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@eteq
Created February 21, 2018 22:33
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"\n",
"from astropy import units as u\n",
"from astropy.coordinates import SkyCoord, GCRS\n",
"from astropy.time import Time"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"from matplotlib import pyplot as plt\n",
"\n",
"plt.rcParams['axes.labelsize'] = 18"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Proper Motion path of Vega\n",
"\n",
"Inspired by https://twitter.com/ziggypao/status/965506022919102464 and http://scienceblogs.com/startswithabang/2016/10/13/how-far-away-are-the-stars-scientists-still-dont-know-synopsis/.\n",
"\n",
"We start by getting parameters for the bright star Vega from [its SIMBAD page](http://simbad.u-strasbg.fr/simbad/sim-id?Ident=VEGA). The actual numbers are mainly from Hipparcos (via [van Leeuwen 2007](http://dx.doi.org/10.1051/0004-6361:20078357))."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<SkyCoord (ICRS): (ra, dec, distance) in (deg, deg, pc)\n",
" (279.23473479, 38.78368894, 7.67872226)\n",
" (pm_ra_cosdec, pm_dec) in mas / yr\n",
" (200.94, 286.23)>"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"vega = SkyCoord('18 36 56.33635 +38 47 01.2802', unit=(u.hourangle, u.deg),\n",
" distance=(130.23*u.marcsec).to(u.pc,u.parallax()),\n",
" pm_ra_cosdec=200.94*u.marcsec/u.yr, \n",
" pm_dec=286.23*u.marcsec/u.yr, obstime='J2000')\n",
"vega"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It might first seem natural to simply plot Vega's course over several years in the center-of-earth frame (GCRS):"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"t = Time('J2018.14') + np.linspace(0, 1, 100)*u.yr\n",
"delta_t = t - vega.obstime\n",
"gcrs = GCRS(obstime=t)\n",
"\n",
"vega_gcrs = vega.transform_to(gcrs)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x119b802b0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.scatter(vega_gcrs.ra.deg, vega_gcrs.dec.deg, c=delta_t.to(u.year))\n",
"plt.colorbar().set_label('Years since J2000')\n",
"plt.xlabel(r'$\\alpha$')\n",
"plt.ylabel(r'$\\delta$')\n",
"plt.tight_layout()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This plot is hard to interpret because the change in the axes are so small. Lets try it again, but as change since J2000. We'll also plot up the expected path from a linear proper motion:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x119cf85c0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"deltara = vega_gcrs.ra-vega.ra\n",
"deltadec = vega_gcrs.dec-vega.dec\n",
"\n",
"dra_linear = (delta_t*vega.pm_ra_cosdec/np.cos(vega.dec)).to(u.arcsec)\n",
"ddec_linear = (delta_t*vega.pm_dec).to(u.arcsec)\n",
"\n",
"plt.scatter(deltara.arcsec, deltadec.arcsec, c=delta_t.to(u.year))\n",
"plt.colorbar().set_label('Years since J2000')\n",
"\n",
"plt.plot(dra_linear, ddec_linear,c='r')\n",
"\n",
"plt.xlabel(r'$\\Delta \\alpha_{\\rm J2000}$')\n",
"plt.ylabel(r'$\\Delta \\delta_{\\rm J2000}$')\n",
"plt.tight_layout()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This clearly reveals two issues: we see no sign of the proper motion, *and* the apparent parallax effect is way too large. It turns out these are expected, but for not-immediately obvious reasons."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Space Motion\n",
"\n",
