PX/uqaXS1R5Nry5la//ujhFw9D++Xxu/siBo+OGrbvXPMmqLWvz3NDnusSYXfhV2oVwLrdyGeC0tmfPnha3p/I6cWIy3pt2889brHvwC1f1cmkqw43v+5sW7z+94KaUSuLKSdIUScslNUgq63DCM3f/gi/94nPMavSWG+fSlO8AJ1yaf2Tkp4rLLL+T3113SfEpqY07Ws4gPjLxGHmeDOs/NBwmzffq1Py0LzdPuDbdwrlukVQD/BA4B5gATJM0oVzbr6ur48NTT6JPn3yfXp1LW27/BR5/wbFxk4U1t96Y8ddfODflkqXn8lPqW3Y09tswQfOOKIRGPmEmjjrAh9mvUpOBBjNbZWZ7gHsBH47auYzJbYDzr/d/Pkq0CnI+8ZVLUyxVZTCAPiHWMfjmZaelXKJ0DdMgJKNGxbEgPfaraqOA1xPv14RlMUkzJM2VNHfjxo0456pPbgOcmFTsf9NOp+M8ufD4w6NE4hf8I+8/Jp3CVIgHTrshSij6T8HEQ5NvTLNIbt+09Q+9RcxqZj82s3ozqx85cmQvFcs5V065DnDiIdPNkMRjW+5It0AV4Ibp57U4Khbd+vn0ClNBZhx0Vtz35uQhRzNw4MC0i+S6bw0wJvF+NLAupbI453qILAPPu9bX19vcuXPTLoZzDpA0z8zq0y5HeyTVAiuA04G1wBzgcjNb2lZ+P784V1lKPcfkc3AT51xumVmjpGuAWUANcEd7wY1zrnpVVIAj6V+AvwOae/V9ycxmplci51wWhfOKn1ucy7CKCnCCW83slrQL4ZxzzrnqletOxs4555zLpkoMcK6RtEjSHZLancnQx6lwzjnnXHt6PcCR9ISkJW28LgR+BIwHJgHrge+0tx0fp8I555xz7en1PjhmdkYp+ST9BHikh4vjnHPOuQyqqFtUkg5OvL0YWJJWWZxzzjlXvSrtKaqbJE0iGjB2NfD36RbHOeecc9UoEyMZS9oIvLqPmzkA2FSG4lSrvNcffB+Uq/7vMrPMdIzrxvklT8dRXuqal3pCddS1pHNMJgKccpA0t5KHl+9pea8/+D7Ie/3LJU/7MS91zUs9IVt1rag+OM4555xz5eABjnPOOecyxwOcoh+nXYCU5b3+4Psg7/Uvlzztx7zUNS/1hAzV1fvgOOeccy5zvAXHOeecc5njAY5zzjnnMidzAY6k1ZIWS1ogaW5Y9lFJSyUVJNUn8o6VtCvkXSDptsS630lanlh3YFjeT9J9khokPSdpbG/XsSNdqX9YN1HSs2H9Ykn9w/LjwvsGSf8hSWH5cEmzJa0Mf9udEDUtZdwHmT8GJF2RqN+CsH5SWFe1x0BaJE0Jx0yDpOvTLk85hQmQN0hakliWuWNB0hhJT0laFv7NfDYsz2Jd+0t6XtLCUNdvhOXvDue2leFc1zftsnaLmWXqRTQC8gGtlr0XeA/wO6A+sXwssKSd7bTIm1j+GeC2kJ4K3Jd2nfeh/rXAIuCY8H4EUBPSzwMnAgIeBc4Jy28Crg/p64Fvp13nHtwHmT8GWuU5GliVeF+1x0BK+70GeBkYB/QFFgIT0i5XGet3MnBs8pyZxWMBOBg4NqSHACuACRmtq4DBIV0HPAecANwPTA3LbwM+nXZZu/PKXAtOW8xsmZktL9PmLgTuCulfA6c3X9lWqg7qfxawyMwWhnybzaxJ0ZxgQ83sWYuO8J8BF4XPJOt/V2J5RevqPuhkc1k6BpKmAb+EeF64TB0DvWAy0GBmq8xsD3Av0b7KBDP7PfDnVoszdyyY2Xozmx/S24BlwCiyWVczs+3hbV14GXAa0bkNqriuWQxwDHhc0jxJM0rI/25JL0h6WtKHWq27MzTbfzXxAzYKeB3AzBqBLURX/ZWiK/U/HDBJsyTNl3RdWD4KWJPItyYsAzjIzNZDdCIADixj2culHPugWdaPgaTLCAEO1X8MpCE+LoLkPsuqTB8L4fbz+4haNjJZV0k1khYAG4DZRK2QfwnnNqji47jSJtssh5PMbF3oLzFb0kvhyqMt64F3mtlmSccBD0o60sy2AleY2VpJQ4D/Bj5GdBXb1pV6JT1r35X61wIfBI4HdgJPSpoHbG0jbyXVsTP7vA/M7EnycQwAIOn9wE4za+5fUel1rES+zzJE0mCif/efM7OtFd5I222hxXqSpP2BB4huZ++VrXdLVR6Za8Exs3Xh7wai/1mTO8i728w2h/Q8osj18PB+bfi7DfhFYjtrgDEAkmqB/di72TY1Xak/UV2eNrNNZrYTmEl0j30NMDqRbzSwLqTfCLcvmm9jbChvDfZdmfZBXo6BZlMptt5AlR8DKYmPiyC5z7Iqk8eCpDqi4OYeM/tNWJzJujYzs78Q9dE7Adg/nNugio/jTAU4kgaFq20kDSLqX7Gkg/wjJdWE9DjgMGCVpFpJB4TldcD5ie08DFwV0pcCvw19FFLX1foDs4CJkgaGg/kU4MXQ/LpN0gnhtsyVwEPhM8n6X5VYXhHKtQ9ydAwgqQ/wUaI+I0DcBF+Vx0CK5gCHhSdQ+hIFjQ+nXKaelrljIRzv/wksM7PvJlZlsa4jQ8sNkgYAZxD1OXqK6NwG1VzXtHs5l/NF9PTCwvBaCnw5LL+Y6OpqN/AGMCss/6uQbyEwH7ggLB8EzCN6umYp8D2KT9b0B34FNBA9ZTIu7Xp3t/5h3fSQdwlwU2J5fVj2MvADiqNejwCeBFaGv8PTrndP7IOcHQOnAn9sY1tVeQykvP/PJXrq5uXmfZ+VF1EL33rg7XAs/W0WjwWiW9YW/u0vCK9zM1rXicALoa5LgK+F5ePCua0hnOv6pV3W7rx8qgbnnHPOZU6mblE555xzzoEHOM4555zLIA9wnHPOOZc5HuA455xzLnM8wHHOOedc5niA45xzzrnM8QDHOedcxZF0sSSTdEQXPzdW0q4wv1JPlW1AmKNuT/OAoK7yeIDjOiVpf0mfSbx/pge+Y6+TUji53Z14Xytpo6RHEsu2J9JN4aSzVNJCSf8oqY+fjJyrStOAuUQjQnfVy2Y2qczliZnZrrD9qpzCIC88wHGl2B+IAxwz+0APfU/rk9IO4KgwhDjAmcDaDj6/y8wmmdmRIe+5wNf9ZORcdQkTXZ5CNFrytMTyIyU9IWmFpK9K+r6k4zvZ1lhJL0n6qaQlku6RdIakP0haKWlyIu+DkuaFi6QZYdkgSf8bLpqWSLqsh6rtyswDHFeKfwPGh1aQm5tbTbp44pgu6fmwjdub5wArwaPAeSE9jZYTQrbLookmZwDXhLllnHPV4yLgCTNbBOyQdKyk5ilSPgscA3wSGGVmc0rY3qFE061MBI4ALieakuELwJcS+T5hZscRTVNyraQRwBRgnZkdY2ZHAY+VpYaux3mA40pxPaF1xcy+2GpdpycOSe8FLgNOCi0pTcAVJX73vcDUcHKbCDxXaqHNbBXRMX5gqZ9xzlWEacD9IX1/eH8G8IKZLTWzXUBf4Dslbu8VM1tsZgWiOdqetGieosXA2ES+ayUtBP5INDP8YSHPGZK+LelDZrZlH+vmeklt51mc69ArZrYYQFJ84pCUPHGcDhwHzAmNKQOADaVs3MwWSRpLdIKb2Y3yeeuNc1UktJpMBi4Ji+4Dnga2Ek2KjKRDgO1m9ocSN7s7kS4k3hcIv4OSTiUKok40s52Sfgf0N7MVko4juuX9LUmPm9kN3aye60Ue4Lh91emJgyjIuMvM/rmb3/EwcAvRrNcjSv2QpHFErUUlBVPOuYpwKTDTzHYDmNkrkv5E1Bo7OuT5FlELTjntB7wZgpsjgBMgDqb+bGY/D7fnRgAQLwAAAX5JREFUP17m73U9xAMcV4ptwJB9+PyTwEOSbjWzDZKGA0PM7NUSP38HsMXMFoerrE5JGgncBvwgNEU756rDNGCipNWJZSOIbi1NlLQcuB3oJ+nfzexzZfrex4BPSVoELCe6TQVwNHCzpALwNvDpMn2f62Ee4LhOmdnm0HF4CVGn365+/kVJXwEel9SH6CRxNVBSgGNma4j6+bQgqZaWLUgDwmPmdUAjcDfw3a6W1zmXHjM7tczbWw0clXj/8bbWhRajc9rZzKxylsn1DvnFrasEoZ/NI+EphVI/cwzwEzOb3GnmKP9qoN7MNnWnjM65yidpDPAMsLmnxsIJQ1c8C4wEjjazP/fE97h94y04rlI0AftJWlDKSUnSp4BrgU6bpxMnozqivkHOuYwys9eJnoDqye/YBfTYQIKuPLwFxznnnHOZ4+PgOOeccy5zPMBxzjnnXOZ4gOOcc865zPEAxznnnHOZ4wGOc8455zLHAxznnHPOZY4HOM4555zLnP8H/9hsSUaWTQkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116e49ac8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "origin = coord.ICRS(ra=14.745*u.deg, dec=71.512*u.deg,\n",
    "                    distance=71.634*u.pc,\n",
    "                    pm_ra_cosdec=32.123*u.mas/u.yr,\n",
    "                    pm_dec=86.63*u.mas/u.yr,\n",
    "                    radial_velocity=17.4123*u.km/u.s)\n",
    "b = Barycenter(origin=origin, t0=Time('J2000'))\n",
    "\n",
    "orb = KeplerOrbit(P=54*u.day, a=0.1*u.au, e=0.3,\n",
    "                  omega=2.124*u.rad, M0=0*u.rad, t0=Time('J2000'),\n",
    "                  Omega=121.53*u.deg, i=61*u.deg,\n",
    "                  barycenter=b)\n",
    "\n",
