{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Existence of spherical photon orbits in Kerr spacetime\n", "\n", "This Jupyter/SageMath notebook is relative to the lectures\n", "[Geometry and physics of black holes](https://luth.obspm.fr/~luthier/gourgoulhon/bh16/)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 9.3.beta5, Release Date: 2020-12-27'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Functions $\\ell(r_0)$ and $q(r_0)$ for spherical photon orbits\n", "\n", "We use $m=1$ and denote $r_0$ simply by $r$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "a, r = var('a r') " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( a, r \\right) \\ {\\mapsto} \\ -\\frac{a^{2} {\\left(r + 1\\right)} + {\\left(r - 3\\right)} r^{2}}{a {\\left(r - 1\\right)}}\n", "\\end{math}" ], "text/plain": [ "(a, r) |--> -(a^2*(r + 1) + (r - 3)*r^2)/(a*(r - 1))" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lsph(a, r) = (r^2*(3 - r) - a^2*(r + 1))/(a*(r -1))\n", "lsph" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( a, r \\right) \\ {\\mapsto} \\ -\\frac{{\\left({\\left(r - 3\\right)}^{2} r - 4 \\, a^{2}\\right)} r^{3}}{a^{2} {\\left(r - 1\\right)}^{2}}\n", "\\end{math}" ], "text/plain": [ "(a, r) |--> -((r - 3)^2*r - 4*a^2)*r^3/(a^2*(r - 1)^2)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qsph(a, r) = r^3 / (a^2*(r - 1)^2) * (4*a^2 - r*(r - 3)^2)\n", "qsph" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The radii of the two horizons:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "rp(a) = 1 + sqrt(1 - a^2)\n", "rm(a) = 1 - sqrt(1 - a^2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Critical radii $r_{\\rm ph}^{**}$, $r_{\\rm ph}^*$, $r_{\\rm ph}^+$, $r_{\\rm ph}^-$, $r_{\\rm ph}^{\\rm ms}$ and $r_{\\rm ph}^{\\rm pol}$ " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}a \\ {\\mapsto}\\ \\cos\\left(\\frac{2}{3} \\, \\pi + \\frac{2}{3} \\, \\arcsin\\left(a\\right)\\right) + \\frac{1}{2}\n", "\\end{math}" ], "text/plain": [ "a |--> cos(2/3*pi + 2/3*arcsin(a)) + 1/2" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rph_ss(a) = 1/2 + cos(2/3*asin(a) + 2*pi/3)\n", "rph_ss" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}a \\ {\\mapsto}\\ 4 \\, \\cos\\left(\\frac{4}{3} \\, \\pi + \\frac{1}{3} \\, \\arccos\\left(-a\\right)\\right)^{2}\n", "\\end{math}" ], "text/plain": [ "a |--> 4*cos(4/3*pi + 1/3*arccos(-a))^2" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rph_s(a) = 4*cos(acos(-a)/3 + 4*pi/3)^2\n", "rph_s" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}a \\ {\\mapsto}\\ 4 \\, \\cos\\left(\\frac{1}{3} \\, \\arccos\\left(-a\\right)\\right)^{2}\n", "\\end{math}" ], "text/plain": [ "a |--> 4*cos(1/3*arccos(-a))^2" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rph_p(a) = 4*cos(acos(-a)/3)^2\n", "rph_p" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}a \\ {\\mapsto}\\ 4 \\, \\cos\\left(\\frac{1}{3} \\, \\arccos\\left(a\\right)\\right)^{2}\n", "\\end{math}" ], "text/plain": [ "a |--> 4*cos(1/3*arccos(a))^2" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rph_m(a) = 4*cos(acos(a)/3)^2\n", "rph_m" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We add the radius of the marginally stable orbit:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}a \\ {\\mapsto}\\ -{\\left(-a^{2} + 1\\right)}^{\\frac{1}{3}} + 1\n", "\\end{math}" ], "text/plain": [ "a |--> -(-a^2 + 1)^(1/3) + 1" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rph_ms(a) = 1 - (1 - a^2)^(1/3)\n", "rph_ms" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "as well as the radius of outer and inner polar orbits:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}a \\ {\\mapsto}\\ 2 \\, \\sqrt{-\\frac{1}{3} \\, a^{2} + 1} \\cos\\left(\\frac{1}{3} \\, \\arccos\\left(-\\frac{a^{2} - 1}{{\\left(-\\frac{1}{3} \\, a^{2} + 1\\right)}^{\\frac{3}{2}}}\\right)\\right) + 1\n", "\\end{math}" ], "text/plain": [ "a |--> 2*sqrt(-1/3*a^2 + 1)*cos(1/3*arccos(-(a^2 - 1)/(-1/3*a^2 + 1)^(3/2))) + 1" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rph_pol(a) = 1 + 2*sqrt(1 - a^2/3)*cos(1/3*arccos((1 - a^2)/(1 - a^2/3)^(3/2)))\n", "rph_pol" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}a \\ {\\mapsto}\\ 2 \\, \\sqrt{-\\frac{1}{3} \\, a^{2} + 1} \\cos\\left(\\frac{2}{3} \\, \\pi + \\frac{1}{3} \\, \\arccos\\left(-\\frac{a^{2}}{{\\left(-\\frac{1}{3} \\, a^{2} + 1\\right)}^{\\frac{3}{2}}} + \\frac{1}{{\\left(-\\frac{1}{3} \\, a^{2} + 1\\right)}^{\\frac{3}{2}}}\\right)\\right) + 1\n", "\\end{math}" ], "text/plain": [ "a |--> 2*sqrt(-1/3*a^2 + 1)*cos(2/3*pi + 1/3*arccos(-a^2/(-1/3*a^2 + 1)^(3/2) + 1/(-1/3*a^2 + 1)^(3/2))) + 1" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rph_pol_in(a) = 1 + 2*sqrt(1 - a^2/3)*cos(1/3*arccos((1 - a^2)/(1 - a^2/3)^(3/2)) + 2*pi/3)\n", "rph_pol_in" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plots for $a=0.95 \\, m$" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\rm ph}^{**} = -0.477673658836338\n", "\\end{math}" ], "text/plain": [ "r_{\\rm ph}^{**} = -0.477673658836338" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\rm ph}^{\\rm ms} = 0.539741795874205\n", "\\end{math}" ], "text/plain": [ "r_{\\rm ph}^{\\rm ms} = 0.539741795874205" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\rm ph}^{*} = 0.658372153864346\n", "\\end{math}" ], "text/plain": [ "r_{\\rm ph}^{*} = 0.658372153864346" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_- = 0.687750100080080\n", "\\end{math}" ], "text/plain": [ "r_- = 0.687750100080080" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_+ = 1.31224989991992\n", "\\end{math}" ], "text/plain": [ "r_+ = 1.31224989991992" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\rm ph}^+ = 1.38628052846298\n", "\\end{math}" ], "text/plain": [ "r_{\\rm ph}^+ = 1.38628052846298" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\rm ph}^- = 3.95534731767268\n", "\\end{math}" ], "text/plain": [ "r_{\\rm ph}^- = 3.95534731767268" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a0 = 0.95\n", "show(LatexExpr(r'r_{\\rm ph}^{**} = '), n(rph_ss(a0)))\n", "show(LatexExpr(r'r_{\\rm ph}^{\\rm ms} = '), n(rph_ms(a0)))\n", "show(LatexExpr(r'r_{\\rm ph}^{*} = '), n(rph_s(a0)))\n", "show(LatexExpr(r'r_- = '), n(rm(a0)))\n", "show(LatexExpr(r'r_+ = '), n(rp(a0)))\n", "show(LatexExpr(r'r_{\\rm ph}^+ = '), n(rph_p(a0)))\n", "show(LatexExpr(r'r_{\\rm ph}^- = '), n(rph_m(a0)))" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gq = plot(qsph(a0, r), (r, -2, 0.9), thickness=2, legend_label=r'$q$', \n", " axes_labels=[r'$r_0/m$', r'$\\ell/m,\\ q/m^2$'],\n", " frame=True, gridlines=True) \\\n", " + plot(qsph(a0, r), (r, 1.1, 5), thickness=2)\n", "show(gq, ymin=-4)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "gl = plot(lsph(a0, r), (r, -2, 0.99), color='red', thickness=2, legend_label=r'$\\ell$') \\\n", " + plot(lsph(a0, r), (r, 1.002, 5), color='red', thickness=2)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(gq+gl, ymin=-5, ymax=10)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "def qmin(a1, r):\n", " l0 = abs(lsph(a1, r))\n", " if l0 < a1:\n", " return -(a1 - l0)^2\n", " return 0" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "gqmin = plot(lambda r: qmin(a0, r), (r, -2, 5), color='grey', thickness=2, fill=-8)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "scrolled": false }, "outputs": [], "source": [ "hor = line([(rp(a0), -10), (rp(a0), 30)], color='black', thickness=2) \\\n", " + line([(rm(a0), -10), (rm(a0), 30)], color='peru', thickness=2)\n", "llim = line([(-2, a0), (5, a0)], color='red', thickness=1.5, \n", " linestyle=':', legend_label=r'$|\\ell| = a$') \\\n", " + line([(-2, -a0), (5, -a0)], color='red', thickness=1.5, \n", " linestyle=':')" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 18 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = gq + gl + gqmin + hor + llim\n", "for r1 in [rph_ss(a0), rph_s(a0), rph_p(a0), rph_m(a0)]:\n", " graph += point((r1, qsph(a0, r1)), size=60, color='blue', zorder=100)\n", "graph += text(r'$r_{\\rm ph}^{**}$', (rph_ss(a0) + 0.1, 2), fontsize=14, zorder=101)\n", "graph += text(r'$r_{\\rm ph}^*$', (rph_s(a0) + 0.23, 