"The first thing missing from the above is the proper motion shift (or space motion). This is not in the calculation above because there are a lot of subtleties and assumptions that are associated with space motions that need to be thought about. So the user must manually apply these so that they know what they're getting into. Astropy provides a method to do the simplest of these: a linear real space proper-motion correction:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"vega_sm = vega.apply_space_motion(t)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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uYfKml/kzcwEiisevtHlnPR1HriHtuAS+HNmK9IYVA3fHY2iReCkdkweV4zTx4ERhhYj5wFAR+VxVfy+ukYicgLNthiVEGGPKRq4vm7fX3UN63nY8osRl5HPx/T/T9JsUVnU/hlmPtMBb0YULiJNK9G70GlVj64R72BEvSlPJ7wG+B34WkZn8kxBRsHxRe5waqVnAfSXp3IKTMSYoi3d+zbQtb4E4VWhqrs7g8qE/UXVLNl/f14yf+9QDEQRIjD2WHvWHW2AKWvRN66nqr4HyRc8CFwIX7zvFP2nlXmAGcLeqripJ/xacjDEH5Vc/36d+ycxtY1H14gZOmr6JSx5ZRk7lGD4cczqbT6sGKDESw+k1ruSs5L7hHnZUcbL1ois4AQSm8y4Rkao4WxTV4Z9FuFuAZapaoq0y9rHgZIwp1l7vHl5b8zB78rag6sPj9dPt+RWc/tF6NrSuwcTnTiG3ZiwoxLji6ZR8LW2qF7kxqjmEaLtyKkhVdwNzQtmnBSdjTJE2Za3nvQ0vkpafggcf1VKy6XXXQo5dnsb3/Y7j66Et8Me4EBUquKowuPGrJMRUCfewo1I0LsItTEQaUah8kaquP9z+LDgZYw7wXcoMPt8yHiUXEWi4KJVr7vmRmGwvHz3Tll8vqINLFBROTDyL847pb4GplKKxKnlgY9cHcbbMOGC7YhHZibNlxmOquqMkfVtwMsb8ba83g+lbJvP9zi8BxYPSedzvdBv5M6kNKjH+rTPZ0bgKCriJo3OtK+icfHm4hx31ojFbT0Tq46SHN8DJ2iuqfNEZwC3Av0XkTFXdGGz/FpyMMQBkejN5/NcH2evdhQDxmV76PPIjJ8/exPJz6/HfR9qQn+DGrUqVmOr0bHArx1ey/T1DQgWvP+rKFz0NJACnq+qi4hqJSDtgeqD91cF2bsHJGMMPqT/w8cb3yfFl4BY/9dbv5oa75pO0cS9Tbz+Z7/o2RVyCCzcVY6oypMkTVImpFu5hHzWidLPB84HnDxaYAFR1oYi8CNxRks4tOBlTzs3YOpNJmycBWbgETv3qT/o9+iN5Fdy8NqoLa1vXRACPujjnmMvomnwJMa7YcA/7qBNt03pABSAtyLY7A+2DZsHJmHJqZ24ar/3xJuuzVoNAnE+5YuQSzv1oFWtPSmLs0x3YneyUTnOLh+61e9GlVvcwj/roFI33nIAVwHUiMjawXXuRRCQOuCHQPmgWnIwph/bkZfDwL4+S4c3AJZCYmsVN98/hhGUpfHPVCUwcehq+GBduFarHVOfuZiOoHFM13MM+qkVhcHoSmIxTvuhNii9fNBBoDFxWks4tOBlTzkzaOJ1Jm6cjkgcoTZZtZ8j9c6iQmc/oEWey5KKGAAjCsQnHc+Pxt1lgKmPRuM5JVaeISB/gReA5nAvAwgTYAfRT1Skl6d+CkzHlRL7fy4SN05i2dZZThkiVCyaspPfIhaTWrsTzr5zPpsbVQJVYVwy96/ehU3LncA+7fFDwRmGFCFX9SEQmAecCbTmwfNEi4OuDTfsVJ+KCk4hsADIAH+BV1TbFtGuLcxl5lap+Gjh2Lc6CMHAWfY0r+xEbE/m256TywIrnyPDuAfzEZ3kZ9PR3tJ+1jiVnN2D0w2eRWzkGASq6E7jm2GtoX6N9uIddbkTpPScAAoFneuAjZCIuOAV0UdXU4k6KiBsnZ35mgWPVgWE4uzMqsEREpqrqrrIerDGR7Jfda3j+97fY483AhZ+6f6Vz5/1fUffPdD4Z1Ibp/U5CXYJbXVSPqcETJz1CnNuy8Y60aA1OZSVSg9Oh3AJMxLmM3OcCYJaqpgGIyCycMu4fHfnhGRMZxqz7jGlb56LkIALt5qxjyONz8Ma6efylbvzapjZuUQSha63OXF6vhwWmMIjGe077iMhxQCtgO7BQVQ+49yQiLYCLVfWZYPuNxOCkwFciosCbqjq64EkRqQtcCnRl/+BUFyhYGmNT4NgBRGQgTgYJDRo0CN3IjYkQO3LTGbNuCvNSFwNKnN9Pn7d+5NIPl/FHi2ReeOw80o6pBIBHYhnQqDedkm0aL5w0CoOTiLwM3Fzg0G8i0l9VFxdqeipOdl9UB6eOqrpFRJKBWSKySlXnFjj/EnCPqvoKbftc1He2qOwRAgFvNECbNm2KbGNMtNqRs4shPz1DljcLgMT0bO55ZAYn/rSFGZe2ZMytHfDFunAj1ImvxZAm/WlcqWF4B22irkKEiFyBM4v1I85MVn3gOmCeiPRR1Uml6T/igpOqbgn8myIik4F2QMHg1Ab4OBCYkoBuIuLFuVLqXKBdPUK8v4gxkUxV+WzTPMas/5w8zcMlSvOV27hv2JdU3p3DyAe6MOeiZoiAR9zUjk/m8RP/j4qeEi3cN2VAFXz+qMvWuxVYjHNB4QcQkRdw1j59LCL9VPXjw+08ooKTiCQALlXNCDw+HxhRsI2qNirQfiwwTVU/CyREPCEi+wp+nU8J96w3Jpq9sWYK07b8gI88XCjdJv/Mja/OIzW5Ene9cQXrmyThUsWDi+sb9eScWh3wuKKu2OhRKnT3nETkXZwt01NUtVXg2CnAKJxq4V5gsKouLOK1zwDdARcwC7itqHtIAScAT+4LTACq+qeInIWTufe+iLhUdfzhfB4RFZyAWsDkwFWRBxivqjNEZBCAqo4q7oWqmiYij+Lk1QOM2JccYczRbMPe7Qz75X02ZW0BgYS8fG57/hvOmfU7C9s35PkHziWzcjwCuInhliZX0zm57SH7NUdWCO85jQVeBd4rcOwZ4BFV/VJEugWedy74IhHpAHQETgocmg90ovgZqAo4y372o6qZInIRToAaJyIuirnFcjARFZxUdR1wchHHiwxKqtq/0PN3gXfLZHDGRKCNWancuPgVsn05eATqbk5n+LDPabQ+lXE3nMEn17RFXeARFw0T6vDUSbeQYNN4ESeU65xUda6INCziLfbtBlkVZ4FsUcOIB2Jx7uHH4GTgFecvnCy9osaQLSLdgWnAGAos+wlWRAUnY0xwVJUXVk1h6pYFKD4A2n+/lvuemonfLTzwVA+Wnn4sAC6EUxKbcW/z/iR44sM5bFMcde47BSlJRApmw40unNVchKHATBF5DmfKrsMBQ1D9QUS+BbbiBKdXVfW3g/Q5Dydz+vaiThYIUNOBbpTw6smCkzFRJtubxwu/TeGr7UvxqR+3388N731Pv/ELWN0kmeGPXMz2Y6qCX4l1eXioxbW0TyryD1wTQUqQrZdaXOWcg7gJuF1VJ4pIT+AdnJJDfxORxkBznGQycLKlzy6ULV3QBOCMg7VR1ZxAgPoUaF2SAVtwMiaKrN6zlZsWvkWOZgFK1d1ZDH9yGu1++pNpF7Vi5C1d8ca5ESApNpE7m/WkXY3m4R62OQRFyjpb71rgtsDjCcDbRbS5FFigqnsBRORLnG3Wiws83+CsXzooVc3BSdAoEQtOxkQBVWVeyioe+vkTsn15eFxK89VbefzRKVTblcnTt5/P9O7OfewY3DROqMMbbW/GJVGXnlxulWBa73Bs4Z/khq7AH0W0+Qv4j4g8iTOt1wlnXWlYWHAyJsKpKg8un8Cc7SvJ8+cjKP+avow735hNWrUEBr94Nb83rYUouMVFn2O7cHXDLhaYokyosvVE5COcTLwkEdmEU3P0P8DLIuIBcghUyBGRNsAgVR2AM/XWFWdTQAVmqOrnIRnUYbDgZEwE27A3ladWTmNx2h8oSoXcfO5+/SsumfUzP7