    "t1 = Time('J2000') + np.linspace(0, orb.P.to(u.day).value, 10000)*u.day\n",
    "xyz = orb.orbital_plane(t1)\n",
    "XYZ = orb.reference_plane(t1).cartesian\n",
    "\n",
    "orbit_style = dict(marker='', linestyle='-', linewidth=2, color='#888888')\n",
    "body_style = dict(marker='o', linestyle='none', color='tab:red',\n",
    "                  markersize=12, zorder=100)\n",
    "barycen_style = dict(marker='+', color='#888888', mew=2, ms=8)\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(8,4.5),\n",
    "                         sharex=True, sharey=True)\n",
    "\n",
    "axes[0].plot(xyz.x, xyz.y, **orbit_style)\n",
    "axes[0].plot(0, 0, **barycen_style)\n",
    "\n",
    "axes[1].plot(XYZ.x, XYZ.y, **orbit_style)\n",
    "axes[1].plot(0, 0, **barycen_style)\n",
    "\n",
    "lim = 0.7\n",
    "for j in [0, 1]:\n",
    "    axes[j].set_xlim(-lim, lim)\n",
    "    axes[j].set_ylim(-lim, lim)\n",
    "\n",
    "\n",
    "axes[0].set_xlabel('$x$ [{0:latex_inline}]'.format(xyz.x.unit))\n",
    "axes[0].set_ylabel('$y$ [{0:latex_inline}]'.format(xyz.x.unit))\n",
    "\n",
    "axes[1].set_xlabel('$X$ [{0:latex_inline}]'.format(xyz.x.unit))\n",
    "axes[1].set_ylabel('$Y$ [{0:latex_inline}]'.format(xyz.x.unit))\n",
    "\n",
    "axes[0].set_title('orbital plane')\n",
    "axes[1].set_title('reference plane')\n",
    "\n",
    "fig.tight_layout()\n",
    "\n",
    "# --------------------\n",
    "# plot 2\n",
    "\n",
    "t2 = Time('J2000') + np.linspace(0, 3*orb.P.value, 10000)*orb.P.unit\n",
    "icrs = orb.icrs(t2)\n",
    "# TODO: this is only necessary because the released version of Astropy\n",
    "# doesn't support velocity transforms in SkyOffsetFrame\n",
    "_icrs = coord.ICRS(icrs.spherical.without_differentials())\n",
    "_origin = coord.ICRS(origin.spherical.without_differentials())\n",
    "offset = _icrs.transform_to(coord.SkyOffsetFrame(origin=_origin))\n",
    "# offset = icrs.transform_to(coord.SkyOffsetFrame(origin=origin))\n",
    "\n",
    "style = dict(marker='o', s=2, cmap='viridis')\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(8, 4.5))\n",
    "\n",
    "axes[0].scatter(t2.mjd, icrs.radial_velocity,\n",
    "                c=t2.mjd, **style)\n",
    "axes[0].set_xlabel(r'time [${\\rm MJD}$]')\n",
    "axes[0].set_ylabel(r'radial velocity [{0:latex_inline}]'\n",
    "                   .format(icrs.radial_velocity.unit))\n",
    "axes[0].set_title('line of sight')\n",
    "\n",
    "axes[1].scatter(offset.lon.wrap_at(180*u.deg).milliarcsecond,\n",
