{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# SageMath para físicos\n", "***\n", "Rogério T. C." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Aula II.1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## O problema de Kepler" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Na mecânica clássica, o problema de Kepler é um caso especial do problema de dois corpos, no qual os dois corpos interagem por uma força central que varia em intensidade com o inverso do quadrado da distância $\\mathbf{r}$ entre eles. O problema consiste em encontrar a posição dos dois corpos ao longo do tempo, dadas suas massas, posições e velocidades. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos considerar o caso em que a posição de uma das massas coincide com a do centro de massa (como no sistema sol+planeta). Por se tratar um problema de força central, o movimento é confinado em um plano. Isso nos permite descrevê-lo em coordenadas polares." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "O potencial e a energia cinética são dados respectivamente por\n", "$$V(r) = -\\frac{GMm}{r} \\quad \\text{e} \\quad T = \\frac{1}{2}m\\left(\\dot{r}^2+r^2\\dot{\\phi}^2\\right).$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%display latex\n", "reset()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Variáveis dinâmicas" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "var('t m G M', domain='positive')\n", "phi(t) = function('phi')(t)\n", "r(t) = function('r')(t)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "assume(r(t)>0)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[t > 0, m > 0, G > 0, M > 0, r\\left(t\\right) > 0\\right]$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[t > 0, m > 0, G > 0, M > 0, r\\left(t\\right) > 0\\right]\n", "\\end{math}" ], "text/plain": [ "[t > 0, m > 0, G > 0, M > 0, r(t) > 0]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "assumptions()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vetor posição" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\cos\\left(\\phi\\left(t\\right)\\right) r\\left(t\\right),\\,r\\left(t\\right) \\sin\\left(\\phi\\left(t\\right)\\right)\\right)$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\cos\\left(\\phi\\left(t\\right)\\right) r\\left(t\\right),\\,r\\left(t\\right) \\sin\\left(\\phi\\left(t\\right)\\right)\\right)\n", "\\end{math}" ], "text/plain": [ "(cos(phi(t))*r(t), r(t)*sin(phi(t)))" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R = vector([r(t)*cos(phi(t)),r(t)*sin(phi(t))]);R" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}r\\left(t\\right)$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r\\left(t\\right)\n", "\\end{math}" ], "text/plain": [ "r(t)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R.norm().simplify_trig().canonicalize_radical()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Potencial" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{G M m}{r\\left(t\\right)}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{G M m}{r\\left(t\\right)}\n", "\\end{math}" ], "text/plain": [ "-G*M*m/r(t)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "V = -G*M*m/(r(t));V" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Energia cinética" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, {\\left(\\cos\\left(\\phi\\left(t\\right)\\right) r\\left(t\\right) \\frac{\\partial}{\\partial t}\\phi\\left(t\\right) + \\sin\\left(\\phi\\left(t\\right)\\right) \\frac{\\partial}{\\partial t}r\\left(t\\right)\\right)}^{2} m + \\frac{1}{2} \\, {\\left(r\\left(t\\right) \\sin\\left(\\phi\\left(t\\right)\\right) \\frac{\\partial}{\\partial t}\\phi\\left(t\\right) - \\cos\\left(\\phi\\left(t\\right)\\right) \\frac{\\partial}{\\partial t}r\\left(t\\right)\\right)}^{2} m$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, {\\left(\\cos\\left(\\phi\\left(t\\right)\\right) r\\left(t\\right) \\frac{\\partial}{\\partial t}\\phi\\left(t\\right) + \\sin\\left(\\phi\\left(t\\right)\\right) \\frac{\\partial}{\\partial