ZuyPB7LmZPorNbbZzE8MTJfTk96YQwj9qUlGrogpOq9i7m1AH3fAJlhgYEHvuAG4N9HxFJKeHQfEA68DPwlqp+fbDGFpyMiVBrMrbTd/5ocjUHgLrb03n28Uk0W7udd3p34K0+Z4JHcCu0rFqf+1peQaNKtcI8anO4orDw6zpKloEnOOnslwJXiMg1qlpsYe6QBCcRqQ9UBjJUdeOh2htjiuf1+3hz9VzeWfMdPvUhLjhzyVoef3YKLlXuGHYF805vggjEiocWVevxatvriXXZ35rRrIzvOYWcqp5xOK8TkSRgNnAPB9k14rB/mkUkBqfK7HVAIoHCqyKyC2ch7AOqmne4/RtTHqkqdy+ZyJxtq/Hiw6XKjR/O48aP5/FHo2TufuByNtVORAAXLkac1JPOtVrY/aUopwj+6Kutd1hUNVVE3uYQFcpL86fWazirg3sDP+HMJSYCp+HcgHuFEsxfGlPeLd25kTsXTWR7bjoA1TKzefKFzzhryVo+79KKJ2++iJz4GEShgieWZ0/rwxlJjcM8ahMqUXbhVFqzgeEHa1Ca4HQF0ERVdxY4loqzF9NSYDUWnIwJytKdm7hu/nvk+vMRgebrt/LyU/+lVtoeHht8ERMuPA0EYnHTtkYjXmjTh3h3TLiHbUIlhAkR0UBVfwV+PVib0gQnPcjrPZS7PwSMKbl8v487F07m662/oTjFnf/9zTIefnM6uypXpN8T/VnZrA4AboTzardi+EmXEuu2+0tHHfuNuZ/S/IR/AHwZqAS+DNiNU1DwFOAB9q+Ia4wpZHdeNnctmsL87Wvx4SfO6+WBt7/kqllLWHBiI+6683LSEhPAr8S7PbzT4VpOqW47Nx+tytOVUzBKE5zuwAlCL+HsgKg4SRF/4dRteqLUozPmKPVjygb+M/8TcgI5Q3V27Gbk859w0potjL6sI69c3RWf24UAjSrV5PFTe3By9frhHbQpU9GWrVfWDjs4BRZsjQBGiEhV/kkl3x2qwRlztPH6/Uz/61fuXTwVr/pBoOOKtbz44gRivF5uvvsqZp/h1MKLEzdnJjfm1fa9wjxqU9ZUQctJtl6wQjVxXQUnOAnO9J4xphCv30//OR+xdOcm8tWPS/3cOGUuQz/+hrX1anLzXVfxZ90aiEKsy83QludwzXGnh3vY5giJ9isncXaJvRJnF/JaOMuJfhaRxMCxuaq6Ldj+QrHO6XqcFPJ9x22dkzGF/JK2jQcWfsnK9K0oSpXsbJ59fRLnLl7F5x1P5IFBPcipEIsoxLtjeO/sfpxUvU64h22OpCgOTiISD3yBU9MvD2ejwhcDp/fiLC0ahbPMKCiluY58DWfDql5AMs7uick46546BAZjTLm3MGUjPb96nxVpW1HghD+3Mfn+UXRaupoR13XnjluvIDsuFhdCp1qNmXbeIAtM5Y6gGtxHhBqGs8V7b+BY+GdzKlX1ApOAC0vSoa1zMqaM5HjzeXrpHMatXoKiiMAl85bxxNufsadiPH0evp6fmh3rlCFyuelauwkvt78cl0TsLyBTlqL4ygnoCbytqp+ISI0izq8GLi9Jh7bOyZgy4Fel7+xPWJ66Fb8qsT4vD344nX6zfuTHZg259bZepCZWAoV4l4d3z+5F26QGiAWm8in6F+HWA5Ye5HwmTm5C0GydkzEh9u2mtdw5fxpp+dkA1Nq1mzdeGc9pazby9kUdeab3BXg9zm61iTEVGNO5FydVrx3eQZvwi+7gtAs45iDnmwNbS9KhrXMyJoS+/usPBn83hTy/FwTa/7aWka9/RMXcfIbc0psvTj8RUGLFzb+ObcGTp3cjxuUO97BNJIjuuaZvgP4i8lzhEyJSDydx7uOSdGjrnIwJgcz8PAZ8PZGFKRvxOXM0DPxyHvf8dwbrj0mi1/19WFs3GQHc4ubqxqfx4Gnn4HbZ2hYTEN3BaQSwEFgAfBg41lVEzgJuBvw42d1Bi7h1TiKyAcjA2TXRq6ptCp3vATyK88l6gaGqOj9wzoezxTDAX6p6SWnGYkwwtmft5cbZk1mxcxs+lEo5OTz79gQuWrKS6W1bcfeAK8isEAeqVHDHML379TSqUj3cwzaRRInqaT1VXSUi5wNjgKcDh+8P/LsauEZVN5Skz0hd59RFVVOLOTcbmKqqKiInAf8FmgXOZavqKYf5nsaU2PR1q7j9uy/IwwtAk83bGfXa+xybksajvbrxzoVnQiDJ4bSkujzV/iILTKZI0b4IV1UXiEgLnO3gm+NcrPwB/Kiq/pL2F4r9nHpxBPdzUtW9BZ4mEO0XwyYq5Xi9fLxqOY/8+C1+9YMLLlm4jKfHfEpmfBx97hrAj82PA6CCy8OVjU9kxBnnh3nUJqL5o/fKaR9VVWBx4KNUInGdkwb6UOAZ0wgCAAAgAElEQVRNVR1duIGIXIpz1ZYMdC9wKl5EFuNM9z2lqp8V9QYiMhAYCNCggVV5NiWT7c3n0s8+ZO3uNPx+xePzc9+k6QyYNZ/FjY9l8E19SKleBRQqxcTycLtzuLLxieEetolwEsV/ZovI2UBXVR1ezPnhwGxVnRdsn5G4zqmjqm4RkWRgloisUtW5+72x6mRgcuAL8ihwbuBUg8BrjwO+EZEVqrr2gIE7AW80QJs2baL4R8IcaQu2bOTe72awISMdBZJ37+G10R/Qbs0GxpzTgcd7dscb48GFUCkmlikX96VRVZvGM4egRPsc0P1A1kHOtwTaAkckOJXJOidV3RL4N0VEJgPtgLnFtJ0rIseLSJKqphZ47ToRmQOcChwQnIw5HDPWreb22V+Q7c8HgbZ/rOf10R9QKSeHWwb0Zurpp4A4mwJedlxL7mnbiZoVEsI9bBMVJKoTInB+7x+QRl7AD8BdJekwotY5iUgC4FLVjMDj83FSFAu2aQysDSREnIZT02+niFQDslQ1V0SScOo8PXPYn50xAbtzcnhk3jdMWrNvV2nl+m/nc//E6WxMqsY1Qwfwez1nEW2cy83VzU5h2BldrNqDKZnovnJKxMmyLk4mUK0kHUbaOqdaONN1+8Y2XlVniMigwHuOwqnP1E9E8oFs4KpAoGoOvCkifpyCtk8F9qk35rDler1c9ul4/tqTDkDF3Fye/nAC/1qynJmntOT/+vdkT4UKiELVuHjGd+tJy6RaYR61iUrRHZy24sxUFedUIKUkHYZknVMgIJV68a2qrgNOLuL4qAKPn+afPPqCbb4H7K6zCZlJv63koe9mk+XNR1GO25HCqLfe4/htKTz974t444LOIIILqJ1QmQ8vvopGVUv0x6ExDiXas/W+BG4QkQ8LJz2IyJnAdcDYknRYquAkIlfiTJ/9DLwXKI2+79x0Ve1e7IuNiVCqyscrf2b4d9+S5/cBcNHyFTzz4Sfkejz0veU/fN+sCagS63Jzw0ltuOv0s6yauCmVaM7Ww0lMuwz4VkQ+w8lDUJwrph7ATgrdojmU0izCvQ24D5gO3APcKCIXqWpaoMlZh9u3MeGyMyuLfpMn8nvaDnwobp+Pu6Z9yY2z57C0YQMG39CXrdWdNecxLg+3tW7P4NNOt/tLpvSiODip6lYR6Qi8hROkLitw+htgkKpuLkmfpblyGgxcoKrLRcSNs+j2GxHpGghQ9n+riSp/padz3WeT+TM9HZ9LScrIYOTYD2i/Zi3vn9mexy7rQV6MB5dC1dh4vr76OmpUrBjuYRsTEQLLdrqKyDFAE5wY8Luqbj+c/koTnGqr6vLAoHzAYBF5HueyritR/XeAKW/GLV3KU999Ry5OlZVT1v/J62Peo1pWJnde04tJ7f4p8dipfkMe63KeBSYTUlE+rfc3Vd0GbCttP6UJTjtEpJGqri8wqDtF5CXg21L2bcwRkZGby