    "                offset.lat.milliarcsecond,\n",
    "                c=t2.mjd, **style)\n",
    "axes[1].set_xlabel(r'$\\Delta\\alpha$ [{0:latex_inline}]'.format(u.mas))\n",
    "axes[1].set_ylabel(r'$\\Delta\\delta$ [{0:latex_inline}]'.format(u.mas))\n",
    "axes[1].set_title('sky offset')\n",
    "axes[1].set_xlim(-2, 37)\n",
    "axes[1].set_ylim(-2, 37)\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_orbit(origin, orb, nsteps, filebase=\"planet_ref\",\n",
    "               reference=True):\n",
    "    \n",
    "    if nsteps<100:\n",
    "        ntimes = nsteps * 100\n",
    "    else:\n",
    "        ntimes = nsteps\n",
    "    print(ntimes, nsteps)\n",
    "        \n",
    "    steps = np.arange(0,ntimes,ntimes//nsteps)\n",
    "    \n",
    "    t1 = Time('J2000') + np.linspace(0, orb.P.to(u.day).value, ntimes)*u.day\n",
    "    xyz = orb.orbital_plane(t1)\n",
    "    XYZ = orb.reference_plane(t1).cartesian\n",
    "\n",
    "    body_style = dict(marker='o', linestyle='none', color='k',\n",
    "                      markersize=10, zorder=100)\n",
    "    barycen_style = dict(marker='+', color='#888888', mew=2, ms=8)\n",
    "    style = dict(marker='o', s=2, cmap='magma',zorder=10,vmax=t1.mjd[-1],vmin=t1.mjd[0])\n",
    "    print(style[\"vmax\"],style[\"vmin\"])\n",
    "    icrs = orb.icrs(t1)\n",
    "    \n",
    "#     if reference is True:\n",
    "#         xmin0, xmax0 = min(XYZ.x.value), max(XYZ.x.value)\n",
    "#         ymin0, ymax0 = min(XYZ.y.value), max(XYZ.y.value)\n",
    "        \n",
    "#     else:\n",
    "#         xmin0, xmax0 = min(xyz.x.value), max(xyz.x.value)\n",
    "#         ymin0, ymax0 = min(xyz.y.value), max(xyz.y.value)\n",
    "#     print(xmin0,xmax0,ymin0,ymax0)\n",
    "    xmin0, xmax0, ymin0, ymax0 = -0.2,0.2,-0.2,0.2\n",
    "\n",
    "    xmin1, xmax1 = min(t1.mjd), max(t1.mjd)\n",
    "    ymin1, ymax1 = min(icrs.radial_velocity.value), max(icrs.radial_velocity.value)\n",
    "    print(xmin1,xmax1,ymin1,ymax1)\n",
    "\n",
    "    # Now plot\n",
    "    for i,idx in enumerate(steps):\n",
    "        fig, axes = plt.subplots(1, 2, figsize=(8,4.5))\n",
    "\n",
    "        axes[0].plot(0, 0, **barycen_style)\n",
    "\n",
    "        if reference is False:\n",
    "            axes[0].scatter(xyz.x[:idx], xyz.y[:idx],\n",
    "                            c=t1.mjd[:idx], **style)\n",
    "            axes[0].plot(xyz.x[idx],xyz.y[idx],**body_style)\n",
    "\n",
    "            axes[0].set_xlabel('$x$ [{0:latex_inline}]'.format(xyz.x.unit))\n",