t}r\\left(t\\right)\\right)}^{2} m + \\frac{1}{2} \\, {\\left(r\\left(t\\right) \\sin\\left(\\phi\\left(t\\right)\\right) \\frac{\\partial}{\\partial t}\\phi\\left(t\\right) - \\cos\\left(\\phi\\left(t\\right)\\right) \\frac{\\partial}{\\partial t}r\\left(t\\right)\\right)}^{2} m\n", "\\end{math}" ], "text/plain": [ "1/2*(cos(phi(t))*r(t)*diff(phi(t), t) + sin(phi(t))*diff(r(t), t))^2*m + 1/2*(r(t)*sin(phi(t))*diff(phi(t), t) - cos(phi(t))*diff(r(t), t))^2*m" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T = m/2*diff(R,t)*diff(R,t);T" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, m r\\left(t\\right)^{2} \\frac{\\partial}{\\partial t}\\phi\\left(t\\right)^{2} + \\frac{1}{2} \\, m \\frac{\\partial}{\\partial t}r\\left(t\\right)^{2}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, m r\\left(t\\right)^{2} \\frac{\\partial}{\\partial t}\\phi\\left(t\\right)^{2} + \\frac{1}{2} \\, m \\frac{\\partial}{\\partial t}r\\left(t\\right)^{2}\n", "\\end{math}" ], "text/plain": [ "1/2*m*r(t)^2*diff(phi(t), t)^2 + 1/2*m*diff(r(t), t)^2" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T = T.simplify_trig();T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lagrangiana" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, m r\\left(t\\right)^{2} \\frac{\\partial}{\\partial t}\\phi\\left(t\\right)^{2} + \\frac{1}{2} \\, m \\frac{\\partial}{\\partial t}r\\left(t\\right)^{2} + \\frac{G M m}{r\\left(t\\right)}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, m r\\left(t\\right)^{2} \\frac{\\partial}{\\partial t}\\phi\\left(t\\right)^{2} + \\frac{1}{2} \\, m \\frac{\\partial}{\\partial t}r\\left(t\\right)^{2} + \\frac{G M m}{r\\left(t\\right)}\n", "\\end{math}" ], "text/plain": [ "1/2*m*r(t)^2*diff(phi(t), t)^2 + 1/2*m*diff(r(t), t)^2 + G*M*m/r(t)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "L = T-V;L" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Equações de Euler-Lagrange\n", "$$ \\displaystyle {\\frac {\\partial L}{\\partial q_{i}}}(t,{\\boldsymbol {q}}(t),{\\dot {\\boldsymbol {q}}}(t))-{\\frac {\\mathrm {d} }{\\mathrm {d} t}}{\\frac {\\partial L}{\\partial {\\dot {q}}_{i}}}(t,{\\boldsymbol {q}}(t),{\\dot {\\boldsymbol {q}}}(t))=0$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\frac {\\partial L}{\\partial q_{i}}(t,{\\boldsymbol {q}}(t),{\\dot {\\boldsymbol {q}}}(t))=0 \\Rightarrow {\\frac {\\partial L}{\\partial {\\dot {q}}_{i}}}(t,{\\boldsymbol {q}}(t),{\\dot {\\boldsymbol {q}}}(t))=C$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Usaremos as quantidades conservadas no lugar das equações de Euler-Lagrange" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Variáveis simbólicas para energia e momento angular" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ell}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ell}\n", "\\end{math}" ], "text/plain": [ "l" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('E', domain='real')\n", "var('l', latex_name=r'\\ell', domain='positive')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Energia conservada" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}E = \\frac{1}{2} \\, m r\\left(t\\right)^{2} \\frac{\\partial}{\\partial t}\\phi\\left(t\\right)^{2} + \\frac{1}{2} \\, m \\frac{\\partial}{\\partial t}r\\left(t\\right)^{2} - \\frac{G M m}{r\\left(t\\right)}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}E = \\frac{1}{2} \\, m r\\left(t\\right)^{2} \\frac{\\partial}{\\partial t}\\phi\\left(t\\right)^{2} + \\frac{1}{2} \\, m \\frac{\\partial}{\\partial t}r\\left(t\\right)^{2} - \\frac{G M m}{r\\left(t\\right)}\n", "\\end{math}" ], "text/plain": [ "E == 1/2*m*r(t)^2*diff(phi(t), t)^2 + 1/2*m*diff(r(t), t)^2 - G*M*m/r(t)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq_E = E == T+V;eq_E" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "def formal_derivative(f, x):\n", " r\"\"\"\n", " The formal derivative of `f` with respect to the symbolic function `x`.