9uLFvP6ooX41FkJ2fd//+OBKVPZmpjIZUNv4bf6dQGo4PFwW7v23Ni6XXgHbY5O0b3OCfi75mp9oAZFzJ6p6sJg+ypNAJkN9Mepo1fwzYeKyEicunvGRKxd2dn0GPcBKVmZ+FWpkJfLYxMncumSJXzTojm39+nNnoSKoFCjQkUe73ouFxzfJNzDNkcjBUpcGjVyiEg88BROWbi4oprgfJZBb15WmuB0c3GvV9Vbi9p0yphIMfuPtTz01dekZGWiAsfuTOX1cWNpum0bL1x4Ia+dew7qdhEjLqpXqMDnV19DzQSr9mDKTpRP672IU0v1m8DHzoM3P7TSLMLNA4rdEkNV/zrcvo0pS+8vXsqz380ny+eUITrnl1947pOP8LlcXD9gAHObNQMBF8L1p5zG4HbtqBIfH+5hm6NddAeny4EJqnpVqDosTSr5rYdoojhVyher6h+H+z7GhMr2jL0MmzGb2WvXAeDCz9BZMxj8zWx+qVuPwddey+bq1RGcMkRDO3RgYNu24R20KT+iOzgl4NzqCZnSTOtdGkSbKkALEblbVV8pxXsZUyp7cnK49N0PSctyCidXy9rLCx+/z5lr/uCTdqfzSI9LyY2JwaVQp0oVxl1xOQ2rWbUHc2SIhm5aT0TeBS4GUlS1VeDYKcAoIB5nS6HBRSUniEgD4G3+qZfaLcgdbH8CGoXkEwgozbRel2DaBXarnYazDsqYI27MD0t4Yc7/yFUfCpy4+S9e/XAsNTL3ct/lPZnQ7nQA3CIcX70643peTnKlSmEdsymHQpetNxZ4lf13hngGeERVvxSRboHnnYt47XvA46o6S0QqEXyaxv3AJBH5SFV/PuyRF1Dm6d6q+rOIfFHW72NMYX5V3pi7gFH/W0Su3wei9Fq0gIemTSKlchWuGnQLK+vWB78S63FzT+ez6Nf6VKv2YMJCQpStF9hKqGHhwzgzWeBsbbTlgPd3tlj3qOqsQD97C7c5iN44O1IsDmxXtB7wHTg0HRJshwcNToGU8DqqekXgeSJOfaSOQD6wEPhQVX88WD+qOijYARkTCpvSd3Pte5+yefceFIjz5jFs2iSu+Gkhc5ucwJ1XXUN6RSf7rqInhgfO7cxVp1jdYBNGwU/rJQV2/N5ndFE7hhcyFJgZyKJ2AR2KaNMUSBeRSThTdF8D9waKLBxKwd/x5xbTRoHQBCecLdDHFnj+CXAezlYVsTgbAQ4RkenANaq6J9g3NqasrN6eynUfTGRnZhYK1EvfyciPx9Jy62Ze7XI+r3Y9H7/LhUeE2pUr88XAfsTHxIR72KY8K9k9p1RVbXPoZvu5CbhdVSeKSE+cPfcKBxEPTk3UU3Gugj7BWcv6ThD9VyjheA7pUMHpGGAjgIi0AToBVwETVdUvIifjlEIfAswXkTNU9WBb9RpTpp6fNY9xPywlV30gcPYfv/HsxA8QhYF9BjCnWYu/1613a9aUB87vYoHJRIayzda7Frgt8HgCTtJDYZuApYGtiwhUFz+DIIKTquaGaJx/O1Rwyi/wuDvwtqpOKDCg5cBQEZkKzATuxCmdbswRlZaZxUtff8+nS3/Bp4rgZ8jcrxjy3Sx+r1Wbm6+6jk01aiAK8R4Pj3Y/l0tObB7uYRvzj7INTltwLi7mAF2Bopb3LAKqiUhNVd0RaLe4iHZHxKGC02agceDxOcDLRTVS1W9EZAzQCwtO5gjbvGs3V7wxnj25OfgVquZk8uzkD+m0ZhWTTmnLI90vJyc2FoB6iVV47OLzaN+oQZhHbcz+QphK/hFOJl6SiGzCKTH3H+BlEfEAOThlhvbNiA1S1QGq6hOR/wNmi5MVtARnC4yi3uN1nHB6S2AW7fUghha6hAicvZoGBxIhOuJcHRXnJ6BvsG9sTGmpKp8vW8Vj078hIzcPFWixdRMjPx1LcsZuhnW/go/btAeXEON2Ub9aIhNu6EWluKJKfxkTZiEKTqrau5hTrYtouxgYUOD5LOCkIN5mEM6Ib8epFBRM0ltIEyIexYnAg3FSA1uKyKCC26YX0BonIhtzRLwwYz7jFywjy+cFgcuWLmTYl5+yM6ESffrfzM91jwWc1KTbu3Tk6rYnU8HuL5lIFMJFuEdIBfi7jN3fz0PpoMFJVTOAdiLSCic4xQILReQmYBKwEicgXQBcD0wN9QCNKWzDjl08+OlMfvprKwjE+vN54KvJ9Fy6gO8bNuHOy/qyK6GSU4bI7WbEv86lxyktwj1sYw4uioJT4QSIcCRE7HvjXwIPMwtsxTuMf76cAmwF7g71AI0paHPaHnq+Mp7M3DxwQe3du3hx8lhO2rqRNzucw8jOF+FzuXCLcMIxSbzR59/UqmLVHkwUiKLgFCwRaQlUBxaoav6h2hdU4goRqpoC9BCRpsCZQBJOCuJU9s/uMyZkVJUXv5jP2LlL8KEo0H797zw39QM8fh83X34ds5s5i2g9Ipxcrzaj+v6byvF2f8lEPiHqpvX2EygE3klVLy9wbAzQL/D0dxE5W1VTg+2zNLX1VgOrA4NojVOr6SqcHRAPm4hsADJwSl94Cy82E5EeOPfC/DgFDIeq6vzAuWuBBwNNH1PVcaUZi4kMXp+fxyd/w2eLV/6dJv6fBd9w67wvWVOzFrdd2p8/aySDH2I9Lp6+8kIuPPGEcA/bmJKJ4uCEkwz3d9q5iJyNs7ZqEvALzqzavo+glGbLjOrANcANOLve7tvpMBS6HCTCzgamqqoGisr+F2gWGM8woE1gHEtEZKqq7grRmEwY/L5lBwNHTSQtOxsFKudk88SM8XRds5JpzU9j2IVXkh3IvkusEMdjl1/AOS2OD++gjSkpDV1tvTBpyP6FZi8DtgM9A6nmVYEelGVwEpF9yQ+X4GzHm4FT4igOp/hfmSpUjDCBfwLiBcAsVU0LjHMWcCHwUVmPyYSeqrJs/RYGjZ5MVl4+6oKmqVt4acoYau/ZxePnXMr4084EEWLFRdPaSXw85GpcLivaaqJUdF85VQIyCzzvCnytqvtC7gqctVZBCyo4iUgjnDJF1wL1cKbUvsaJlJNVNUdE7iE0wUmBr0REgTeLKmgoIpcCTwLJOJUrAOoSKLUUsClwzEQZVeXB8TOZuWw1uV6nDNHFvy5m2KwJ7ImvQP+rhrCsnrN1jACXtz2RO7ufZYHJRLVovueEU4Fi395R9YGW7L9NUiIH2Tm9KIeqSn41zrRdJ5zlIiuAkTiVyLeV5I1KoKOqbhGRZGCWiKxS1bkFG6jqZGByYF7zUZwChkX9Ziry2y0iAwmskG7QwCoFRJJtuzJ4etK3fLtyHT5VPD4vd8+dQu/l/2NRveP4v4v7sbNSFacMUYyHkf0voUPTY8M9bGNKL7qD0xfATSLix6l4no9TxGGfljjFZIN2qCunD3DWMb0MvK+qy0rS+eFQ1S2Bf1NEZDJO5fO5xbSdKyLHi8i+jMHOBU7Xw6kjVdTrRgOjAdq0aRPdPxJHkdWbd9D/pU/I9OajQK2MdJ774j1O2bqBMa0789KZ3fG53QhwQp2aDLviXE6sf0yYR21MCCjRHpweAU4D7sBJVLtz3+9yEYnHuQdVogS1QwWnPJxtfS/B2edjl6r+WdJRB0tEEgCXqmYEHp+Ps39UwTaNgbWBhIjTcBYG78QprfSEiOzbW/t84L6yGqsJHZ/fz4S5P/PC1Lnken2oQNvNf/DsF+8T583nju7XMqvJySDOotoW9ZJ5d/CVxHjc4R66MSETzdN6gQS2jiJSE8gstDuFC+f+/7qS9BnMlhnX4CRAPAIMF5F5OPeaJgQqSIRSLZzpun1jG6+qM0RkEECgbNLlQD8RycfZV+oqVVUgTUQexamsCzBiX3KEiWwPjZvBN8vXkOvzAcp1S77l1h+ms6FaMrdf3J/11WsBzjbqD19xDt1aNyPGbYHJHF2iPFsPgEA188LHsoCDbkhblEOVL0rH2Yv+1cBVyg04lcffBl4RkSk4geqrkr5xMe+3Dji5iOOjCjx+Gni6mNe/C7wbirGYsvfrn9sY9t5XrNm6EwQSvDmMmP0R565dwczGJzPsvKvIio1HcO4vvXj9v+jYrGG4h21M2YjiK6eyEHQquar+BPwkInfgXL3cgLPo9iqcfPatZTJCc1Ra9VcKA56fQHa+U7T1uLRtPD9jDPV27+S5My/h/VM6oSJ4XC7aNq7HM9d2p2pCfLiHbUzZiP57TiF3OOWLcoHxwHgRaYgz5Xctzta+9uU1B5Xv9fHEB1/z+Y+/sm8W4/w1Sxn27SdkxcQxsMcgltRrDAIel3BWs4Y8e113YmMOe724MRFPKDrduDwr1f/xqroBeFhEhvFPZXJjipSb7+W+0dP5/pcN+BU8fh+3Lvica1bMZdkxDbn7gmvZkVAV8UNsjIvXh1xGmyb1wz1sY44M+9N+PyH5czSQkDAj8GHMAZb8vpHbR35GZr4XgKTsPTz99ThO3bae8a3O4sUO/8Lrdn4cayVW4on+F9G6Sb1wDtmYIyqas/XKgs2VmDLl9yvzf17HPW98Tp7PDwKnbFvPU7PHUSk/l/vOuYaZTU4DnDTx05s34KWbehDI2DSm/DgKsvUKE5HKQKKqbjxk40IsOJky4/X6uO2lySxdvZl8nx9B6f3LXG5bOI3NlWswuNsg1ibVBgW320Xfc1sz8OIzLDCZ8if6dsLdj4j0xqnuc3OBY8NxdokQEfkO+JeqZhbTxQEsOJky8efWNJ4YM4tlazbjAyp4c3lo/iecv345c45tybBOvdkbVxHxQ4W4GN6+qyfNGiSHe9jGhE8UBydgMAUW2YrIqcBDOOubVuOslx0KPB5shxacTMgt+W0jdzw/mWyvFxU4Nn07z8wZR8PdKbzSpjtjT+oCLkGA1k3rcW+frjSqXaptwIyJetF85QQ0xdm7aZ+ewG6ga6AweD5OYXALTubIy8v38v60RbwzZQE+v6Iu6LLhZ4bN/5hcTww3XzCQRXWaIgJxHg/tWx3LMzddYtXEjYFov3KqCqQXeH4OzpYZOYHnP+KsiQ2aBScTEqrKbU9PYuWarfh8ilt93PzTF/RdOYcVSQ24t8u1bE9IBIW4GDdPDOzGWScfb4HJGDgaNhvcDhwPICI1cNa9vl/gfEVKGH4tOJlSW/TLnzz+5ldsS9uDilAtN4PH571P6+1rmXBCB15s24N8twcXUDE+ltf+7wpaHmfVxI3ZT3RfOc0BhojINpyrJmH/LTOaAptL0qEFJ1MqPy7fwN3Pf/b3poAn7tjAE/PGUSUvm+Ede/PlcW1QIMbl4px2Tbmv/7lUjI8N97CNiShC1N9zGgacibPfH8CzgVqpiIgbp+TdlJJ0aMHJHJasnDweGfkF85eudZZnqHL52u8Z+tNUtldMZMAFA/ijurMRscflonvHFtx33Xk2jWdMcaI4OKnqBhFpjlO4e7eqri5wuhJOpt6SkvRpwcmUWGZWLrc/PpHf1m3HrxDvy+WeRRO58M+fmF+nOY90uJqMuIqgUCE2hjEjetOoblK4h21MRBONzugkIpWAZ3ASICYVPq+qu4FPStqvBSdTIt8tWM0jL00nx+/cva23N5Unvx/Hcbu38eaJFzK2VVdUXAA0qlOdR4d0t8BkzKFEcVVyVd0rItdRwiujQ7HgZILi9fmZOWclz4z6Cq9fwQVnbv2VhxZ+hF9c3N5pAAtrnwAK8R43F57dknsHnBfuYRsTNaI8W28V0CCUHVpwMoeUnZPHkPs/Zv2mVHw+xYWfAb/M5NpV3/BbtXrc374f2ypXd9LEY90M7NmRXt3ahHvYxkSVKE+IeA54UUTGqur6UHRowckc1O9rt/PkyC9Yt3EnfoWqeZkMX/whbVP+YGqjdrxwyr/J88TiUkioEMeYp6+hbq3EcA/bmOgT3cGpLk6q+EoRmQz8AWQVaqOq+mywHVpwMsX6dv4qnnj5S3LynTTx5rv+4rGF75OYu5cnT7uSaQ3boS4nDbZTuybc0q8ztWtWCfewjYk+UV74FXiqwOPexbRRwIKTOXyZWbmM+WA+E6b95PwxJ8olG37kthVT2BlfhZs6DWF1Yj0EiPd46H5OK+4YcG6YR21MlIvu4NQ81B1acDL7yc/3ctPtH7Bp6y5UlVi/lztWTKbbxsX8mNyUR9pczZ7YBACqJMTx2F09OLWV7VZrTGlE+yJcVf091H1acDJ/mzNvFS+88hW79+agQO3cNB5d/D5N92xhbNNzGNPsPPziwi1ClSoVeO3xXjSoWz3cwzbmqCD+KI5OZcCCkwFg5te/8PzLMwJliIQzUlbx4M8fI8Dd7a7jh1rNQSHG4+ay7qcysO9ZxMbYj48xIRHCdU4i8i5wMZCiqq0Cx04BRgHxgBcYrKoLi3l9FeA3YHLBzQODeF8X0A04HagGuAo1UVUdEmx/EffbRUQ2ABmAD/CqaptC5/sA9wSe7gVuUtXlwbzWHGj37iweHj6Jn3/bjAKifq5dO5tr137D2srH8GCbvmxNqIEAHreL3pe2ZUCfM223WmNCLITrnMYCrwLvFTj2DPCIqn4pIt0CzzsX8/pHge9K8oYikgjMAk7DmaXUwL8UeKxA9AangC6qmlrMufVAJ1XdJSIXAaNxInUwrzUF7N6dxS1D32fLlnQUpXJ+Ng+u+JjTU1fzZZ3TeLHVpeS6Y3H5hUqV4xj7+vUkVa8U7mEbc3QK0ZWTqs4VkYZF9L4vlbYqsKWo14pIa6AWMAMoyR/3j+LU1bsF+BZYCfwL2ISzVXsDnKu5oEVqcCqWqn5f4OkCoF64xhLNpk5Zwmuvf01+YJ67yd7NjFj+IUk5e3i+xb+ZWv90CFwdNT/hGB6++18WmIwpQyVIiEgSkcUFno9W1dGHeM1QYKaIPIcz3dbhgPd3puWeB/ribHtREhcDH6jq64H9nACyA7NaV4rIfOBhnOAVlEgMTgp8JSIKvHmIL/oNwJclfa2IDAQGAjRoENKKGxEvL9fLpImLeHfMd3h9ThmiC7cuYeiqKaTHJHBruxv5LbEBAsTFeLimV3v6Xn3Az7ExJpQUCL7wa+ph3LK4CbhdVSeKSE/gHaDw+o/BwBequvEwpu3r4FwsgHNPC5z7W/tMBO4kyoNTR1XdIiLJwCwRWaWqcws3EpEuOMHpzJK+NhC0RgO0adOm3KTIpKdncvOgsexIzcDn8xPj93LL79O4eMsillQ/nkdb9SI93rk6qpQQx5Abz+Gi808M86iNKR/KuLbetcBtgccTgLeLaNMeOEtEBuNscxErIntV9d4g+t+Fs9stOPf9vThVI/bJBUqU2htxwUlVtwT+TQmUwWgH7BdgROQknC/uRaq6sySvLa+WL/2TZ574nO0pe1CB5NxdDF/5ESdkbGb8sZ14t/H5+MWFByGxSkXeHn0DiYkVD92xMabUjsA6py1AJ5wda7vilBfaj6r2+Xs8Iv2BNkEGJgL9NQ/04xeR5UA/ERkDuIE+OPkCQYuo4CQiCYBLVTMCj88HRhRq0wCYBPQtuKFVMK8tryb9dyHvvvktOfleEKH1zj94YNV/cauPh1pdw/9qtgCc/0G6dzuZ/v3OssBkzJGkWpJpvYMSkY9wMvGSRGQTzi61/wFeFhEPkEPgtoaItAEGqeqAUr7tV8BtInKLquYBLwHvA6mAHycJI+i0dIiw4ISTJTI5MN/pAcar6gwRGQSgqqNwbqrVAF4PtNuXMl7ka4/8pxA5dqXt5a1XZzNr5goAxKVc/ddcrv1zNhsSkhne8mo