    "            axes[0].set_ylabel('$y$ [{0:latex_inline}]'.format(xyz.y.unit))\n",
    "\n",
    "            axes[0].set_title('orbital plane')\n",
    "            \n",
    "        else:\n",
    "            axes[0].scatter(XYZ.x[:idx], XYZ.y[:idx],\n",
    "                            c=t1.mjd[:idx], **style)\n",
    "            axes[0].plot(XYZ.x[idx],XYZ.y[idx],**body_style)\n",
    "            print(idx,XYZ.x[idx],XYZ.y[idx])\n",
    "            axes[0].set_xlabel('$X$ [{0:latex_inline}]'.format(XYZ.x.unit))\n",
    "            axes[0].set_ylabel('$Y$ [{0:latex_inline}]'.format(XYZ.y.unit))\n",
    "\n",
    "            axes[0].set_title('reference plane')\n",
    "        \n",
    "        axes[0].set_xlim(xmin0,xmax0)\n",
    "        axes[0].set_ylim(ymin0,ymax0)        \n",
    "\n",
    "\n",
    "        axes[1].scatter(t1.mjd[:idx], icrs.radial_velocity[:idx],\n",
    "                       c=t1.mjd[:idx], **style)\n",
    "        axes[1].set_xlabel(r'time [${\\rm MJD}$]')\n",
    "        axes[1].set_ylabel(r'radial velocity [{0:latex_inline}]'\n",
    "                          .format(icrs.radial_velocity.unit))\n",
    "        axes[1].set_title('line of sight')\n",
    "        axes[1].set_xlim(xmin1,xmax1)\n",
    "        axes[1].set_ylim(ymin1,ymax1)     \n",
    "        \n",
    "        plt.savefig(\"figures/{0}_{1:0>3}.png\".format(filebase,i+1),dpi=600,\n",
    "                    bbox_inches=\"tight\")\n",
    "\n",
    "        plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 100\n",
      "51598.5 51544.5\n",
      "51544.5 51598.5 -3.9700243131121353 32.96660156792009\n",
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     ]
    }
   ],
   "source": [
    "origin = coord.ICRS(ra=14.745*u.deg, dec=71.512*u.deg,\n",
    "                    distance=71.634*u.pc,\n",
    "                    pm_ra_cosdec=32.123*u.mas/u.yr,\n",
    "                    pm_dec=86.63*u.mas/u.yr,\n",
    "                    radial_velocity=17.4123*u.km/u.s)\n",
    "b = Barycenter(origin=origin, t0=Time('J2000'))\n",
    "\n",
    "orb = KeplerOrbit(P=54*u.day, a=0.1*u.au, e=0.3,\n",
    "                  omega=2.124*u.rad, M0=0*u.rad, t0=Time('J2000'),\n",
    "                  Omega=121.53*u.deg, i=61*u.deg,\n",
    "                  barycenter=b)\n",
    "\n",
    "plot_orbit(origin,orb,100,reference=True,filebase=\"planet_ref\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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