2), fontsize=14, zorder=101)\n", "graph += text(r'$r_{\\rm ph}^+$', (rph_p(a0) + 0.25, 2), fontsize=14, zorder=101)\n", "graph += text(r'$r_{\\rm ph}^-$', (rph_m(a0) + 0.2, 2), fontsize=14, zorder=101)\n", "graph.set_legend_options(handlelength=2)\n", "show(graph, xmin=-1.5, xmax=4.5, ymin=-7, ymax=28)\n", "graph.save('gik_spher_orb_exist.pdf', xmin=-1.5, xmax=4.5, ymin=-7, ymax=28)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Zoom:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 22 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gq_stable = plot(qsph(a0, r), (r, 0, rph_ms(a0)), thickness=5) \n", "gl_stable = plot(lsph(a0, r), (r, 0, rph_ms(a0)), thickness=5, color='red') \n", "graph = gq + gq_stable + gl + gl_stable + gqmin + hor + llim\n", "for r1 in [rph_ss(a0), rph_s(a0), rph_p(a0), rph_m(a0)]:\n", " graph += point((r1, qsph(a0, r1)), size=60, color='blue', zorder=100)\n", "graph += text(r'$r_{\\rm ph}^*$', (rph_s(a0) + 0.12, 0.15), fontsize=14, zorder=101)\n", "graph += text(r'$r_{\\rm ph}^+$', (rph_p(a0) + 0.09, 0.15), fontsize=14, zorder=101)\n", "r1 = rph_ss(a0)\n", "graph += text(r'$r_{\\rm ph}^{**}$', (r1, 0.15), fontsize=14, zorder=101)\n", "graph += line([(r1, 0), (r1, qsph(a0, r1))], linestyle='--', color='blue')\n", "r1 = rph_ms(a0)\n", "graph += text(r'$r_{\\rm ph}^{\\rm ms}$', (r1, -0.2), color='black',\n", " fontsize=14, zorder=101)\n", "graph += line([(r1, 0), (r1, lsph(a0, r1))], linestyle='--', color='black')\n", "graph.set_legend_options(handlelength=2)\n", "show(graph, xmin=-1, xmax=1.5, ymin=-1.5, ymax=2)\n", "graph.save('gik_spher_orb_exist_zoom.pdf', xmin=-1, xmax=1.5, ymin=-1.5, ymax=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plots for $a=0.5 \\, m$" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "a0 = 0.5" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 14 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gq = plot(qsph(a0, r), (r, -2, 0.9), thickness=2, legend_label=r'$q$', \n", " axes_labels=[r'$r_0/m$', r'$\\ell/m,\\ q/m^2$'],\n", " frame=True, gridlines=True) \\\n", " + plot(qsph(a0, r), (r, 1.1, 5), thickness=2)\n", "gl = plot(lsph(a0, r), (r, -2, 0.99), color='red', thickness=2, legend_label=r'$\\ell$') \\\n", " + plot(lsph(a0, r), (r, 1.002, 5), color='red', thickness=2)\n", "gqmin = plot(lambda r: qmin(a0, r), (r, -2, 5), color='grey', thickness=2, fill=-8)\n", "hor = line([(rp(a0), -10), (rp(a0), 30)], color='black', thickness=2) \\\n", " + line([(rm(a0), -10), (rm(a0), 30)], color='peru', thickness=2)\n", "llim = line([(-2, a0), (5, a0)], color='red', thickness=1.5, \n", " linestyle=':', legend_label=r'$|\\ell| = a$') \\\n", " + line([(-2, -a0), (5, -a0)], color='red', thickness=1.5, \n", " linestyle=':')\n", "graph = gq + gl + gqmin + hor + llim\n", "for r1 in [rph_ss(a0), rph_s(a0), rph_p(a0), rph_m(a0)]:\n", " graph += point((r1, qsph(a0, r1)), size=60, color='blue', zorder=100)\n", "graph.set_legend_options(handlelength=2)\n", "show(graph, xmin=-1.5, xmax=4.5, ymin=-7, ymax=28)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 12 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gq_stable = plot(qsph(a0, r), (r, 0, rph_ms(a0)), thickness=5) \n", "gl_stable = plot(lsph(a0, r), (r, 0, rph_ms(a0)), thickness=5, color='red') \n", "graph = gq + gq_stable + gl + gl_stable + gqmin + hor + llim\n", "show(graph, xmin=-1, xmax=1.5, ymin=-0.2, ymax=0.6)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "Graphics object consisting of 12 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(graph, xmin=-1, xmax=1.5, ymin=-0.01, ymax=0.01)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plots for $a=0.998\\, m$" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "a0 = 0.998" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 14 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gq = plot(qsph(a0, r), (r, -2, 0.999), thickness=2, legend_label=r'$q$', \n", " axes_labels=[r'$r_0/m$', r'$\\ell/m,\\ q/m^2$'],\n", " frame=True, gridlines=True) \\\n", " + plot(qsph(a0, r), (r, 1.001, 5), thickness=2)\n", "gl = plot(lsph(a0, r), (r, -2, 0.999), color='red', thickness=2, legend_label=r'$\\ell$') \\\n", " + plot(lsph(a0, r), (r, 1.001, 5), color='red', thickness=2)\n", "gqmin = plot(lambda r: qmin(a0, r), (r, -2, 5), color='grey', thickness=2, fill=-8)\n", "hor = line([(rp(a0), -10), (rp(a0), 30)], color='black', thickness=2) \\\n", " + line([(rm(a0), -10), (rm(a0), 30)], color='peru', thickness=2)\n", "llim = line([(-2, a0), (5, a0)], color='red', thickness=1.5, \n", " linestyle=':', legend_label=r'$|\\ell| = a$') \\\n", " + line([(-2, -a0), (5, -a0)], color='red', thickness=1.5, \n", " linestyle=':')\n", "graph = gq + gl + gqmin + hor + llim\n", "for r1 in [rph_ss(a0), rph_s(a0), rph_p(a0), rph_m(a0)]:\n", " graph += point((r1, qsph(a0, r1)), size=60, color='blue', zorder=100)\n", "graph.set_legend_options(handlelength=2)\n", "show(graph, xmin=-1.5, xmax=4.5, ymin=-7, ymax=28)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 12 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gq_stable = plot(qsph(a0, r), (r, 0, rph_ms(a0)), thickness=5) \n", "gl_stable = plot(lsph(a0, r), (r, 0, rph_ms(a0)), thickness=5, color='red') \n", "graph = gq + gq_stable + gl + gl_stable + gqmin + hor + llim\n", "show(graph, xmin=-1, xmax=1.5, ymin=-1.5, ymax=2.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solutions of the cubic equation $2 r^3 - 3 m r^2 + a^2 m = 0$" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}2 \\, r^{3} + a^{2} - 3 \\, r^{2}\n", "\\end{math}" ], "text/plain": [ "2*r^3 + a^2 - 3*r^2" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P = 2*r^3 - 3*r^2 + a^2 \n", "P" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a0 = 0.95\n", "plot(P.subs({a: a0}), (r, -0.7, 1.5))" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}x^{3} + \\frac{1}{2} \\, a^{2} - \\frac{3}{4} \\, x - \\frac{1}{4}\n", "\\end{math}" ], "text/plain": [ "x^3 + 1/2*a^2 - 3/4*x - 1/4" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdep = (P/2).subs({r: x + 1/2}).simplify_full()\n", "Pdep" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "pp = -3/4\n", "qq = 1/2*(a^2 - 1/2)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2}\n", "\\end{math}" ], "text/plain": [ "1/2" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sqrt(-pp/3)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-a^{2} + \\frac{1}{2}\n", "\\end{math}" ], "text/plain": [ "-a^2 + 1/2" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "3*qq/(2*pp)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-2 \\, a^{2} + 1\n", "\\end{math}" ], "text/plain": [ "-2*a^2 + 1" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "3*qq/(2*pp)*sqrt(-3/pp)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = Graphics()\n", "for k in range(3):\n", " rk = 1/2 + cos(2/3*asin(a) + 2*k*pi/3)\n", " g += plot(rk, (a, 0, 1), color=hue((3-k)/3), thickness=2)\n", "g" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Checking that $x_1 = \\cos\\left(\\frac{2}{3}\\arcsin(a) + \\frac{2\\pi}{3}\\right)$ is a solution:" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\cos\\left(\\frac{2}{3} \\, \\pi + \\frac{2}{3} \\, \\arcsin\\left(a\\right)\\right)^{3} + \\frac{1}{2} \\, a^{2} - \\frac{3}{4} \\, \\cos\\left(\\frac{2}{3} \\, \\pi + \\frac{2}{3} \\, \\arcsin\\left(a\\right)\\right) - \\frac{1}{4}\n", "\\end{math}" ], "text/plain": [ "cos(2/3*pi + 2/3*arcsin(a))^3 + 1/2*a^2 - 3/4*cos(2/3*pi + 2/3*arcsin(a)) - 1/4" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s = Pdep.subs({x: cos(2/3*asin(a) + 2*pi/3)}) \n", "s" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\n", "\\end{math}" ], "text/plain": [ "0" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s.expand_trig().simplify_trig().reduce_trig().expand_trig()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot of the critical radii as functions of $a$" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 10 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = plot(rph_p, (0, 1), axes_labels=[r'$a/m$', r'$r_0/m$'], \n", " color='green', thickness=1.5, legend_label=r'$r_{\\rm