2J9T8+/5S335n0rt3+/AO2phyKlRXTqpaXG271kW0XQwcEJhUdSxOSnqwngRGBgITqvph4N7/NThLez5V1XEl6C+yglNgz/mTizg+qsDjART9xSzyteVV5t4cBl/7Nmlpe0GVBF8Od6+ZRIe0VcyueTIvNP03Oe5YBKhZswrDR1zGCSfUDvewjSm/ovjut6p6gd2Fjo0Hxh9unxEVnExoTJ+0hDdf/oqcXC8qcFzWNh5e/TG1ctN55biLmVLHSRP3uIWayVV5+bV+1KhhaeLGhFM019YrKJCSXg3YHQhah6VweQkT5T4ZN59Rz88gJycfBM7dsYyXf3mLOF8+d7a8gSnHnA7qVHu4fkAnxn04yAKTMeGmgE+D+4hQInKiiHwBZALbgbMDx5NFZLqIdC5Jf3bldJTYvjWdYbePZ/3aHQB41MugDTO5JGURyys35LGmPUmPrYTg1McbOORc/n1F2/AO2hjzt2i+chKRVsD3OGnknwJX7zsXyJ5OAvrjZAsGxYLTUSBlWzq39h3N7nRn48mk/D08uPa/NM/czITaHXmnwbn4xI3bJSTVrMKbHwwkISH+EL0aY46oEGXrhcmjwA6c2noenNTxgmYBV5akQwtOUe6912bzyZh5eP+/vTuPr6I6/zj++WZllV1EkEVFrVIFitoKAuWHWqWKWlSsWrFoxbaAaOsKrlVbXIq2trjUVlTcpdKWRaWi/bmCClSsAoKWEClCQBFCSHKf3x8z+fUSkpCQmztzyfN+veaVyZxzJ08uw31yzpw5J7ywj9j8Cdeseoa8RBk3738G/+jQCwiGiffp14MrrjvVE5NzMZTJLSeCLrzbzWxT0vRFyf5NMItErXlyylDFW0uYdu88Zj7+FmWJBAjOWPcGFxT+nYIm7bj5gLNY3bQDKjfy8nMYd9Uwjvtu76jDds5VJYVLZkSkGVBUQ3mdb2x7cspAawuKGH/OVDZ/WUyi3GiW2M7lBTMZ8MVHvNL6UO7qdgrbcvIBaNuuBWOvHsYxgw6JOGrnXHWCGSIyOjutBPrUUD4Y+LAuJ/TklEHMjLfnf8idk57lyy+KQaJbyXomffI0nbZv5L7Ox/Hc3t8Mh4lnsU/n1tz72BiaNM2LOnTn3C4oxiPxauFJ4Kpwdoql4TEDkPQTYBjBxK+15skpgzx05xz+8tjrbCsNVqsdtPF9JqyZxdbsfK7Y/1zeb9kNLFjp4sxRAxhx3jGemJzLBJnfrTcZOAGYB/yT4Lf5VThKrxvB4oW/qcsJPTllgLWri5j6i+d569VlGJCdlWD02pc5fcMCljbrwi1dT6coby9kkJeXzbhJpzD05Jpa2M65eEnd3HpRMLNt4UoRlxOM1EsQjNz7mGDKudvNrLwu5/TkFHOff7aJn546ha1flYBE2/ItXLPmz/QqLuC5dkfyh32GUK5sBHTv2ZGrJ59J1/33jjps51wdZdpoPUlPAReb2UaAcF6928INSTLb/YzrySmmzIwn7p3H9N++RFl5MBqvV3EBVxc+T7PEdm7rMpxXWh0KiJycLLod2JHJf7yQ5i18mLhzGSnzWk6nAwMkXWxmf6lcWJ/EBJ6cYsnM+N0NM3jhqbcpKwtawqdtXMjoDa/wWW4bru46kk/zO0DCyMnNYvz1pzJ0eF92Y/VK51wcWIMvNtgQBgN/BP4s6WFgvJltTtXJPTnFzKoPC7nhhw+wbm3wb9zUSrn08zkM3LKM15r35K5Ow9ianY+AJk1ymXDLCAaeeB6BEdgAAA+jSURBVHi0QTvn6i+RWS0nM/vfcOHXyQRLvA+RNNrM5qXi/J6cYmTVh4VcduoUtm3dDtnZdCktYtK6mXQu3cgf2g3kmdZHASInS3Q/eB/ufOLH5OXnRh22cy4FMvE5JzMrBsZKehZ4CHhB0n3Am9XUn1bbc3tyigEz4+6fP8685xZSVha07ftvWcZl6+eyXTlcu88IFjfvBgTDxPuf0ItxN3/PE5Nze5IMTE4VzGy+pAHAIuDicEsmguHlnpwyxZdFXzH1umd59S/vUV6eIAvjgi9fZ8Tmd/lXfidu3ftk1ue0hEQwDdGk+0bRb6DP9uDcHsUIBl9nKElDCFpO7YH7gTfqe05PThH6+P3VXHHarykuLsOA1uVbuWrjHI4oWcPMFofzQJtBlGUHraN9u7dj/G1ncvjRB0QbtHMu5YRlZLeepKYE95wuAQqBE8zsxVSc25NTBBKJBK88t4C7fz6dkuJSyMrikNL/cG3RbFpYCbe3OY6/tzgUgNwcccBhXbjjmbFk52RHHLlzrsEkMqvpJOkY4E/AgcAjwDgz+6LGF9WBJ6cITB7zEG/Mfo+S7QkEnPzVEi7a/Brrs1twWfsRrMrtAGZkZWdxwZXDGHbuAE9Mzu3JMrNb71VgPXCamT2f6pN7ckqjVUsLuOfyR/jXwlUA5GclGL/5VYZsW85b+d25o81QvspuGpQ1yWXSA6P5xuCvRRmycy5NMrBbbwZwiZmtb4iTe3JKk1UfFDDh+NvYVhxMQ7Rv4ksmbXqJbuVFPNz8KJ5s3hcjiyzBYUcfwOVTzqNjl7ZRh+2cS5cMS05mVqeVbevKk1MDKyst48GJT/L8Ay9jFkwZ/s3tn/LzLfMpJ4uJrYbxbv5+SME0RL2+eSA3PnqJDxN3rlHJ7IlfG0LskpOkT4DNQDlQZmb9KpWfA1wZfvsVQbNycVj2HeBuIBt40Mx+ma64q1JenuDW83/H23MXk0hANsYPit9hZMlilmW35xcth7IuuyUkEmTn5XD9w2PoN+SwKEN2zkXB8ORUSeySU+jbNfRjrgIGmdlGSScSjKk/WlI2cC9wHFAALJA008w+SE/IO3r/tY+4aeTdfLFxCwCtVMpV216hb1khs/IO5vfNv0Wpgre/RaumTHxoDL39+SXnGq0MX2ww5eKanKplZq8nffsm0CXcPwpYYWYrASQ9AQwH0p6cFs1fysThd1C6vQyyxMGJDUwqmU8rK+GupsfyQv5BYJCTl0OfgQdzw3QfJu5co+ctpx3EMTkZwfxMBtxnZvfXUHc0MDvc7wysTiorAI6u6kWSfgT8CKBr1671DrhCWWkZN464i3fm/ZPycsCMk0qXc0npAorUjAlNT2RF3t7IDGVnccK5/bn4lrM8MTnX2BkZN/FrQ4tjcupvZoWS9gZelPShmb1auVK46uJoYEDFoSrOVeW/dpjw7gfo169fSq6I9Ws2cOeFU3nv5aUkEpCnBOPKF3B8+UoWZO3Lr5oMYLOaQFkZeU3zuGPuNRzUt0cqfrRzLuP5gIjKYpeczKww/LpO0gyC7rodklM4TfuDwIlmtiE8XADsl1StC8F0Gg1u0cvvM+mUX1KyrQyAfWwL1yVe40DbyCPZX2d67tdJELSODurTg3G/GUXP3t3TEZpzLlN4ctpBrJKTpOZAlpltDvePB26qVKcr8BxwnpktSypaAPSU1ANYA4wEvt/QMScSCW79/hS2bSmBrCyOss+4KhHMFj8xZzALcoJbYvn5ufQd2ovrn7zUFwV0zu3Mk9MOYpWcgI7AjPDDOweYbmZzJI0BMLOpwHVAO+B3Yb0yM+tnZmWSfgrMJRhK/pCZLW3ogD9dupriLSUAnJH4kB/ZElbQmpuy+7NWwTDx/KZ5/GTK+Qw9Z4AnJufczswIblS7CrFKTuFIuyOqOD41af9C4MJqXj8LmNVgAVYhNz8XCyds/NRaMkfd+Y36UqrcYLXaZrlMfmEiBx/ps4k752rgLacdxCo5ZaLOPTvRoUs71iz/jLfpxNt0AkR2tjhm+JGMveeHtOnYOuownXNx5qP1dpIVdQCZThI3/vlKWnVoRbOWTclvlkd+k1wGjfgWEx+/1BOTc652zGq37YKkhyStk/R+0rHekt6UtEjSQklHVfG63pLekLRU0hJJZ6X4N6wTbzmlQNdDOjP9379nwexFFK3dRK8Bh9D9sP12/ULnnKuQum69PwG/Zccl0ScDN5rZbEknhd8PrvS6rcAPzGy5pH2BdyTNNbNNqQqsLjw5pUhuXi7HDD8y6jCccxkpdc85mdmrkrrv/APYK9xvRRWP2SSPfg6fNV0HdAA8OTnnXKNk1GW0XntJC5O+v38XM+kAXArMlXQHwe2cY2qqHHb75QEf1zaoVPPk5JxzcVD7ltP6yqs11MIlwAQze1bSmcAfgKFVVZTUiWDZ9fPNLLL1eX1AhHPORc6C0Xq12XbP+QSTFwA8TTDzzk4k7QX8DZhoZm/u7g9LBU9OzjkXNQOzRK223VQIDAr3hwDLK1eQlEew9Po0M3t6d39Qqni3nnPOxUGKnnOS9DjBSLz2kgqA64GLgLsl5QDbCFdlkNQPGBNObnAmMBBoJ2lUeLpRZrYoJYHVkScn55yLg9SN1ju7mqJvVFF3IeGMO2b2KPBoSoJIAU9OzjkXNZ9bbyeenJxzLgYq5uh0AU9OzjkXOV9ssDJPTs45FzWf+HUnnpyccy4OonveNZY8OTnnXMQMMG857cCTk3PORc0M89F6O/Dk5JxzceDdejuQNfIRIpI+Bz6NOo5aaA+sjzqIOvKY08NjTo/qYu5mZh3qc2JJc8Lz18Z6M/tOfX5eJmj0ySlTSFq4GzMRR8pjTg+POT0yMeZM5hO/Ouecix1PTs4552LHk1Pm2NVKl3HkMaeHx5wemRhzxvJ7Ts4552LHW07OOedix5NTDEjKlvSepL9WUfZrSYvCbZmkTUll50taHm7nZ0jM5UllM2MUc1dJL4flSySdlFR2taQVkj6SdELcY5bUXVJx0vs8NZ0x1yLubpLmhTHPl9QlqSyu13RNMUd2Te/J/CHceBgP/AvYq3KBmU2o2Jc0FugT7rclWOGyH8HsJ+9ImmlmG9MS8W7EHCo2s94NH16Vqo0ZmAg8ZWa/l3QoMAvoHu6PBA4D9gVeknSQmaXrcf46xxyWfRzh+ww1x30HwVLgD0saAtwGnBfna7q6mMOyKK/pPZa3nCIW/gU2DHiwFtXPBh4P908AXjSzovA/74tAWh7Mq0fMkalFzMZ/P5RaAYXh/nDgCTMrMbNVwArgqIaMtUI9Yo5ULeI+FJgX7r9M8B5DvK/p6mJ2DcSTU/SmAFcANc5dIqkb0AP4e3ioM7A6qUpBeCwddjdmgCaSFkp6U9KpDRhjZbuK+QbgXEkFBC2QseHxOL/PN1B1zAA9wi6qVyQd27Bh7mRXcS8Gvhfunwa0lNSOeL/X1cUM0V3TezRPThGS9F1gnZm9U4vqI4FnkrqTVEWdBh96Wc+YAbqGT9l/H5gi6YCGiDNZLWM+G/iTmXUBTgIekZRFvN/n6mL+jOB97gNcBkyXVFVXVcrVMu6fAYMkvQcMAtYAZcT7va4uZojgmm4MPDlFqz9wiqRPgCeAIZIerabuSHbsHisA9kv6vgvp6dapT8yYWWH4dSUwnx3vRzWU2sQ8GngqjO0NoAnBXGdxfp+rjDnsgtwQHn8H+Bg4KA0x1ypuMys0s9PD5HlteOwLYvxe1xBzVNf0ns/MfIvBBgwG/lpN2cHAJ4TPpYXH2gKrgDbhtgpoG/OY2wD54X57YDlwaBxiBmYDo8L9rxF8KIpgIMRiIJ+gi3IlkB3zmDtUxAjsT/BXflqvjV3E3R7ICvdvAW4K92N7TdcQc+TX9J66ecsphiTdJOmUpENnE9yU//8uDjMrAm4GFoTbTeGxSNQmZoIP0IWSFhPcVP6lmX2QzjiTVYr5cuCiMLbHCT70zcyWErROPgDmAD+x9I3U20ltYgYGAkvC488AY6K8NmCnuAcDH0laBnQk+LCP+zU9mCpiJmbX9J7EZ4hwzjkXO95ycs45FzuenJxzzsWOJyfnnHOx48nJOedc7Hhycs45FzuenJxzzsWOJyfnnHOx48nJZSxJbSRtk2SSzo06Hudc6nhycpnsHIJphUoI5plzzu0hfIYIl7HCGaL3AmYSLBTX08w+jjYq51wqeMvJZSRJfYHewCPANIIJTy+ooX4fSTMkbQy3ZyS1lbRv2DV4dppCd87VgrecXEaSdC/wY+AAM1spaQnBDNHdzCxRqe7ZwMPAEuBRgtnFxwG/BnKAbwNHVH6dcy46npxcxpHUhGB5iKVmdmx47GfA7cBJZjY7qe7+wFLgn8BAM9sWHn+NYImG7sA5ZvZcWn8J51yNvFvPZaLTCVpJ05KOPQaUAz+sVHc8wSJ8YysSU2glcAjBUhgzGi5U59zu8OTkMtFoYBvhKrAAZvYZ8BLBiqbtk+qeAqwws7eqOdek5DWnJM2XdKmkfEkPSFop6StJyyVdmvxCSTmS7pZUJGmTpAcl5aeq3LnGzJOTyyiSehDcI5pp4TLZSaYBecC5Yd2KbrsFVZyqI0G34KxqflQOsBY4nmBE4BnA1ZLOSqpzDTAI6AX0JFg197YUljvXaHlycpnmAoKRedOqKJsBbOa/zzztE37dkFxJ0kDguMrHk5nZFjObZGYrzCxhZouAvwH9k6pdCPzCzArN7HPgBuACSVkpKneu0fL/BC5jhB/ao4D/AHMrl5tZMcGy5L0kHQlsCouOSDpHC+C+8NvmdfjZOcAAghF/SGoN7Ae8l1TtXaA1sF99y2sbl3N7qpyoA3CuDo4n+OBeBPxMUlV1Ku7ZjDazMZLeBo6V9AjwOnAR0B6YAxwf3kd6MrxnVZN7gC/4b4utZfg1uWtxU1JZop7lzjVqnpxcJqnorusdbjUZKWkCcCbwW+BUYARBS+XYsM6zBM86zQaqTU6S7iRoNQ0xs+3h4c3h11bA+nC/dVJZfcuda9Q8ObmMYWZn7MbLPgVOrqbssF29WNIU4H8IElNFEsHMNklaTZAkK6ZM6kPQ+lltZon6lNfh93Nuj+T3nJyrhqR7gKEEienzKqo8CFwbToHUgWBAwx+TZpqob7lzjZa3nJzbmUnqBowlmPF8VdL9rX+Y2Ynh/q0E96+WEvyh9zTB8HBSVO5co+XTFzmXRNK7wJ1m9ljUsTjXmHm3nnMhSYcT3IdaGHUszjV2npycAyTdB8wCrjSzj6KOx7nGzrv1nHPOxY63nJxzzsWOJyfnnHOx48nJOedc7Hhycs45FzuenJxzzsWOJyfnnHOx48nJOedc7Hhycs45Fzv/B6CZZL8VRgPlAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x119b7ccf8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"deltara = vega_sm.ra-vega.ra\n",
"deltadec = vega_sm.dec-vega.dec\n",
"\n",
"plt.scatter(deltara.arcsec, deltadec.arcsec, c=delta_t.to(u.year))\n",
"plt.colorbar().set_label('Years since J2000')\n",
"plt.plot(dra_linear, ddec_linear,c='r')\n",
"\n",
"plt.xlabel(r'$\\Delta \\alpha_{\\rm J2000}$')\n",
"plt.ylabel(r'$\\Delta \\delta_{\\rm J2000}$')\n",
"plt.tight_layout()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Indeed now the ICRS coordinates lie along the expected space motion path. What about in GCRS?"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"vega_sm_gcrs = vega_sm.transform_to(gcrs)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x119b806d8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"deltara = vega_sm_gcrs.ra-vega.ra\n",
"deltadec = vega_sm_gcrs.dec-vega.dec\n",
"\n",
"plt.scatter(deltara.arcsec, deltadec.arcsec, c=delta_t.to(u.year))\n",
"plt.colorbar().set_label('Years since J2000')\n",
"plt.plot(dra_linear, ddec_linear,c='r')\n",
"\n",
"plt.xlabel(r'$\\Delta \\alpha_{\\rm J2000}$')\n",
"plt.ylabel(r'$\\Delta \\delta_{\\rm J2000}$')\n",
"plt.tight_layout()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see (from the slight mismatch of the yellow and purple circles) that the space motion has been included... But the change over the year is still much higher than the distance would suggest (Should be ~130 marcsec)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Stellar aberration\n",
"\n",
"The GCRS system is the position on object would be at viewed from the center of the earth, which *includes* the effect of the aberration of starlight (as well as the smaller amplitude gravitational light deflection effects). This effect is large enough to swamp, and is intrinsic to the GCRS frame (and indeed, according to GR is a *real* physical effect). But actual observations are not tied to the actual physical location of a star. They are almost always tied to a *local* frame that is fixed by other objects much more distant. So to see the \"proper motion of Vega\", we can compare the GCRS position of Vega to a fictitious object at the same location but much more distant."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"vega_background = SkyCoord(ra=vega.ra, dec=vega.dec, distance=1*u.Tpc) # a Teraparsec is very far relative to Vega\n",
"vega_background_gcrs = vega_background.transform_to(gcrs)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x119f74b70>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"deltara = vega_sm_gcrs.ra-vega_background_gcrs.ra\n",
"deltadec = vega_sm_gcrs.dec-vega_background_gcrs.dec\n",
"\n",
"plt.scatter(deltara.arcsec, deltadec.arcsec, c=delta_t.to(u.year))\n",
"plt.colorbar().set_label('Years since J2000')\n",
"plt.plot(dra_linear, ddec_linear,c='r')\n",
"\n",
"plt.xlabel(r'$\\Delta \\alpha_{\\rm J2000}$')\n",
"plt.ylabel(r'$\\Delta \\delta_{\\rm J2000}$')\n",
"plt.tight_layout()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that's what we were looking for! Let's try it again for multiple years:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"t_long = Time('J2018.14') + np.linspace(0, 3, 1000)*u.yr\n",
"delta_t_long = t_long - vega.obstime\n",
"gcrs_long = GCRS(obstime=t_long)\n",
"\n",
"vega_sm_gcrs_long = vega.apply_space_motion(t_long).transform_to(gcrs_long)\n",
"vega_background_gcrs_long = vega_background.transform_to(gcrs_long)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11a14efd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(10, 8))\n",
"\n",
"deltara = vega_sm_gcrs_long.ra-vega_background_gcrs_long.ra\n",
"deltadec = vega_sm_gcrs_long.dec-vega_background_gcrs_long.dec\n",
"\n",
"dra_linear_long = (delta_t_long*vega.pm_ra_cosdec/np.cos(vega.dec)).to(u.arcsec)\n",
"ddec_linear_long = (delta_t_long*vega.pm_dec).to(u.arcsec)\n",
"\n",
"plt.scatter(deltara.arcsec, deltadec.arcsec, c=delta_t_long.to(u.year))\n",
"plt.colorbar().set_label('Years since J2000')\n",
"plt.plot(dra_linear_long, ddec_linear_long,c='r')\n",
"\n",
"plt.xlabel(r'$\\Delta \\alpha_{\\rm J2000}$')\n",
"plt.ylabel(r'$\\Delta \\delta_{\\rm J2000}$')\n",
"plt.tight_layout()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Huzzah!"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python3",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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