ph}^+$', \n", " fill=rph_m, fillcolor='palegreen',\n", " frame=True, gridlines=True, axes=True) \\\n", "+ plot(rph_m, (0, 1), linestyle='--', color='green', thickness=1.5, \n", " legend_label=r'$r_{\\rm ph}^-$') \\\n", "+ plot(rph_s, (0, 1), color='green', linestyle=':', thickness=2, \n", " legend_label=r'$r_{\\rm ph}^*$', fill=rph_ss, fillcolor='palegreen') \\\n", "+ plot(rph_ss, (0, 1), color='green', linestyle='-.', thickness=1.5, \n", " legend_label=r'$r_{\\rm ph}^{**}$') \\\n", "+ plot(rph_ms, (a, 0, 1), color='blue', linestyle='-', thickness=1.5, \n", " legend_label=r'$r_{\\rm ph}^{\\rm ms}$', fill=0, fillcolor='darkseagreen') \\\n", "+ plot(rp, (0, 1), color='black', thickness=1.5, legend_label=r'$r_+$') \\\n", "+ plot(rm, (0, 1), color='darkgoldenrod', thickness=2, legend_label=r'$r_-$') \n", "graph.set_legend_options(handlelength=2, loc=(1.02, 0.36))\n", "show(graph)\n", "graph.save('gik_spher_orb_range.pdf')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Properties of the spherical orbit at $r=r_{\\rm ph}^{**}$" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph = plot(lambda a: lsph(a, rph_ss(a)), (0, 1), color='red', thickness=2, \n", " legend_label=r'$\\ell_{\\rm ph}^{**}$',\n", " axes_labels=[r'$a/m$', r'$\\ell_{\\rm ph}^{**}/m,\\ \\ q_{\\rm ph}^{**}/m^2$'],\n", " frame=True, gridlines=True, axes=False) \\\n", " + plot(lambda a: qsph(a, rph_ss(a)), (0.001, 0.999), color='blue', thickness=2,\n", " legend_label=r'$q_{\\rm ph}^{**}$')\n", "graph.set_legend_options(handlelength=2)\n", "graph.save(\"gik_ell_q_rss.pdf\")\n", "graph" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{1}{4}\n", "\\end{math}" ], "text/plain": [ "-1/4" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lsph(1, rph_ss(1))" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{9}{16}\n", "\\end{math}" ], "text/plain": [ "-9/16" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qsph(1, rph_ss(1))" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-0.562500000000000\n", "\\end{math}" ], "text/plain": [ "-0.562500000000000" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n(_)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "th_s = lambda a: arcsin(sqrt(abs(lsph(a, rph_ss(a)))/a))" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph = plot(th_s, (0.0001, 0.9999), color='blue', thickness=2, \n", " axes_labels=[r'$a/m$', r'$\\theta^{**}_{\\rm ph}$'],\n", " frame=True, gridlines=True, axes=False)\n", "graph.save(\"gik_theta_ss.pdf\")\n", "graph" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.523598775598299\n", "\\end{math}" ], "text/plain": [ "0.523598775598299" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n(pi/6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Angular momentum of the circular photon orbits in the equatorial plane" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = plot(lambda a: lsph(a, rph_s(a)), (0, 1), color='red', thickness=2, \n", " linestyle=':', legend_label=r'$\\ell_{\\rm ph}^{*}$',\n", " axes_labels=[r'$a/m$', r'$\\ell/m$'],\n", " frame=True, gridlines=True, axes=False) \\\n", " + plot(lambda a: lsph(a, rph_p(a)), (0, 1), color='red', thickness=2, \n", " legend_label=r'$\\ell_{\\rm ph}^+$') \\\n", " + plot(lambda a: lsph(a, rph_m(a)), (0, 1), color='red', thickness=2, \n", " linestyle='--', legend_label=r'$\\ell_{\\rm ph}^-$')\n", "graph.set_legend_options(handlelength=2)\n", "graph.save(\"gik_ell_circ_equat.pdf\", ymin=-8, ymax=6)\n", "show(graph, ymin=-8, ymax=6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Stability of the photon spherical orbits " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generic function $\\mathcal{R}(r)$:" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( a, {\\ell}, q, r \\right) \\ {\\mapsto} \\ r^{4} - a^{2} q + {\\left(a^{2} - {\\ell}^{2} - q\\right)} r^{2} + 2 \\, {\\left({\\left(a - {\\ell}\\right)}^{2} + q\\right)} r\n", "\\end{math}" ], "text/plain": [ "(a, l, q, r) |--> r^4 - a^2*q + (a^2 - l^2 - q)*r^2 + 2*((a - l)^2 + q)*r" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "l = var('l', latex_name=r'\\ell')\n", "q = var('q')\n", "R(a, l, q, r) = r^4 + (a^2 - l^2 - q)*r^2 + 2*(q + (l - a)^2)*r - a^2*q\n", "R" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Function $\\mathcal{R}(r)$ for a spherical orbit:" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [], "source": [ "r0 = var('r_0')" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{r_{0}^{6} - {\\left(2 \\, r^{2} - 8 \\, r - 9\\right)} r_{0}^{4} - 6 \\, r_{0}^{5} + r^{4} - 4 \\, {\\left(a^{2} + 4 \\, r\\right)} r_{0}^{3} + {\\left(r^{4} + 8 \\, a^{2} r + 6 \\, r^{2}\\right)} r_{0}^{2} - 2 \\, {\\left(2 \\, a^{2} r^{2} + r^{4}\\right)} r_{0}}{r_{0}^{2} - 2 \\, r_{0} + 1}\n", "\\end{math}" ], "text/plain": [ "(r0^6 - (2*r^2 - 8*r - 9)*r0^4 - 6*r0^5 + r^4 - 4*(a^2 + 4*r)*r0^3 + (r^4 + 8*a^2*r + 6*r^2)*r0^2 - 2*(2*a^2*r^2 + r^4)*r0)/(r0^2 - 2*r0 + 1)" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R0(a, r0, r) = R(a, lsph(a, r0), qsph(a, r0), r).simplify_full()\n", "R0(a, r0, r)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We check that $r_0$ is a double root of $\\mathcal{R}(r)$:" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{{\\left(r^{2} r_{0}^{2} + 2 \\, r r_{0}^{3} + r_{0}^{4} - 4 \\, a^{2} r_{0} - 2 \\, r^{2} r_{0} - 4 \\, r r_{0}^{2} - 6 \\, r_{0}^{3} + r^{2} + 2 \\, r r_{0} + 9 \\, r_{0}^{2}\\right)} {\\left(r - r_{0}\\right)}^{2}}{{\\left(r_{0} - 1\\right)}^{2}}\n", "\\end{math}" ], "text/plain": [ "(r^2*r0^2 + 2*r*r0^3 + r0^4 - 4*a^2*r0 - 2*r^2*r0 - 4*r*r0^2 - 6*r0^3 + r^2 + 2*r*r0 + 9*r0^2)*(r - r0)^2/(r0 - 1)^2" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R0(a, r0, r).factor()" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}2 \\, {\\left(r - 3\\right)} r_{0}^{3} + r_{0}^{4} + {\\left(r^{2} - 4 \\, r + 9\\right)} r_{0}^{2} + r^{2} - 2 \\, {\\left(2 \\, a^{2} + r^{2} - r\\right)} r_{0}\n", "\\end{math}" ], "text/plain": [ "2*(r - 3)*r0^3 + r0^4 + (r^2 - 4*r + 9)*r0^2 + r^2 - 2*(2*a^2 + r^2 - r)*r0" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s = (R0(a, r0, r)*(r0 - 1)^2/(r - r0)^2).simplify_full()\n", "s" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\n", "\\end{math}" ], "text/plain": [ "True" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bool(s*(r - r0)^2 == R0(a, r0, r).factor().numerator())" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{0}^{4} + {\\left(r_{0}^{2} - 2 \\, r_{0} + 1\\right)} r^{2} - 4 \\, a^{2} r_{0} - 6 \\, r_{0}^{3} + 2 \\, {\\left(r_{0}^{3} - 2 \\, r_{0}^{2} + r_{0}\\right)} r + 9 \\, r_{0}^{2}\n", "\\end{math}" ], "text/plain": [ "r0^4 + (r0^2 - 2*r0 + 1)*r^2 - 4*a^2*r0 - 6*r0^3 + 2*(r0^3 - 2*r0^2 + r0)*r + 9*r0^2" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s.collect(r)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{0}^{3} - 4 \\, a^{2} - 6 \\, r_{0}^{2} + 9 \\, r_{0}\n", "\\end{math}" ], "text/plain": [ "r0^3 - 4*a^2 - 6*r0^2 + 9*r0" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b = r0^3 - 6*r0^2 + 9*r0 - 4*a^2\n", "b.factor()" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\n", "\\end{math}" ], "text/plain": [ "True" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bool(R0(a, r0, r) == (r - r0)^2*(r^2 + 2*r0*r + r0*b/(r0 - 1)^2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check of the formula\n", "$$\\mathcal{R}(r) = (r - r_0)^2 \\left( r^2 + 2 r_0 r - a^2 \\frac{q}{r_0^2} \\right)$$" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\n", "\\end{math}" ], "text/plain": [ "True" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bool(R0(a, r0, r) == (r - r0)^2*(r^2 + 2*r0*r - a^2/r0^2*qsph(a, r0)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot of $\\mathcal{R}(r)$ for various values of $r_0$" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [], "source": [ "Rss(a, r) = R0(a, rph_ss(a), r)\n", "Rs(a, r) = R0(a, rph_s(a), r)\n", "Rp(a, r) = R0(a, rph_p(a), r)\n", "Rm(a, r) = R0(a, rph_m(a), r)\n", "Rms(a, r) = R0(a, rph_ms(a), r)" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\rm ph}^{**} = -0.477673658836338 m\n", "\\end{math}" ], "text/plain": [ "r_{\\rm ph}^{**} = -0.477673658836338 m" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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KlEtOQUqSVKRGjIBhw2DIEOjUKetqlEsuwpeUNy7Cl9rvyy+/3u/x4YfLesuh8v3KFsMRMEmSitAf/gBvvw3331/W4atiuQZMkqQi8+abaeH9qaem9hMqPwYwSZKKzEknwZprpn0fVZ6cgpQkqYjcd1+advzb32DllbOuRvniInxJeeMifKltPv8cunWDTTeFkSMrZu1XZXyVC3AETFLO1dXVUVdXR1NTU9alSCXl97+H995L+z1WSPiqWI6AScobR8Ck1nv99TT6dfrp8JvfZF1NQVVk1DSAScobA5jUOjHCrrumEPbyy7DSSllXVFAVGcCcgpQkKWO33po22h4xouLCV8WyDYUkSRn617/gF7+AAw+Evn2zrkaFYgCTJClDv/wlzJkDl16adSUqJKcgJUnKyNixcMMNcPXVsPbaWVejQnIRvqS8cRG+tGhffglbbpk63o8bB8tU7pyUi/AlSVJh/O53MG0aDB1a0eGrYvmSS1qkK6+8kh49elBVVUVVVRU9e/Zk5MiRWZcllbypU1PT1TPOgJqarKtRFpyClLRI9913Hx06dGDjjTcG4KabbuKiiy5iypQpdOvWbYnHOwUpLWzuXOjVCz74AF54AVZYIeuKMleRU5AGMEltsvrqq3PRRRdx5JFHLvG+BjBpYVddBcceC6NHw047ZV1NUajIAOYaMEmt0tTUxF133cXMmTPp2bNn1uVIJentt1PbiZ/9zPBV6QxgkhbrxRdfpGfPnnz55ZesssoqDB06lJpFLFppbGyksbHxq383NDQUqkyp6MUIRx8N1dVw0UVZV6OsuQhf0mJtuummPPfcc4wfP55jjz2WAQMGMHXq1BbvO2jQIKqrq7+6dO3atcDVSsVr8GB46KHU86u6OutqlDXXgElqk1122YWNNtqIq6++eqHPtTQC1rVrV9eAqeLNmJHOdtx77xTE9A2uAZOkJYkxfiNkza9jx4507NixwBVJxS3GtOi+Y0e3G9LXDGCSFumss86ib9++dO3alU8//ZQ77riDsWPH8uCDD2ZdmlQy7rwThg+Hv/0NVl8962pULAxgkhbpgw8+4Kc//SkzZsygurqaHj168OCDD9KnT5+sS5NKwkcfwfHHw/77w777Zl2NiolrwCTljX3AVOn6908L76dOhS5dsq6maLkGTJIk5cbw4XD77XDLLYYvLcwRMEl54wiYKtVHH0H37vD976cgFipyjKfVKvK7Yx8wSZJyaN5Zj01N8Ne/Gr7UMqcgJUnKodtuS2c83nUXrL121tWoWDkCJklSjrz7bjrrsX//dOajtCgGMEmSciBGOPJIWGkluPzyrKtRsXMKUpKkHLj66tRyYsQIWG21rKtRsXMETFLO1dXVUVNTQ21tbdalSAXxxhtw2mlw9NHQt2/W1agU2IZCUt7YhkKVoKkJevWC996D55+HTp2yrqjkVOR5ok5BSpK0FC6+GJ56Ch57zPCl1nMKUpKkdpo8Gc45B04/HX74w6yrUSlxClJS3jgFqXL22Wfw3/8NVVVpBGz55bOuqGQ5BSlJklrn5JNT36/77zd8qe0MYJIktdHf/gbXXQfXXgv/9V9ZV6NS5BowSZLa4J134Gc/g/32gyOOyLoalSoDmCRJrdTUBIcemrrdu9G2loZTkJIktdLFF8PYsTB6NKy+etbVqJQ5AiZJUivM33Kid++sq1Gpsw2FpLyxDYXKhS0n8qoiJ3KdgpQkaQlOPNGWE8otA5gkSYsxeDDccAPceKMtJ5Q7rgGTlHN1dXXU1NRQW1ubdSnSUnnlFTj2WDjsMBgwIOtqVE5cAyYpb1wDplL2+eewzTYQI0ycCCuvnHVFZcs1YJIkKTnhBJg2DSZNMnwp9wxgkiQtYPBguP76tO6rpibralSOXAMmSdJ8XPelQnANmKS8cQ2YSo3rvjLhGjBJkiqZ675UKAYwSZJw3ZcKyzVgkqSK9/zzcMwxrvtS4bgGTFLeuAZMpeCTT2Drrb/e53HFFbOuqOK4BkySpEoydy4cfHAKYY88YvhS4RjAJEkV69e/hgcfhJEjYcMNs65GlcQAJkmqSPffDxdcAL/9Ley2W9bVqNK4BkxS3rgGTMXq9dfTuq8dd4R77oFlPCUtSxW5BswfOUk5V1dXR01NDbW1tVmXIi1k5kzYZx/o0gVuusnwpWw4AiYpbxwBU7GJEfr3h/vugwkToFu3rCsSFToC5howSVLFuOwyuOMOuPNOw5ey5cCrJKkiPPoonHZauhxwQNbVqNIZwCRJZe+NN1Lo2mknGDQo62okA5gkqcw1NMCPfgSdO8OQIbCsi29UBPwxlCSVraam1On+nXfSovvVVsu6IikxgEmSytbZZ8OIEanp6mabZV2N9DUDmCSpLN16K1x4IVx8MfTtm3U10je5BkySVHYmToQjj4TDDoNTTsm6GmlhBjBJUll55x3o1w/++7/hqqsgVGSbTxU7A5gkqWx8+instRcst1za47Fjx6wrklrmGjBJUlmYMwcOPBCmTYMnn4S11866ImnRDGCSpJIXI5x4IowaBSNHQvfuWVckLZ5TkJJyrq6ujpqaGmpra7MuRRXi0kvhyivTpU+frKuRlizEGHPxODl5EEnlpaGhgerqaurr66mqqsq6HJWpYcNg333h9NPh97/Puhq1Q0WeJuEImCSpZE2eDP37w377we9+l3U1UusZwCRJJemtt2DvvaFHDxg8GJbxfzSVEH9cJUklp74+tZtYYQW4915YccWsK5LaxrMgJUklpbExrfmaPh2efhrWWivriqS2M4BJkkrG3LkwYEDq8zVqFGy+edYVSe1jAJMklYQY4dRT4c474e67YYcdsq5Iaj8DmCSpJFxySer3dcUVaQpSKmUuwpe0SIMGDaK2tpZOnTqx1lpr0a9fP1599dWsy1IFuuUW+OUv4Zxz4Nhjs65GWnoGMEmL9NhjjzFw4EDGjx/Pww8/zJw5c9h1112ZOXNm1qWpgowaBYcfDkccARdckHU1Um7YCV9Sq3300UestdZaPPbYY+zQigU4dsLX0po8GXbcMV2GDYNlXThTjiqyE74/ypJarb6+HoDVV1+9xc83NjbS2Nj41b8bGhoKUpfK09SpsPvusMUWMGSI4UvlxSlISa0SY+SUU05h++23p3v37i3eZ9CgQVRXV3916dq1a4GrVLmYNi1tqr3OOvDAA7DyyllXJOWWU5CSWmXgwIE88MADPPHEE3z7299u8T4tjYB17drVKUi1yYwZ8MMfpo+feALWXjvbepR3TkFKUktOOOEE7r33XsaNG7fI8AXQsWNHOnbsWMDKVG7+/W/YdVf48kvDl8qbAUzSIsUYOeGEExg6dChjx45lww03zLoklbFPP4W+feH992HcONhgg6wrkvLHACZpkQYOHMhtt93G8OHD6dSpE++//z4A1dXVrOjux8qhL7+Efv3glVdgzBi3GFL5cw2YpEUKoeWlGTfccAOHHXbYEo+3DYVaY84c2H9/eOihdHGLoYrjGjBJml+O/kCTFqmpCQ47LJ3pOHy44UuVwwAmScrE3Llw1FFw++3pssceWVckFY59wCRJBTd3Lvz85zB4MNx8M/z4x1lXJBWWI2CSpIKKEY4/Hq67Dm64Afr3z7oiqfAMYJKkgokRfvELuPJKuPZaGDAg64qkbDgFKUkqiBjh9NPhsstSADvyyKwrkrJjAJMk5V2McPbZcPHF8Oc/wzHHZF2RlC2nICVJeRUjnHkmXHhhCmAnnJB1RVL2HAGTlHN1dXXU1NRQW1ubdSnKWIxwyikpfP3pT3DqqVlXJBUHO+FLyhs74Ve2uXPTaNcVV0BdHRx3XNYVqUjZCV+SpFyY1+fruuvgmmtSw1VJXzOASZJyqqkpneF4881w441w6KFZVyQVHwOYJCln5sxJvb2GDIFbboGf/CTriqTiZACTJOXE7Nmpq/2wYXDHHbD//llXJBUvA5gkaak1NsKBB8KIEXD33fA//5N1RVJxM4BJkpbKzJmw334wdmwa/dpjj6wrkoqfAUyS1G6ffAJ77gkvvphGv3baKeuKpNJgAJMktcuMGbDbbvDee/Doo2DfXan1DGCSpDZ7803o0yet/Ro3Dmpqsq5IKi1uRSRJapOXXoLtt4dlloEnnzR8Se1hAJMktdr48bDDDtClCzzxBKy/ftYVSaXJACZJapWHH4ZddoFu3WDMmBTCJLWPAUxSztXV1VFTU0Otq7LLxi23pPYSvXrBQw/BqqtmXZFU2kKMMRePk5MHkVReGhoaqK6upr6+nqqqqqzLUTvECBdeCGeeCYcfDldfDcstl3VVKjMh6wKy4AiYJKlFTU1wwgkpfJ17Llx3neFLyhXbUEiSFvLFF3DwwTB8OPz1r/Czn2VdkVReDGCSpG/4179g773h+edTANtrr6wrksqPAUyS9JVp06Bv3xTCxoyBbbbJuiKpPLkGTJIEwLPPQs+eMGcOPP204UvKJwOYJIlhw+CHP4T11oOnnoKNN866Iqm8GcAkqYLFCH/4A+y7b+rzNXYsrLVW1lVJ5c8AJkkVatYsOOooOOMMOOssGDIEVlop66qkyuAifEmqQP/+N+y3X9pM+6ab4NBDs65IqiwGMEmqMK+9llpL/PvfMHp0WvslqbCcgpSkCjJmDGy7LXToABMmGL6krBjAJOWcm3EXp2uvhV13he99L7WZ2GijrCuSKpebcUvKGzfjLg6zZsEvfgFXXAHHHAN//rN7OqqoVORm3K4Bk6Qy9sEHcMABMH48XHUV/PznWVckCQxgklS2Jk+GffaB2bPT2q8f/CDriiTN4xowSSpDgwfD9tvDOuvAM88YvqRiYwCTpDIyezacfDIMGAD9+8Njj8G662ZdlaQFOQUpSWXi44/hxz+Gxx+Hyy+H446DUJHLm6XiZwCTpDIwZUpa7zVzJjzyCPTqlXVFkhbHKUhJKmExwjXXQM+e0LlzWu9l+JKKnwFMkkrU55/DYYfB0Uen6yefhPXWy7oqSa3hFKQklaDXXoP994fXX09nPP70p1lXJKktHAGTpBJz992w9dbQ2AgTJxq+pFJkAJOkEjFvS6EDDoDdd0+NVrt3z7oqSe3hFKQklYC334aDDoJJk+Cyy+CEE2wxIZUyR8Ak5VxdXR01NTXU1tZmXUpZGDoUttoK3nkHxo2DE080fEmlLsQYc/E4OXkQSeWloaGB6upq6uvrqaqqyrqckvPll3DqqXDFFanH17XXwuqrZ12VlHMV+eeEU5CSVIReeSVNOb76agpgxxzjqJdUTpyClKQiEiNcf306y3H27HSW47HHGr6kcmMAk6Qi0dAABx8MRx4JP/lJWnDfo0fWVUnKB6cgJakITJqUphw/+ghuvz19LKl8FWwEbNQomDq1UM8mSaVhzhz4zW9gu+1gjTXguecMX1IlKMgIWFMTnHZaeqOZOBFWWaUQzypJxe2NN1IX+wkT4Oyz4Ve/guWWy7oqSYVQkBGwDh3gzjtTI8FjjkmLTCWpUsUI11wDW24JH34ITzwBF1xg+JIqScGmIDfbLPWwufVWuPrqQj2rpKUxbtw49t57b9ZZZx1CCAwbNizrkkrehx9Cv35w9NFpof1zz0HPnllXJanQCnoW5EEHwfHHw0knpT3MJBW3mTNnsuWWW3L55ZdnXUpZuO8+2GILePppGDYsjYK5JEOqTAXvhN/YCD/8Yfor8Nln7eoslYoQAkOHDqVfv36tPsZO+Mmnn6aO9tdcA3vuCdddB126ZF2VVDQqsstdwfuAdewId92V+t0MGABz5xa6AkkqnNGj06jXbbfBVVelUTDDl6RMGrGuvz7ccgvcfz9ceGEWFUjKh8bGRhoaGr5xqVSffpo62O+yC2y4IbzwAvz853a0l5Rk1gl/jz3SKddnnw0jRmRVhaRcGjRoENXV1V9dunbtmnVJmXj00TTqNXgwXH55GgX7zneyrkpSMcl0K6Lzz4e99kpnAr36apaVSMqFM888k/r6+q8u06dPz7qkgvrsMzjuONh5Z9hgA3jxRRg4EJZx0zdJC8h0K6JllklTkdtuCz/6UWpGuOqqWVYkaWl07NiRjh07Zl1GJsaMgSOOSCcY/eUvKYgZvCQtSuZvD1VVMHx4etM6+ODUNV9Scfjss8947rnneO655wCYNm0azz33HG+//Xa2hRWRTz6Bo46CnXaC9dZLa72OP97wJWnxCt6GYlEeeiitCzv9dBg0KBclSVpaY8eOpXfv3gvdPmDAAG688cYlHl/ObShiTGd0n3gifPFFOqHo6KMNXlI7VOSpKUUTwAAuvhh++cvULb9//1w8oqQslWsAmz49re267z7YZ5805bjuullXJZWsigxgma4BW9Cpp6ZFq4cfDl27poatklQsmprgyivhzDOhUyf4299g332zrkpSKSqqwfIQUqfo7bZLe6X94x9ZVyRJycsvw/bbwwknpPWqU6caviS1X1EFMIDll4d77oG11kprwj7+OOuKJFWyL76Ac8+F734X/vMfGDcudbT3jG1JS6PoAhjAaqvBAw9AfX0aCfvyy6wrklSJRoyA7t3h97+H//1feO45l0ZIyo2iDGCQukbfey8880xaE+aekZIK5a230uL6PfdM70UvvggXXJD2spWkXCjaAAapQevNN8Mdd8BZZ2VdjaRyN2tWaoOz+eYwcSIMGQKjRsGmm2ZdmaRyU9QBDGD//eFPf0o9di65JOtqJJWrRx6BHj3SHrXHHQd//zv8+Mduni0pP4qqDcWinHxy6pR/2mmwxhowYEDWFUlanLq6Ourq6mgqga0t3n0XTjkF7rwTdtgB7r47rfuSpHwqqkasi32CmLpM33ADDB0Ke++d72eUtLSKuRHrrFmpger558NKK6VG0Icc4oiXlIGK/K0r+inIeUJIDRB/9KM0LTBuXNYVSSpFMcL998MWW6Stzw47DF59FX76U8OXpMIpmQAGsOyycNtt0LNnGgFr3h9Yklrl5Zdh993T+0fXruk95C9/saeXpMIrqQAGsMIKMGwYbLIJ9OkDL72UdUWSit3HH8Pxx8OWW8Kbb8Lw4fDww2kUTJKyUHIBDKCqCh56CNZZB3bZJU0fSNKCZs+Gyy5Lf7DdfHM6m/qll9JSBqcbJWWpJAMYQOfO6bTxzp1hp53g9dezrkhSMRkxIo1wnXJKWjf6j3/AqafaTFVScSjZAAaw5powejR06pRC2LRpWVckKWsvvQR9+6Yu9uusA88+C1dfnfaXlaRiUdIBDGDtteHRR9NftTvu6EiYVKneeQeOPDKt83rtNbjnnvQH2pZbZl2ZJC2s5AMYpL9yx46FFVdMjRRfeSXriiQVSn192qpsk03S/rGXXpreA/bZx3VekopXWQQwgHXXhcceS53ye/WC55/PuiJJ+TRrFvz5z7DRRil0nXJKGgE/4QRYfvmsq5OkxSubAAbQpQuMGZP6+/TuDZMmZV2RpFybOxduvz1tmP2LX0C/fmmB/f/9H1RXZ12dJLVOWQUwSGdFjh4Nm20GO+8MTzyRdUWSciHG1ANwyy2hf3+oqYEXXoBrr00j4JJUSsougEHqaj1qFHzve7DbbjByZNYVSWqvGNPv8/e/n9Z1rbUWPPUU3HcfdOuWdXWS1D5lGcAAVlkFHnggNWrde2+48casK5IqR11dHTU1NdTW1i7V4zzxRDq7ebfdoEOHNLo9enTajkySSlmIMebicXLyIPkwZw4cdxxccw389rfpbCnPjJIKo6Ghgerqaurr66mqqmr1cZMnw69+BQ8+CFttlX5399jD312pTFXkb/ayWReQb8sum5owrrsunHMOvPdeOnOqQ4esK5O0oJdfTsFr6NC0jvPOO2G//WCZsh2rl1Spyj6AQfqr+bzzUr+wY46BGTPglltgpZWyrkwSwIsvprMY77wTNtgAbroJDj7YP5Qkla+K+rvyZz9LZ1E99FBq2Pruu1lXJFW2Z5+FffeFHj1gwgS48kr4+9/h0EMNX5LKW0UFMEgL8p98Ej78EGpr7RUmZWHCBNhrr3Sm8osvwvXXp+2Dfv5zm6hKqgwVF8AgLeqdOBHWXz+NhA0ZknVFUmV4/HHYdVfYdlt48820FOCVV+Dww2G55bKuTpIKpyIDGKRNvMeMgf33h4MOgnPPTR22JeXe2LGpncQOO8AHH6S1Xi+9lNZ5LVsRK1El6Zsq+q1vhRVg8ODUzPGss9J6lJtvhtVWy7oyqfQ1NaWzGQH+53/SdOOwYWkZgGc1Sqp0Zd8HrLVGjoRDDoGqKrj77vSfhaS2++KL1Pj4kkvgjTcagGruvrueffetso+XpJZU5DuDf4c269sXnnkG1lgDfvCD1Lg1N9lUqgz/+hdccEFaW3n88bD11mnqEaBPH5uoStL8DGDz2WCDtPXJ4YfD0Uen688/z7oqqbhNmwYnngjrrQe//z0ceCD84x9wxx3w3e9mXZ0kFScD2AI6dky9iAYPTguFv/c9mDIl66qk4hIjPP10OoFl443h9tvh9NPh7bfhL3+B73wn6wolqbgZwBbhpz9NU5IdO8L3v5/Ws3iWpCpdY2M6UWWbbWC77dLvyJ//DG+9lXabWGONrCuUpNJgAFuMzTdPDSNPOAFOOw123z1tYyRVmhkzUsBaf/3Upb5zZ3jgAXj1VRg4cOFtverq6qipqaG2tjabgiWpyHkWZCuNGgUDBsCsWWmK5Sc/cVGxyt+ECWmE6667Uof6ww5LC+w326x1xzc0NFBdXU19fT1VVVV5rVVSyarI/00dAWulXXdNW6b06ZOaR/br52iYytOsWXDrrWnqfdttYfx4+MMf0t6pl1/e+vAlSVo0A1gbrLFGOrPrnnvSyEBNTep3ZLsKlYPXX4czzoBvf/vrnnj33pv2aDz5ZKiuzrpCSSofBrB22GcfmDo1dfQ+/HDYc0/45z+zrkpqu8bGtBfqLrvAJpvAX/+aptdffhkefjj9jHfokHWVklR+DGDttPrqqVXFfffBCy+k0bBBg9L0jVTsXnsNfvnLNNp10EHp53bwYHjvPbjssvTzLEnKHwPYUtprL3jlFTjuOPjVr2DLLeHRR7OuSlpYY2Pq19W7N2y6KVx/fWq3MnUqjBuXPl5xxayrlKTKYADLgU6d4OKLU8PWzp1h551hv/3SmhopSzGmXl0nnQTrrgv9+6fbbr01Lar/4x9TuxVJUmEZwHJoiy3SSMLgwTBxYprGOeUU+Pe/s65Mleadd+DCC6F797Qn4513pvWKf/972p+xf39YYYWsq5SkymUfsDz5/HP405/S3njLLQfnnpumKZdfPuvKVK5mzkxn6A4eDKNHp10c9tkn9a/beWdYdtnC12QfMEmtYB8w5c5KK8HZZ6dNiQ84AE49NU313HQTzJmTdXUqF7Nnw0MPpQapXbqkLvWzZ8O118IHH8Btt8Fuu2UTviSp2IUQDsjquQ1gebb22nD11fD882mB/mGHpanJW2+Fpqasq1MpamqCMWPgmGNgnXXSFllPPZV6eL35ZppiPOKI1MdLktSyEMJ2wICsnt8AViDdu6fpoWeeSZ3EDzkk3XbrrY6IacnmzoUnn0z7kn7727DTTvDggyloPfNM2pPxV7+CDTfMulJJKhkHA7dm9eSuAcvIpElw/vkwYkTa4PiUU+DII2HllbOuTMVizhx4/HEYNiyF93feSWcyHnBA6t21zTbFvx+pa8AktULB38lCCMsC/wC6xRg/L/TzgwEsc88/n1pY3H572upl4MC0WH/ttbOuTFn4/PO08fuwYanJ77//nUJXv35w4IHwgx/AMiUwbl1XV0ddXR1NTU289tprBjBJi5NFANsLODDG+NNCP/dXNRjAisNbb8Gll8I116SGmfvuC8ceC716Ff8oh5bOxx/D/fen0DVqFHzxBXTrlkJXv37wve+V7s+AI2CSWiGLAHY7cFOM8cFCP/dXNRjAissnn6Q2Aldemdb1bL55Wmx96KGw6qpZV6dcmDsXJk+GkSPTFPSkSen2nj2/Dl2bbJJlhbljAJPUCgUNYCGEVYAXgU1ijJmtwjaAFakY09lsV14JQ4emXmI//nHaLmbHHd0gudR8/HFqFzFyZLr++OM05dynD+yxB/TtW57TzgYwSa3Q5gAWQtgSOA3YEPg98CRwHtARWBv4dYzxuUUceyiwdYzxxAVu3x44GtgE+C0wEjgW2AxYDugOnBZjHB9C6A/8sPnQLYBzY4xt2ojQAFYCZsyA665LPcRef/3rLWUOOQR69Mi6OrWkoSEtoH/00XR5/vkUqrfaKoWtvn3TiFe59+cygElqhfYEsOtJYel/gROBccBJwH8BDwFXxxhPWMSxD5EC04T5blsGuJHUluIi4FBgCHBPjHFM832uBvo03++lGOM9zbdfAAwE1owxzm3t11Dmb//l4VvfgnPOSY1dJ06EW26BG26Aiy5KLS322y+tGfvud0t3rVCp++KL1ItrXuCaNCn161p33dSF/qSTYNddU98uSVL7hRA2At6LMc4JIawDrA78Lsb4bgihJ/AZcN8iju0CrD9/+GpWC0yJMcbmx1wTeGBe+GrWQBpx+2Be+Gr2QXMNazZ/3LqvwxGw0jR7dlqwfffdMHx4Wju2wQaw995pdGXHHWHFFbOusnx98EEKXE89lfpzPfMMzJoFa64JvXunPl077QQbb1zZodgRMEmt0KZ3yeYGql/EGKeEEF4A/h1j3LGVx54ErB5jPG+B23cA3o4x/jOEMB14Oca4+wL3eYg0PblRnC88hRAuB44AqtqypswAVgZmz07rxe65Jy3qfvvttNFy794pjO2ySxopq+QgsDQaG+GFF1LIevrpFLjeeCN9rmvX1Bpiu+3S97tbN7/P8zOASWqFdr1rhhDWAD4ELogxnt/KYyYCP40xvrqIz29M6g92WozxkvluXxb4BLgrxnjEAse8BkyLMe7WlvqdgiwDyy2XFnP36ZPWGb3yytdn2J16agpoa60FO+yQLr16pS78pdBPqtDmD1vzLi++mJqiduiQ1nDtscfXoatr16wrlqSK1ZsU3sa25s4hhP8iDTy1GL6a7dR8veBj1gKrLHh7CGEL0qjYRa2pYX4GsDITQtprsqYmha/PPkvTZI89li7zAlmnTqm/1NZbQ21tut5ww8oZvZkzJ41ivfwyvPTS19evvfZ12OrWLX1fjjoqfa969HBaV5KKSG+gERjfyvu3Zuuh3sB/gCkL3L5j8/XYBW7v31zD3QAhhCNjjNe1phinICvM55/DhAnpMnlyurz1Vvrc6qvDFluk4FFTk6432wy6dCnNYDZnTpqOfeONtEn1G2+ky+uvpx5rjY3pfp07pxHBbt3S9X//t2ErV5yClNQK7Z2CfIW0IH7HVt7/78COMcb3F3OfGcDEGOP/LHD7KNLar40WuP1V4PkY44+bR8P2jTH+ujX1OAJWYVZaKa1V6t3769s++ihNtU2enKbbHnssdeSfPTt9fsUV0wL/DTZIo2Qbbpg+/ta3Ujhba600olbIkPbZZ6k9x4wZ8N57X3887zJtWgqWTU3p/h06pD03v/Od1P7hqKNS4OrWLdVfigFTkipVCGFtUn+uIa28/7akRfaLC1+bk3qIjV3g9uWA7RbxXGsAjzW3sTiD1AqjVZY6gIUQQn19/dI+jDLUsWNaz7Tddl/fNnt2GjV6/fUUZP75zzSaNHZs6kc2c+bCj7HmmrDGGrDKKmlT8U6d0sfz/t2hwzcvyyzzdUPZWbPSiNTs2em6sTE9R0PD15f6+q8//vLLbz7/CiukRqZduqTrPfb4OixuuGFaq7Xcci1//Z9+mqvvpBobG2mcN7QIfNr8zW1oaMiqJElFrrq6ugr4NLZtSq4LqeXDna28f2umHzsD7wH3LHD7qsBM4JYWjjkROIo0RXlVjPFfraxn6acgQwhVgAlMkiS1V3WMMS9/qTWfwfg6sEWMsWj+5M7FFOSnrRkBa2hooGvXrkyfPj2va0Fqa2uZNG9zvTwqxPOUy9fia1+cz5GP51lwBGzGjBlss802TJ06lXXXXTdnz9OScnldSvW1X1Chfu/B16XYnqOtr311dXU1kM9gtCswoZjCF+QggLVxyJCqqqq8/jJ26NChIIt9C/E85fS1gK99sT1HIZ+nU6dOZfE9K5fnKOTz5Pv3HnxdivE5oPWvfb5GvubTmunHgiu7TlADBw4sm+cpp6+lEMrp+1VOX0uhlMvr4mvfdr4uxfccxSKEsDKwPWlj7aJSsDYUno5euXztK9c777zz1VTEt7/97azLUQH5e1+52vHa5+089BDCIcAPYozH5us52qtgI2AdO3bkvPPOo2PHjoV6ShUJX/vKNe8197WvPP7eV64ie+17AYOzLqIlNmKVlDeOgkhqhYrsxJirACZJC5mvTU3eTjGXpFJkAJOUNyGEAHSi7U0WJamsGcAkSZIKrOzaUEiSJBW7vAWwEMLZIYSnQgifhxD+08pjQgjh/BDCeyGEL0IIY0MI3fJVo/InhLBaCOHmEEJ98+XmEMKqSzjmxhBCXOAyvkAlS2qjEMJxIYRpIYQvQwjPhBB+uJj77tjC73cMIWxWyJq19EIIO4QQ7mv+vzqGEPq14phezT8jX4YQ3gwhHFOAUotaPkfAlgfuAq5swzGnA6cAxwO1wPvAwyGETrkvT3l2G7AVsHvzZSvg5lYc9yDwrfkue+SnPElLI4RwIHAp8H/Ad4HHgZEhhPWWcOimfPN3/B95LFP5sTLwPOn/6iUKIWwIjCD9jHwX+B3w5xDCfnmrsATkfQ1YCOEw4NIY46pLuF8g7UJ+aYzxwubbOpJ2Oz8jxnh1XgtVzoQQNgemAtvGGCc037Yt8DSwWYzx1UUcdyOwaoyxX4FKldROIYQJwLPzN7gMIbwCDIsxntnC/XcExgCrxRj/U6AylWchhAjsE2Mctpj7XAj8KMa4+Xy3XQVsGWPsmf8qi1MxrQHbEFgbGDXvhhhjI/AYsF1WRaldegL188IXQIxxPKkdwZJeyx1DCB+GEF4LIVwTQlgrn4VKarsQwvLA95jv/brZKJb8Oz4lhDAjhDA6hNA7LwWq2PRk4Z+Vh4CtQwjLZVBPUSimALZ28/UHC9z+wXyfU2lYG/iwhds/ZPGv5UjSpqk7AaeSpqEfbR4JlVQ81gA60Lb36xnA0cB+wL7Aq8DoEMIO+SpSRWNtWv5ZWZb0s1SRlm3LnUMI5wPnLeFutTHGye2uaOGu+qGF25SB1r7+zdctvWaLfS1jjEPm++dLIYTJwFvAnsA9ra9UUoG0+v26eenB/MsPng4hdAVOA8blpzwVkZZ+Vlq6vWK0KYABlwN3LOE+/2xfKbzffL026S+ledZi4eSsbLT29e8BdGnhc2vShtcyxjgjhPAWsElrj5FUEB8DTSw82tXW9+vxwCG5KkpF631a/lmZA/yr8OUUhzYFsBjjx6RfvHyYRnqR+gBT4Kt1Br2AM/L0nGqD1r7+IYSngeoQwjYxxonNt30fqAaeau3zhRA6A135ZiCXlLEY46wQwjOk9+uh832qDzC8DQ/1Xfz9rgRPA3svcNuuwOQY4+wM6ikK+ewDtl4IYStgPaBDCGGr5ssq893n7yGEfQCatym5FDgrhLBPCKE7cCPwOamlgUpEjPEVUjuJa0II2zafAXkNcP/8Z0DO//qHEFYJIVwcQugZQtig+Yyp+0iBb+hCTyIpa38EjgohHBFC2DyE8CfS+/1VACGEQSGEwfPuHEI4OYTQL4SwSQihWwhhEGk92OWZVK92a36/3qr5/3iADZv/vV7z57/x2pN+JtYPIfyx+WflCOBI4OLCVl5c2joF2RYXAAPm+/eU5uvewNjmjzcljYrM8wdgReAKYDVgArBrjPHTPNap/DgY+DNfn/lyLwv3jJn/9W8CtgAOBVYl/VU8BjjQ118qPjHGIc2j1OeS+nm9BOwRY3yr+S7fIgWyeZYn/Ye7LvAF8DKwZ4xxROGqVo5sTXp/nuePzdc3AYexwGsfY5wWQtgD+BMwkNRy6sQY498KUm2Rci9ISZKkAiumNhSSJEkVwQAmSZJUYAYwSZKkAjOASZIkFZgBTJIkqcAMYJIkSQVmAJMkSSowA5gkSVKBGcAkSZIKzAAmSZJUYAYwSZKkAjOASZIkFdj/A7ilIrCgunhBAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a0 = 0.95\n", "# show(LatexExpr(r'r_{\\rm ph}^{**} = ') + latex(n(rph_ss(a0))) + L)\n", "show(LatexExpr(r'r_{\\rm ph}^{**} = ' + '{} m'.format(n(rph_ss(a0)))))\n", "plot(lambda r: Rss(a0, r), (-1, 1), axes_labels=[r'$r/m$', r'$\\mathcal{R}(r)$'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A stablle inner orbit:" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_0 = 0.4 m\n", "\\end{math}" ], "text/plain": [ "r_0 = 0.4 m" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r0 = 0.4\n", "show(LatexExpr(r'r_0 = ' + '{} m'.format(float(r0))))\n", "plot(lambda r: R0(a0, r0, r), (-0.2, 1), axes_labels=[r'$r/m$', r'$\\mathcal{R}(r)$'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The marginally stable orbit:" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\rm ph}^{\\rm ms} = 0.539741795874205 m\n", "\\end{math}" ], "text/plain": [ "r_{\\rm ph}^{\\rm ms} = 0.539741795874205 m" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "show(LatexExpr(r'r_{\\rm ph}^{\\rm ms} = ' + '{} m'.format(n(rph_ms(a0)))))\n", "plot(lambda r: Rms(a0, r), (-1, 1), axes_labels=[r'$r/m$', r'$\\mathcal{R}(r)$'])" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\rm ph}^{*} = 0.658372153864346 m\n", "\\end{math}" ], "text/plain": [ "r_{\\rm ph}^{*} = 0.658372153864346 m" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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FlVu2hFat7GuLFmoBiQa//QZ33mlD14MPwtix9j8GESAq/0uhACYiAeN2ADPGzo00b96xbft224LUrBm0awdt29qtZcvQDTEHD9r38d13NkCuWmW3tWttgAM4+2wbyFq1gg4d7Fa7trt1i/9s3Qo33GBbal9/Hf7v/9yuyK9cC2CO49xojPmXK/dWABORQHEjgB06ZAcnf/SRnQl8yxbbSnDRRXaepEsvhU6dbEtSuMvJsd2l33xjA9k330BGBvzyi/36+edDYuKxrUULLUsTjlJToV8/2809c6b9Xo4wrgQwx3E6Ag8ZY3q4cn8FMBHxt5SUFFJSUsjNzWXDhg0BD2C//gqffWZD16xZdnB848Zw7bVw+eV2QWKPJ2C3DylHW/3S049tmZm2paxaNUhIsGGsUye71arldsVSnJwcGDkSXngBuneHd96x4w8jkFsBLAX4yhjzviv3VwATkUAJZAvYkSPw+efw3nvw8ce2m65VK7j+eru1aqXB6kcdPAgrVx4LZGlp8PPPtmWwdWvo0sVunTur2zJUfPMN3HKLfUBk3Di4++6IGe9VlKD/TXUcpyLwHXCBMeZAsO8PCmAiEkCBCGBbtsAbb9ht2za44AL7OH6vXvD73/vlFhHvaCvZggV2mz/f/rk6jh0LdzSQXXyxfdpTgufgQXjqKRu6mjWz/8Fo3drtqgLOjQDWA+hljEkO9r0LalAAE5FA8VcAO3zYdi2+9podD1O9OvTpAwMG2AH0Un4//miD2NFQtmmT3d+ihR0317WrDWS/+52bVUa2+fPt9/SWLfDoozBsWNRMMeFGAHsfeNsYkxrsexfUoAAmIoFS3gCWnQ1//zu8+KJ9Cqx9e7jjDtvaVb26/+uVY7ZssUHs6NOjP/5oW8jatLFh7NJLbZdlJDzM4LbvvrNjvaZPt3+mr71mW7+iSFADmOM41YHVwHnGmCPBvPcJdSiAiUiglDWAbdsGEybA5Mmwf79t7br//qjoiglZmzYdC2Nz59oxZBUq2EH9R1vIOna0A/3FNzt3wpNP2u/zBg3g6aft9BIRPNarOKUOYI7jtAIeBM4GxgBfA48DMUB94AljTGYx5/YD2hlj7jlpfyfgDuA84GngM+BOoBlQCbgQeNAYk+44Th+gc/6pLYDHjDFzS/UeFMBEJFBKG8A2b4Znn4W33rKP3A8aZAcfa4Hh0GKMbbU5GsbmzbOz+1eubOcfO9pClphoVweQE+3YARMn2pbdChXg4Yft93mVKm5X5pqyBLA3sWFpBHAPsBC4Fzgf+ByYbIy5u5hzP8cGpiXH7TsNmAL0B/4G9AOmATOMMfPyj5kMXJ5/3LfGmBn5+58E7gLqGmPyfH0PmhFGRFx3fPDyeGxLwKBBoTsxarRzHDvH2Pnnw8CBNpCtWXMsjE2YAE88YQPFH/5wrIWsXTuoVMnt6t2zYQM8/zy8/badj23QINv1WKeO25WFF8dxzgF+NsYccRynIVAbeNYYs81xnCTgV+DTYs6tBzQ+PnzlSwAyjDEm/5p1gVlHw1e+bGyL246j4Svfjvwa6ub/2rf3oRYwEQmUU7WA7dljw9bLL9vgNWwY/PWvcPrpLhQrfpObayeGPdpCtnAh7Ntnx+116mSfsPzDH2wgq1rV7WoD6+gDJG+8YV/j4uCee+ySQnqgoUCpWsDyJ1A9aIzJcBxnFfA/Y8wlPp57L1DbGPP4SfsvBrYYY350HGcr8F9jTPeTjvkc2z15jjkuPDmOMxH4C1CzNGPKFMBEJGCKC2CHDsGrr9rxLzk5MHw4PPCAglekOnLEzkN2tIUsLc1Onluxoh3U37HjsS0Supvz8mDpUvjwQ3j3XTvWq107+wBJcnJUdzUWp0yD8B3HiQV2Ak8aY0b5eM5SINkYs76Yr5+LnR/sQWPM88ftrwjsAf5ljPnLSedsADYZY64oTf3qghSRoDHGzlY/bJidh+q222xXVYMGblcmgVSxon2CtX17GDHCtpB9+60NYmlp8Omn8NJL9thGjezA/jZt7JI7bdqEx/fHwYPwn//AJ5/Y97Njh51DrW9f+Mtf7Pxq4neXYsPbfF8OdhznfGzDU5HhK1/X/NeTr5kAVD95v+M4LbCtYn/zpYbjKYCJSFCsXAn33QeLFsEVV8CMGXaOKYk+FSocWzj8zjvtvqwsWLzYBrIVK+xYqb177dfq1bNBrE0baN7cTtHQtKm7YwSzs20r11df2e/pxYttCDvvPNvKde21tkWvQgX3aowClwI5QLqPx/cFpvpwzb1Axkn7L8l/nX/S/j75NXwI4DjObcaYN3wpRl2QIhIwR7sgBw708vrrNWne3P5gvaJUDfUSjYyxc49lZNht5Uq7PM+2bceOadDABrGmTaFJE7v+51ln2fUS69Sx61yWJwDl5sJPP9kpODZutK9r1ti1NTdutMfUrm3HtXXuDFdfbcOhlsAqtbJ2Qa7FDoi/xMfj1wGXGGOySjhmO7DUGHPdSfu/wI79Ouek/euBb4wxN+W3ht1gjHnCl3rK3QLmOI7j9XrLexkRiQA5OTnk5OQA9gfojBkHAXj77WyeeMK2dlSqZFsPRE6lTh247DK7HbVvH3z/vX2i8Pvv7XQYaWnwwQd2EfaT/e53dqtd225Vq9pQVqGCnW/rtNNs0PJ67fflvn3HXr1eO57rqAYNbAvXlVfa1tvWrW34O37ern37AvbHEbE8Hk9NYJ8pRYuQ4zj1sfNzTfPx+ETsIPuSwldz7Bxi80/aXwnoWMy9YoEF+dNYDMdOheGTcreAOY5TE1ACExERkbLyGGN8/q9Z/kSsnwNdjTFrfDj+ZWC5MebtEo7phA1ZHY0xm4/bXxf4Fuh90rQUOI7TF7gd2A1MMsZ86fN78EMAc7xe7yknHsvOzqZRo0Zs3brVb4vyFiUhIYFly5YF7PrBvE+kvBd99qF5j0Dc57ffcnj33TyefLIKVaoYhgzZwvDhrVizZg1nnHGG3+5TlEj5XML1sz9ZsP7egz6XULtHaT97j8fjoZQtYKWR/wTj90ALY0zItFGWuwuytH9gNWvWDOhfxgoVKgT8L3uw7hNJ7wX02YfaPfx9n23b7ELCn30G/fvDCy/A/v2/Mnw41KhRIyL+zCLlHsG8T6D/3oM+l1C8B/j+2Zem5auMugFLQil8QQQ+BXnXXXdFzH0i6b0EQyT9eYXbe/noIzulRJUq8O9/28HIYNdxDJZI+VzC7bMPBfpcQu8eIcaXpx+DLmhPQZZ1UV4Jf/rsI9eBAzBkCEyaBNdfD3//+4nLqvz0008FXRFnRsIMm+Iz/b2PXmX47AP23KjjOKcDa4BzjTGHA3WfsghaC1hMTAyPP/44MVqZNeros49Mq1dD7972cfxJk+ws3yc/fn/0M9dnH3309z56hdhn3xOYHWrhCzQPmIiUkjGQkgIPPmgXY/7gA4iPL/pYtYKIiA8C2QL2OvCmMWZxoO5RVhE3BkxEAud//4NbbrFLrdx9N4wbp3XtRCR0GWMGuF1DcRTARMQnK1fCn/5kJ6n89FPo0cPtikREwtdppz5ERKLdW2/BH/5gB9ivXKnwJSJSXgpgIlKsnBwYOBD+8hfo29cuPNy4sdtViYiEv4AFsGeeeYaOHTtSrVo1atWq5dM5xhhGjRpFw4YNqVq1Kpdccgn//e9/A1WiBNCePXtITk7G4/Hg8XhITk5m7969JZ5zyy234DjOCVtiYmJwCpZCdu+Gyy+HKVPg9dftFBMa7yXHe+WVVzj77LOpUqUKbdu2ZdGiRcUeO3/+/EJ/vx3HYd26dUGsWPxh4cKFXHPNNTRs2BDHcfjoo49Oec6CBQto27YtVapU4fe//z2TJk0KfKEhLmAB7NChQ9x4443ceeedPp8zbtw4xo8fz8SJE1m2bBn169fn8ssvZ59WNw07ffr0ITMzk9TUVFJTU8nMzCQ5OfmU53Xv3p3t27cXbLNnzw5CtXKydesgMdG+zp0Lt9/udkUSaqZNm8Z9993Hww8/TEZGBp07d+bKK69ky5YtJZ63fv36E/6On3feeUGqWPxl//79tGrViokTJ/p0/KZNm7jqqqvo3LkzGRkZPPTQQ9xzzz1Mnz49wJWGOGOMP7ZivfXWW8bj8ZR0iDHGmLy8PFO/fn0zZsyYgn2//fab8Xg8ZtKkSac8X0LHmjVrDGDS09ML9i1evNgAZt26dcWe179/f3PdddcFoUIpyZw5xng8xsTHG7NxY/mu5fV6DWC8Xq9fapPQ0b59ezNo0KAT9jVr1syMGDGiyOPnzZtnALNnz54gVCfBApiZM2eWeMywYcNMs2bNTtg3cOBAk5iYWHCZaNxCZgzYpk2byMrKolu3bgX7YmJi6NKlC2lpaS5WJqW1ePFiPB4PHTp0KNiXmJiIx+M55Wc5f/584uLiOP/88xkwYAA7d+4MdLlynMmToXt3SEqCtDQ4++yyXSclJYX4+HgSEhL8W6CEhEOHDrFixYoT/r0G6Nat2yn/jrdp04YGDRrwxz/+kXnz5gWyTAkRixcvLvS9csUVV7B8+XIOHw65+VGDJmQCWFZWFgD16tU7YX+9evUKvibhISsri7i4uEL74+LiSvwsr7zySqZOncrcuXN5/vnnWbZsGV27diUnJyeQ5QqQmwv33w+DBsGdd9ppJjyesl/vrrvuYs2aNSxbtsx/RUrI2L17N7m5uaX697pBgwa89tprTJ8+nRkzZtC0aVP++Mc/snDhwmCULC7Kysoq8nvlyJEj7N6926Wq3FeqecAcxxkFPF7SMcuWLaNdu3ZlLsg5aS0TY0yhfeKOUaNG8cQTT5R4zNEfuEV9Zqf6LHv16lXw6wsvvJB27drRuHFjZs2axQ033FDGquVU9u2Dm2+Gzz6Dl1+GwYPdrkjCRWn+vW7atClNmzYt+H1SUhJbt27lueee4+KLLw5oneK+or5XitofTUo7EetE4IOTd65du3bt0V83adKkTIXUr18fsEm5QYMGBft37txZKDmLOwYPHkzv3r1LPKZJkyasWrWKHTt2FPrarl27SvVZNmjQgMaNG/Pdd9+VulbxzY4dcOWV8MMPMGuW7X4UOZXY2FgqVKhQqLWrtP9eJyYm8t577/m7PAkx9evXL/J7pWLFitSpU8elqtxXqgBmjNkNBKS98Oyzz6Z+/frMmTOHNm3aAHacwYIFCxg7dmwgbimlFBsbS2xs7CmPS0pKwuv1snTpUtq3bw/AkiVL8Hq9dOzY0ef7/fLLL2zduvWEQC7+88MPcMUVcOAALFoELVu6XZGEi8qVK9O2bVvmzJlDz549C/bPmTOH6667zufrZGRk6O93FEhKSuLTTz89Yd8XX3xBu3btqFSpkktVhQA/jeYvZPPmzSYjI8M88cQTpnr16iYjI8NkZGSYffv2FRzTtGlTM2PGjILfjxkzxng8HjNjxgyzevVqc/PNN5sGDRqY7Ozsom4hIax79+6mZcuWZvHixWbx4sWmRYsWpkePHiccc/znv2/fPjNkyBCTlpZmNm3aZObNm2eSkpLMGWecoc8/AFauNKZePWPOP9+YTZsCdx89BRm5PvjgA1OpUiXzxhtvmDVr1pj77rvPnH766ebHH380xhgzYsQIk5ycXHD8Cy+8YGbOnGk2bNhgvv32WzNixAgDmOnTp7v1FqSM9u3bV/AzHTDjx483GRkZZvPmzcaYwp/9xo0bTbVq1cz9999v1qxZY9544w1TqVIl8+GHHx49xPUnEt3YAhbA+vfvb4BC27x58wqOAcxbb71V8Pu8vDzz+OOPm/r165uYmBhz8cUXm9WrVxd1eQlxv/zyi+nbt6+pUaOGqVGjhunbt2+hx8+P//wPHDhgunXrZurWrWsqVapkzjrrLNO/f3+zZcuW4Bcf4ebNM6ZGDWMSEozZuTOw91IAi2wpKSmmcePGpnLlyuaiiy4yCxYsKPha//79TZcuXQp+P3bsWHPOOeeYKlWqmN/97nemU6dOZtasWS5ULeV1dEqRk7f+/fsbYwp/9sYYM3/+fNOmTRtTuXJl06RJE/Pqq68e/2XXw5Abm2OM8UtDmj8uIiKBNXu2XVC7c2eYMQOqVw/s/bKzs/F4PHi9XmrWrBnYm4lIuIrKkfghMw2FiATW9Olw/fV23NennwY+fImISPEUwESiwHvvQa9etvXrX/+CmBi3KxIRiW4KYCIR7rXXoF8/6N/fBrFofuhIRCRUKICJRLAXX4SBA+Guu+D116FCBbcrEhERUAATiVjjx9vlhYYNgwkT4DT9bRcRCRn6J1kkAr34IgwZAiNHwpgxEMWrfYiIhCQFMJEI8/LLx1q+nnnGnfCVkpJCfHw8CQkJwb+5iEgY0DxgIhEkJcUupv3ggzBunPstX5oHTER8EJVt9GoBE4kQkyfb8HX//aERvkREpHgKYCIR4L33YNAguPtueP55hS8RkVCnACYS5j75BG65BW691Q6+V/gSEQl9CmAiYezLL+Gmm6BnTzvPl6aaEBEJD/rnWiRMLVkC110Hl1xiuyA1yaqISPhQABMJQ6tWwZVXQps2MGOG1nYUEQk3CmAiYeb776FbN2jSBP79b6hWze2KRESktBTARMLI9u1w+eVQqxZ8/jl4PG5XJCIiZVHR7QJExDfZ2XDVVXD4MCxYAHXrul2RiIiUlQKYSBg4dAhuuAE2bYKvvoKzznK7IhERKQ8FMJEQl5dn5/latAi++AIuvNDtikREpLwUwERC3NCh8MEH8M9/QpcublcjIiL+oEH4IiFswgQYP96+/vnPblfju5SUFOLj40lISHC7FBGRkOQYY/xxHb9cRESO+eQTuP56eOABeO45t6spm+zsbDweD16vl5o1a7pdjoiEpqhcQE0tYCIhaMUKuPlmu8TQuHFuVyMiIv6mACYSYjZvhh497GD7d9/V+o4iIpFI/7SLhBCvF66+GqpUsV2QmuVeRCQy6SlIkRBx5AjceCNs2wZpaVCvntsViYhIoCiAiYSIIUNg3jy7xFDz5m5XIyIigaQAJhIC3njDTjXxyivQtavb1YiISKBpDJiIy77+Gu68EwYOtK8iIhL5FMBEXLRli13jMSnJtoCJiEh0UAATccn+/XDddVC1Knz4IVSuHLh77dmzh+TkZDweDx6Ph+TkZPbu3Vvs8YcPH2b48OG0aNGC008/nYYNG9KvXz9+/vnnwBUpIhJFFMBEXGAM3HorfPednW6ibt3A3q9Pnz5kZmaSmppKamoqmZmZJCcnF3v8gQMHWLlyJY8++igrV65kxowZbNiwgWuvvTawhYqIRAktRSTigqefhkcfhenTbRdkIK1du5b4+HjS09Pp0KEDAOnp6SQlJbFu3TqaNm3q03WWLVtG+/bt2bx5M2eddZZP52gpIhHxgZYiEpHAmznThq8nngh8+AJYvHgxHo+nIHwBJCYm4vF4SEtL8/k6Xq8Xx3GoVatWscfk5OSQnZ19wiYiIoUpgIkE0erVkJwMf/4zPPJIcO6ZlZVFXFxcof1xcXFkZWX5dI3ffvuNESNG0KdPnxJbskaPHl0wzszj8dCoUaMy1y0iEskUwESCZPduuPZaOPdcmDKl/Gs8jho1CsdxStyWL18OgOMUbuE3xhS5/2SHDx+md+/e5OXl8corr5R47MiRI/F6vQXb1q1by/bmREQinCZiFQmCI0egVy/75OP8+XD66eW/5uDBg+ndu3eJxzRp0oRVq1axY8eOQl/btWsX9U6x3tHhw4e56aab2LRpE3Pnzj3lOK6YmBhiYmJOXbyISJRTABMJgkcegQUL4D//gcaN/XPN2NhYYmNjT3lcUlISXq+XpUuX0r59ewCWLFmC1+ulY8eOxZ53NHx99913zJs3jzp16vincBERURekSKB99BGMHQtjxsAllwT//s2bN6d79+4MGDCA9PR00tPTGTBgAD169DjhCchmzZoxc+ZMAI4cOcKf//xnli9fztSpU8nNzSUrK4usrCwOHToU/DchIhJhFMBEAui776B/f/u045Ah7tUxdepUWrRoQbdu3ejWrRstW7bk3XffPeGY9evX4/V6Afjpp5/45JNP+Omnn2jdujUNGjQo2Erz5KSIiBRN84CJBMj+/ZCYCIcOwbJlEI3TYGkeMBHxQVTOA6YxYCIBYAwMGgQbN8LSpdEZvkREpHgKYCIB8Oqr8N578I9/wAUXuF2NiIiEGo0BE/Gz9HS47z64+264+Wa3qxERkVCkMWAifrRrF1x0ETRqZOf7qlzZ7YrcpTFgIuKDqBwDphYwET/JzbUtXjk58K9/KXyJiEjxNAZMxE+eegrmzYM5c+CMM9yuRkREQpkCmIgfzJ0LTz4JTzwBXbu6XY2IiIQ6dUGKlNOOHdC3rw1eDz3kdjWhISUlhfj4eBISEtwuRUQkJGkQvkg55OXBFVfA6tWQmQn167tdUWjRIHwR8UFUDsJXF6RIOYweDV9+acd9KXyJiIiv1AUpUkYLF8Jjj8Ejj8Af/+h2NSIiEk7UBSlSBrt2QevWcO65tgWsotqSi6QuSBHxQVR2QaoFTKSU8vKgf3+7yPY//qHwJSIipacfHSKl9Nxz8NlndtN8XyIiUhZqARMphcWL7VQTw4dD9+5uVyMiIuFKY8BEfLR3rx33dcYZdp3HSpVcLigMaAyYiPggKseAqQtSxAfGwKBBNoQtWKDwJSIi5aMAJuKDKVNg2jT44ANo3NjtakREJNxpDJjIKWzYAHffDbfeCr16uV2NiIhEAo0BEynBoUPQsSPs2wcrVkD16m5XFF40BkxEfKAxYCJyoocfhlWr7NOPCl8iIuIv6oIUKcYXX9g5v559Ftq2dbua8JKSkkJ8fDwJCQlulyIiEpLUBSlShN27oUULu6Wmwmn6r0qZqAtSRHwQlV2Q+rEichJjYOBAO/5ryhSFLxER8T+NARM5ydtvw4wZMH06NGzodjUiIhKJ9H97keNs3GinnLjlFrjhBrerERGRSKUAJpIvNxf69YPYWHjpJberERGRSKYuSJF8Y8fa6SYWLACNFxcRkUBSC5gIdpLVxx+HESOgUye3qxERkUinaSgk6h04YOf5qlbNtoBVrux2RZFD01CIiA+ichoKdUFK1Bs+HH78EVauVPgSEZHgUACTqJaaChMn2q15c7erERGRaKEuSIlaR2e7b90aZs8GJyobwQNLXZAi4oOo/NdXg/AlKh2d7f7wYXjzTYUvEREJLnVBSlQ6frb7Bg3crkZERKKNWsAk6hyd7f7WWzXbfaCkpKQQHx9PQkKC26WIiIQkjQGTqJKbC5deCj/9BN98AzVquF1RZNMYMBHxQVQOAlEXpESVl16Cr76C+fMVvkRExD3qgpSosXYtPPQQ3H8/XHyx29WIiEg0UxekRIUjR6BjR9i3z064WrWq2xVFB3VBiogP1AUpEqnGjrXBKy1N4UtERNynLkiJeJmZ8MQTdqHt9u3drkZERERdkBLhcnKOha5ly7TWY7CpC1JEfKAuSJFI8+STdvC9wpeIiIQSBTCJWEuWwJgx8NRT0KqV29WIiIgcozFgEpEOHIB+/aBdOxg2zO1q3Ldnzx6Sk5PxeDx4PB6Sk5PZu3evz+cPHDgQx3F48cUXA1ajiEg0UQCTiPTww7Bli13zsaLaeenTpw+ZmZmkpqaSmppKZmYmycnJPp370UcfsWTJEho2bBjgKkVEood+NEnEWbAAXnwRxo+HZs3crsZ9a9euJTU1lfT0dDp06ADA66+/TlJSEuvXr6dp06bFnrtt2zYGDx7M559/ztVXXx2skkVEIp5awCSi7NtnF9m++GK49163qwkNixcvxuPxFIQvgMTERDweD2lpacWel5eXR3JyMkOHDuWCCy7w6V45OTlkZ2efsImISGEKYBJRhg6FnTvhrbfgNH13A5CVlUVcXFyh/XFxcWRlZRV73tixY6lYsSL33HOPz/caPXp0wTgzj8dDo0aNylSziEik048oiRhz5sDkyfDcc/D737tdTeCNGjUKx3FK3JYvXw6A4xSeZscYU+R+gBUrVvDSSy8xZcqUYo8pysiRI/F6vQXb1q1by/bmREQinMaASUTYtw9uvx26doWBA92uJjgGDx5M7969SzymSZMmrFq1ih07dhT62q5du6hXr16R5y1atIidO3dy1llnFezLzc1lyJAhvPjii/z4449FnhcTE0NMTIzvb0JEJEopgElEGDYMfvnFDsAvRYNNWIuNjSU2NvaUxyUlJeH1elm6dCnt85cFWLJkCV6vl44dOxZ5TnJyMpdddtkJ+6644gqSk5O59dZby1+8iEiUUwCTsDd3LkyaBCkp0KSJ29WEnubNm9O9e3cGDBjA5MmTAbjjjjvo0aPHCU9ANmvWjNGjR9OzZ0/q1KlDnTp1TrhOpUqVqF+/folPTYqIiG80BkzC2q+/wm23wSWXwKBBblcTuqZOnUqLFi3o1q0b3bp1o2XLlrz77rsnHLN+/Xq8Xq9LFYqIRBctxi1hbfBg+8TjqlVwzjluVyMn02LcIuKDKBk4ciJ1QUrYWrDAdju+9JLCl4iIhBe1gElY2r8fWraEM86A+fM151eoUguYiPhALWAi4eLhh+HnnyE1VeFLRETCjwKYhJ2vvoIJE+D55+G889yuRkREpPTUBSlh5cABaN0a6taFhQuhQgW3K5KSqAtSRHygLkiRUPfoo7B1K3z6qcKXiIiELwUwCRtpafDCCzBuHGguUBERCWfqgpSwcPAgtGkDtWrB11+r9SvUpaSkkJKSQm5uLhs2bFAXpIiUJCq7IBXAJCwMG2YH3mdkQPPmblcjvtIYMBHxQVQGMHVBSshbssQ+8fjMMwpfIiISGdQCJiHtt9/goovg9NNh8WKoqP8yhBW1gImID9QCJhJqnnwSvv8eVq5U+BIRkcihH2kSspYtg7FjbQi78EK3qxEREfEfdUFKSMrJgbZtISYG0tOhUiW3K5KyUBekiPhAXZAioeLpp2HDBli+XOFLREQij5YxlpCzciWMHg2PPAItW7pdjYiIiP+pC1JCyqFDkJAAjmPHgKn1K7ypC1JEfKAuSBG3PfssrFmj8CUiIpFNXZASMr75xk62OnIktG7tdjUiIiKBoy5ICQmHD0P79pCbawfeV67sdkXiD+qCFBEfqAtSxC1jxsDq1XbZIYUvERGJdOqCFNetXg1PPQXDh9u5vyT8paSkEB8fT0JCgtuliIiEJHVBiquOHIHERDh40E4/ERPjdkXiT+qCFBEfqAtSJNj+9jfIyLALbSt8iYhItFAXpLjmv/+FUaNg6FA7AF9ERCRaqAtSXHHkCHTsCPv22RawKlXcrkgCQV2QIuIDdUGKBMv48bBiBXz9tcKXiIhEH3VBStCtWwePPQYPPGAH4IuIiEQbdUFKUOXmQqdO8L//QWYmVK3qdkUSSOqCFBEfqAtSJNBefNFOtrpokcKXiIhEL3VBStBs2ACPPAL33Qd/+IPb1YiIiLhHXZASFLm50KUL7NhhF92uVs3tiiQY1AUpIj5QF6RIoLz8MqSlwYIFCl8iIiLqgpSA+/57eOghuPtu6NzZ7WpERETcpy5ICai8PLjkEti2DVatgtNPd7siCSZ1QYqID9QFKeJvKSn2icd58xS+oklKSgopKSnk5ua6XYqISEhSC5gEzMaN0KIF3HorTJzodjXiBrWAiYgPorIFTGPAJCDy8uC22yAuDsaMcbsaERGR0KIuSAmISZNg/nz48kuoXt3takREREKLWsDE7378EYYNg0GDoGtXt6sREREJPQpg4lfG2K7HOnVg3Di3qxEREQlN6oIUv3rtNZg7F774AmrUcLsaERGR0KQWMPGbzZvhwQdhwAC4/HK3qxEREQldCmDiF8bY4FWrFvztb25XIyIiEtrUBSl+8eabMGcOfPYZeDxuVyMiIhLa1AIm5bZ1KzzwgJ1wtXt3t6uRouzZs4fk5GQ8Hg8ej4fk5GT27t17yvPWrl3Ltddei8fjoUaNGiQmJrJly5bAFywiEuEUwKRcjIHbb7dzfY0f73Y1Upw+ffqQmZlJamoqqampZGZmkpycXOI5P/zwA506daJZs2bMnz+fb775hkcffZQqVaoEqWoRkcilpYikXCZPtvN9ffaZWr9C1dq1a4mPjyc9PZ0OHToAkJ6eTlJSEuvWraNp06ZFnte7d28qVarEu+++W+Z7aykiEfGBliISKY2NG2HIELjjDoWvULZ48WI8Hk9B+AJITEzE4/GQlpZW5Dl5eXnMmjWL888/nyuuuIK4uDg6dOjARx99VOK9cnJyyM7OPmETEZHCFMCkTPLy7JivunXhuefcrkZKkpWVRVxcXKH9cXFxZGVlFXnOzp07+fXXXxkzZgzdu3fniy++oGfPntxwww0sWLCg2HuNHj26YJyZx+OhUaNGfnsfIiKRRAFMymTCBFi4EN56SxOuumXUqFE4jlPitnz5cgAcp3ALvzGmyP1gW8AArrvuOu6//35at27NiBEj6NGjB5MmTSq2ppEjR+L1egu2rVu3+uGdiohEHk1DIaW2fj2MHAn33guXXOJ2NdFr8ODB9O7du8RjmjRpwqpVq9ixY0ehr+3atYt69eoVeV5sbCwVK1YkPj7+hP3Nmzfnq6++KvZ+MTExxMTE+FC9iEh0UwCTUjlyBPr3h0aN4Nln3a4musXGxhIbG3vK45KSkvB6vSxdupT27dsDsGTJErxeLx07dizynMqVK5OQkMD69etP2L9hwwYaN25c/uJFRKKcuiClVJ57DpYtg7ffhmrV3K5GfNG8eXO6d+/OgAEDSE9PJz09nQEDBtCjR48TnoBs1qwZM2fOLPj90KFDmTZtGq+//jrff/89EydO5NNPP+Wvf/2rG29DRCSiKICJz1avhsceg6FDISnJ7WqkNKZOnUqLFi3o1q0b3bp1o2XLloWml1i/fj1er7fg9z179mTSpEmMGzeOFi1a8Pe//53p06fTqVOnYJcvIhJxNA+Y+OTQIUhMtK8rVoCG+YgvNA+YiPggKucB0xgw8ckzz9gWsCVLFL5ERETKS12QckorVtgA9sgjcNFFblcjIiIS/tQFKSX67Tdo2xaqVIH0dKhUye2KJJyoC1JEfKAuSJGTPfwwfP+9bQVT+BIREfEPBTAp1pdfwvjx8PzzcOGFblcjIiISOdQFKUXaswdatICmTWHOHDhNowWlDNQFKSI+iMouSP1YlUKMgUGDYP9+O+GqwpeIiIh/6UerFDJ1KvzznzBpEpx5ptvVSDhKSUkhPj6ehIQEt0sREQlJ6oKUE2zeDC1bwrXXwkkTpYuUmrogRcQH6oKU6JabC/36Qa1aMHGi29WIiIhELj0FKQWeew4WLYJ588DjcbsaERGRyKUWMAEgIwMefdQutN2li9vViIiIRDaNARMOHrSz3cfE2Nnutdaj+IvGgImID6JyDJi6IIXhw2HTJjvbvcKXiIhI4CmARbnPP4eXX4aXXoL4eLerERERiQ7qgoxiu3fb2e5btoTPPtOEq+J/6oIUER9EZRekfuRGKWNgwAA4dAjeekvhS0REJJjUBRmlXnkFPvrIbg0bul2NiIhIdFG7RxT65hsYMgTuuguuu87takRERKKPxoBFmf37oV07qFwZliyBKlXcrkgimcaAiYgPonIMmLogo8y998KWLXbKCYUvERERd6gLMop88AG88YaddqJZM7erkUiWkpJCfHw8CQkJbpciIhKS1AUZJTZuhNatoUcPmDoVnKhs8JVgUxekiPggKn8iqQUsChw+DDffDHXrwqRJCl8iIiJu0xiwKPDII7ByJXz9NagRQkRExH0KYBFu1iwYN85u7du7XY2IiIiAxoBFtM2boU0b6NTJTriq2e4l2DQGTER8EJUDY/QjOULl5MCNN4LHA2+/rfAlIiISStQFGaEefNDOeP/11/C737ldjYiIiBxPASwCffABTJwIr75qZ70XERGR0KKOqQizbh3cfjv06QMDB7pdjYiIiBRFg/AjyP790KED5OXB0qVQvbrbFUm00yB8EfFBVA7CVxdkhDAGBg2CTZtg2TKFLxERkVCmABYhJk+G996zywzFx7tdjYiIiJREY8AiwOLFcM89cNddduyXiIiIhDYFsDCXlQV/+pOd5X78eLerEbFSUlKIj48nISHB7VJEREKSBuGHsUOH4I9/hI0bYcUKqF/f7YpETqRB+CLiAw3Cl/BhDAweDEuWwIIFCl8iIiLhRAEsTE2YAK+/Dm+9BUlJblcjIiIipaExYGEoNRUeeACGDoVbbnG7GhERESktBbAws3Yt9OoFV18No0e7XY2IiIiUhQJYGPnlF+jRAxo3tvN9VajgdkUiIiJSFhoDFiYOHbLTTezbB19+CTVquF2RiIiIlJUCWBg4+sTj4sUwdy40aeJ2RSIiIlIeCmBh4KWX7BOPU6bAH/7gdjUiIiJSXhoDFuJmz4YhQ2DYMOjf3+1qJFzt2bOH5ORkPB4PHo+H5ORk9u7dW+I5v/76K4MHD+bMM8+katWqNG/enFdffTU4BYuIRDgFsBC2fDncdBNccw08+6zb1Ug469OnD5mZmaSmppKamkpmZibJycklnnP//feTmprKe++9x9q1a7n//vu5++67+fjjj4NUtYhI5NJSRCFq40Y7werZZ9txX9WquV2RhKu1a9cSHx9Peno6HTp0ACA9PZ2kpCTWrVtH06ZNizzvwgsvpFevXjz66KMF+9q2bctVV13FU0895dO9tRSRiPggKpciUgtYCPrlF7jySqhZEz79VOFLymfx4sV4PJ6C8AWQmJiIx+MhLS2t2PM6derEJ598wrZt2zDGMG/ePDZs2MAVV1xR7Dk5OTlkZ2efsImISGEKYCFm3z646irYs8fOeF+3rtsVSbjLysoiLi6u0P64uDiysrKKPW/ChAnEx8dz5plnUrlyZbp3784rr7xCp06dij1n9OjRBePMPB4PjRo18st7EBGJNApgIeS33+D66+1s96mpcM45blckoWzUqFE4jlPitnz5cgAcp3ALvzGmyP1HTZgwgfT0dD755BNWrFjB888/z1//+lf+85//FHvOyJEj8Xq9BdvWrVvL/0ZFRCKQpqEIEUeOwM03Q1qaDV8XXeR2RRLqBg8eTO/evUs8pkmTJqxatYodO3YU+tquXbuoV69ekecdPHiQhx56iJkzZ3L11VcD0LJlSzIzM3nuuee47LLLijwvJiaGmJiYUr4TEZHoowAWAvLyYMAA+Pe/YeZM6NLF7YokHMTGxhIbG3vK45KSkvB6vSxdupT27dsDsGTJErxeLx07dizynMOHD3P48GFOO+3ERvIKFSqQl5dX/uJFRKKcuiBdZgw8+CC8/bbdevRwuyKJNM2bN6d79+4MGDCA9PR00tPTGTBgAD169DjhCchmzZoxc+ZMAGrWrEmXLl0YOnQo8+fPZ9OmTUyZMoV33nmHnj17uvVWREQihlrAXGQMPPoovPACTJwIffq4XZFEqqlTp3LPPffQrVs3AK699lomTpx4wjHr16/H6/UW/P6DDz5g5MiR9O3bl//97380btyYZ555hkGDBgW1dhGRSKR5wFxyNHw98wz87W+2FUwk0mgeMBHxgeYBk+BQ+BIREYluCmBBpvAlIiIiGgMWRMbAI4/YdR0VvkRERKKXAliQ5OXBfffByy/Dc8/BkCFuVyQiIiJuUQALgsOH4S9/galTYfJkuOMOtysSERERNymABdjBg3DTTfD55/D++9Crl9sViYiIiNsUwAIoK8uu7bhqFXzyCXTv7nZFIiIiEgoUwAJk1Sq45hrb/bhwIbRr53ZFIsGTkpJCSkoKubm5bpciIhKSNBFrAPz733Zh7XPPhU8/hTPPdLsiEXdoIlYR8YEmYpXyMcYuK3TttXDZZbBokcKXiIiIFKYA5ieHDsGgQfDAAzBsGEyfDtWru12ViIiIhCKNAfODrVvtk44rVsBbb8Ett7hdkYiIiISyoLWAvfMOZGQE627BM3s2tGkDP/8MX32l8CUiIiKnFpQAlpsLr74KnTrBRx8F446B9+uvtsvx6qshMRFWroT27d2uSkRERMJBUAJYhQrw5Zdw1VVwww0wdqwdsB6uvv4aWrWCd9+FSZPsk4516rhdlYiIiISLoHVBVqsG06bBww/DiBF2aZ6DB4N1d/84eBCGD4fOnaF+ffjmGxg4EJyofIBWREREyiqoT0Gedho89RS8955dlqddu/AYF2YMfPghNGsGL74Io0fbyVXPPdftykRERCQcuTINRd++sHw5VKoEHTrYQBOqE2avXg1du8KNN0LLlvDtt7YVrEIFtysTERGRcOXaPGAXXghLlsCQIbZbslOn0GoN27IF/vpXaN0atm+Hzz6zY73OO8/tykRERCTcuToRa0zMse687GzbJTlgAGze7F5N330Ht90G55xjx6yNG2fXddRC2iIiIuIvITETfqdOkJkJzz9vp6k47zy44w7YtCk49zfGhsBevew4r9mzYcwYGwSHDIHKlYNTh4iIiESHkAhgYMeD3XefDV3PPGOD2Dnn2KkrZsyAw4f9ez9jbMvWQw/Z+3TpYp9qnDjR1jBkiJYSEimrlJQU4uPjSUhIcLsUEZGQ5Bj/TMjl91m99u+3T0r+/e92rFitWjaMXXmlnfD03HPtU5WlsW2bbelasADmzYMNG6B2bfjTn6BPHxvCNKWEiP9kZ2fj8Xjwer3UrFnT7XJEJDRF5U/ekA1gx1u92i5u/fHHtqsSoGZNaNsWmja1c3LVq2f35ebCkSO2xWz7dtuatXGj3bZts+c2awYXXwzXXQeXXaYuRpFAUQATER8ogJVD0Oa1/9//7KLXy5bZqSw2boQdO2DXrsJTWdSrB2efDb//vX1t3doGr7i4YFUrEt0UwETEBwpg5eD6wkJ5eXDggB1LVrGi7Z5Ud6KIuxTARMQHUfnTuqLbBfjLaadp0LyIiIiEh5B5ClJEREQkWiiAiYiIiASZApiIiIhIkCmAiYiIiASZv56CFBEpxHGcmoAX8Bhjst2uR0QkVCiAiUjAOI7jADWAfUb/2IiIFFAAExEREQkyjQETERERCTIFMBEREZEgUwATERERCTIFMBEREZEgUwATERERCTIFMBEREZEgUwATERERCbL/B8fAirAvtucVAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "show(LatexExpr(r'r_{\\rm ph}^{*} = ' + '{} m'.format(n(rph_s(a0)))))\n", "plot(lambda r: Rs(a0, r), (-1, 1), axes_labels=[r'$r/m$', r'$\\mathcal{R}(r)$'])" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\rm ph}^{+} = 1.38628052846298 m\n", "\\end{math}" ], "text/plain": [ "r_{\\rm ph}^{+} = 1.38628052846298 m" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "show(LatexExpr(r'r_{\\rm ph}^{+} = ' + '{} m'.format(n(rph_p(a0)))))\n", "plot(lambda r: Rp(a0, r), (-1/2, 2), axes_labels=[r'$r/m$', r'$\\mathcal{R}(r)$'])" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\rm ph}^{-} = 3.95534731767268 m\n", "\\end{math}" ], "text/plain": [ "r_{\\rm ph}^{-} = 3.95534731767268 m" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "show(LatexExpr(r'r_{\\rm ph}^{-} = ' + '{} m'.format(n(rph_m(a0)))))\n", "plot(lambda r: Rm(a0, r), (-1/2, 5), axes_labels=[r'$r/m$', r'$\\mathcal{R}(r)$'])" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( a, {\\ell}, q, r \\right) \\ {\\mapsto} \\ 2 \\, a^{2} - 2 \\, {\\ell}^{2} + 12 \\, r^{2} - 2 \\, q\n", "\\end{math}" ], "text/plain": [ "(a, l, q, r) |--> 2*a^2 - 2*l^2 + 12*r^2 - 2*q" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R2(a, l, q, r) = diff(R(a, l, q, r), r, 2).simplify_full()\n", "R2" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( a, r \\right) \\ {\\mapsto} \\ \\frac{8 \\, {\\left(r^{3} - a^{2} - 3 \\, r^{2} + 3 \\, r\\right)} r}{{\\left(r - 1\\right)}^{2}}\n", "\\end{math}" ], "text/plain": [ "(a, r) |--> 8*(r^3 - a^2 - 3*r^2 + 3*r)*r/(r - 1)^2" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R2o(a, r) = R2(a, lsph(a, r), qsph(a, r), r).simplify_full().factor()\n", "R2o" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Computation of $\\frac{\\mathrm{d}q}{\\mathrm{d}r_0}$" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{4 \\, {\\left(r^{3} - a^{2} - 3 \\, r^{2} + 3 \\, r\\right)} {\\left(r - 3\\right)} r^{2}}{a^{2} {\\left(r - 1\\right)}^{3}}\n", "\\end{math}" ], "text/plain": [ "-4*(r^3 - a^2 - 3*r^2 + 3*r)*(r - 3)*r^2/(a^2*(r - 1)^3)" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dqdr(a, r) = diff(qsph(a, r), r).simplify_full().factor()\n", "dqdr(a, r)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us check that marginally stable orbits correspond to an extremum (actually a maximum) of $q(r_0)$:" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\n", "\\end{math}" ], "text/plain": [ "0" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dqdr(a, rph_ms(a)).simplify_full()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The maximum at $r_0 = 3 m$ does not depend on $a$:" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}27\n", "\\end{math}" ], "text/plain": [ "27" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qsph(a, 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "while for $r_0 = r_{\\rm ph}^{ms}$, we have" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{3 \\, {\\left(a^{4} + 2 \\, a^{2} + {\\left(4 \\, a^{2} - 3\\right)} {\\left(-a^{2} + 1\\right)}^{\\frac{2}{3}} - 6 \\, {\\left(a^{2} - 1\\right)} {\\left(-a^{2} + 1\\right)}^{\\frac{1}{3}} - 3\\right)}}{{\\left(-a^{2} + 1\\right)}^{\\frac{2}{3}} a^{2}}\n", "\\end{math}" ], "text/plain": [ "3*(a^4 + 2*a^2 + (4*a^2 - 3)*(-a^2 + 1)^(2/3) - 6*(a^2 - 1)*(-a^2 + 1)^(1/3) - 3)/((-a^2 + 1)^(2/3)*a^2)" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qms = qsph(a, rph_ms(a)).simplify_full()\n", "qms" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{3 \\, {\\left({\\left(-a^{2} + 1\\right)}^{\\frac{1}{3}} a^{2} - 4 \\, a^{2} - 6 \\, {\\left(-a^{2} + 1\\right)}^{\\frac{2}{3}} + 3 \\, {\\left(-a^{2} + 1\\right)}^{\\frac{1}{3}} + 3\\right)}}{a^{2}}\n", "\\end{math}" ], "text/plain": [ "-3*((-a^2 + 1)^(1/3)*a^2 - 4*a^2 - 6*(-a^2 + 1)^(2/3) + 3*(-a^2 + 1)^(1/3) + 3)/a^2" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "q1 = SR(qms._sympy_().simplify())\n", "q1" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\n", "\\end{math}" ], "text/plain": [ "0" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(qms - q1).simplify_full()" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [], "source": [ "qms = q1" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{38}{729} \\, a^{10} + \\frac{4}{81} \\, a^{8} + \\frac{1}{27} \\, a^{6}\n", "\\end{math}" ], "text/plain": [ "38/729*a^10 + 4/81*a^8 + 1/27*a^6" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "taylor(qms, a, 0, 10)" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}3\n", "\\end{math}" ], "text/plain": [ "3" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qms.subs({a: 1})" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(qms, (a, 0, 1), axes_labels=[r'$a/m$', r'$q_{\\rm ms}/m^2$'],\n", " thickness=2, frame=True, gridlines=True)" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{2 \\, {\\left(r^{3} - a^{2} - 3 \\, r^{2} + 3 \\, r\\right)}}{a {\\left(r - 1\\right)}^{2}}\n", "\\end{math}" ], "text/plain": [ "-2*(r^3 - a^2 - 3*r^2 + 3*r)/(a*(r - 1)^2)" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dldr(a, r) = diff(lsph(a, r), r).simplify_full().factor()\n", "dldr(a, r)" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\n", "\\end{math}" ], "text/plain": [ "0" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dldr(a, rph_ms(a)).simplify_full()" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{3 \\, a^{2} - {\\left(a^{2} - 3\\right)} {\\left(-a^{2} + 1\\right)}^{\\frac{1}{3}} - 3}{{\\left(-a^{2} + 1\\right)}^{\\frac{1}{3}} a}\n", "\\end{math}" ], "text/plain": [ "(3*a^2 - (a^2 - 3)*(-a^2 + 1)^(1/3) - 3)/((-a^2 + 1)^(1/3)*a)" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lms = lsph(a, rph_ms(a)).simplify_full()\n", "lms" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{4}{27} \\, a^{5} + \\frac{1}{3} \\, a^{3} + a\n", "\\end{math}" ], "text/plain": [ "4/27*a^5 + 1/3*a^3 + a" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "taylor(lms, a, 0, 6)" ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}2\n", "\\end{math}" ], "text/plain": [ "2" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lms.limit(a=1)" ] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(lms, (a, 0, 1), color='red', thickness=2,\n", " axes_labels=[r'$a/m$', r'$\\ell_{\\rm ms}/m$'],\n", " frame=True, gridlines=True) \\\n", "+ plot(a, (a, 0, 1), color='black', linestyle='--')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot of spherical orbits in the meriodinal plane" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Choice of a radial function $\\hat r$" ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r \\ {\\mapsto}\\ \\frac{1}{2} \\, r + \\frac{1}{2} \\, \\sqrt{r^{2} + 4}\n", "\\end{math}" ], "text/plain": [ "r |--> 1/2*r + 1/2*sqrt(r^2 + 4)" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R2(r) = (r + sqrt(r^2 + 4))/2\n", "R2" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r \\ {\\mapsto}\\ \\frac{1}{2} \\, r + \\frac{1}{2} \\, {\\left(r^{4} + 16\\right)}^{\\frac{1}{4}}\n", "\\end{math}" ], "text/plain": [ "r |--> 1/2*r + 1/2*(r^4 + 16)^(1/4)" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R4(r) = (r + (r^4 + 16)^(1/4))/2\n", "R4" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(2.41421356237309, 2.18920711500272\\right)\n", "\\end{math}" ], "text/plain": [ "(2.41421356237309, 2.18920711500272)" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n(R2(2)), n(R4(2))" ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(6.16227766016838, 6.00921669843456\\right)\n", "\\end{math}" ], "text/plain": [ "(6.16227766016838, 6.00921669843456)" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n(R2(6)), n(R4(6))" ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "g = plot(R4, (-8, 8), color='green',\n", " axes_labels=[r'$r/m$', r'$\\hat{r}/m$'])\n", "show(g, aspect_ratio=1, frame=True, gridlines=True)" ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "image/png": 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