\n", " \"\"\"\n", " tempX = SR.symbol()\n", " return f.subs({x: tempX}).diff(tempX).subs({tempX: x})" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\n", "\\end{math}" ], "text/plain": [ "0" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "formal_derivative(L,phi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Momento angular conservado" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}m r\\left(t\\right)^{2} \\frac{\\partial}{\\partial t}\\phi\\left(t\\right) = {\\ell}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}m r\\left(t\\right)^{2} \\frac{\\partial}{\\partial t}\\phi\\left(t\\right) = {\\ell}\n", "\\end{math}" ], "text/plain": [ "m*r(t)^2*diff(phi(t), t) == l" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq_phi = formal_derivative(L,diff(phi,t)) ==l;eq_phi" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial t}\\phi\\left(t\\right) = \\frac{{\\ell}}{m r\\left(t\\right)^{2}}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial t}\\phi\\left(t\\right) = \\frac{{\\ell}}{m r\\left(t\\right)^{2}}\n", "\\end{math}" ], "text/plain": [ "diff(phi(t), t) == l/(m*r(t)^2)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq_phi1 = solve(eq_phi,diff(phi(t),t))[0];eq_phi1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Substituindo o momento angular na energia conservada" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}E = \\frac{1}{2} \\, m \\frac{\\partial}{\\partial t}r\\left(t\\right)^{2} - \\frac{G M m}{r\\left(t\\right)} + \\frac{{\\ell}^{2}}{2 \\, m r\\left(t\\right)^{2}}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}E = \\frac{1}{2} \\, m \\frac{\\partial}{\\partial t}r\\left(t\\right)^{2} - \\frac{G M m}{r\\left(t\\right)} + \\frac{{\\ell}^{2}}{2 \\, m r\\left(t\\right)^{2}}\n", "\\end{math}" ], "text/plain": [ "E == 1/2*m*diff(r(t), t)^2 - G*M*m/r(t) + 1/2*l^2/(m*r(t)^2)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq_E1 = eq_E.subs(eq_phi1);eq_E1" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial t}r\\left(t\\right) = \\frac{\\sqrt{2 \\, G M m^{2} r\\left(t\\right) + 2 \\, E m r\\left(t\\right)^{2} - {\\ell}^{2}}}{m r\\left(t\\right)}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial t}r\\left(t\\right) = \\frac{\\sqrt{2 \\, G M m^{2} r\\left(t\\right) + 2 \\, E m r\\left(t\\right)^{2} - {\\ell}^{2}}}{m r\\left(t\\right)}\n", "\\end{math}" ], "text/plain": [ "diff(r(t), t) == sqrt(2*G*M*m^2*r(t) + 2*E*m*r(t)^2 - l^2)/(m*r(t))" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq_r = solve(eq_E1,diff(r(t),t))[1];eq_r" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pela regra da cadeia,\n", "$$\\frac{d\\phi}{dr}=\\frac{\\frac{d\\phi}{dt}}{\\frac{dr}{dt}}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\displaystyle \\phi = \\int \\frac{d\\phi}{dt}\\left(\\frac{dr}{dt}\\right)^{-1}dr$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Usaremos a variável simbólica $\\varphi$ no lugar da função $\\phi$ e uma variável simbólica para a função $r(t)$." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "vr = var('vr', latex_name='r', domain='positive')\n", "vp = var('vp', latex_name=r'\\varphi')" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{r}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{r}\n", "\\end{math}" ], "text/plain": [ "vr" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vr" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\int \\frac{d\\phi}{dt}\\left(\\frac{dr}{dt}\\right)^{-1}dr$$" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\int \\frac{{\\ell}}{\\sqrt{2 \\, G M m^{2} {r} + 2 \\, E m {r}^{2} - {\\ell}^{2}} {r}}\\,{d {r}}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\int \\frac{{\\ell}}{\\sqrt{2 \\, G M m^{2} {r} + 2 \\, E m {r}^{2} - {\\ell}^{2}} {r}}\\,{d {r}}\n", "\\end{math}" ], "text/plain": [ "integrate(l/(sqrt(2*G*M*m^2*vr + 2*E*m*vr^2 - l^2)*vr), vr)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "phrt = integral((eq_phi1.rhs()/eq_r.rhs()).subs({r(t):vr}),vr, hold=True);phrt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculando a integral" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\arcsin\\left(-\\frac{G M m^{2}}{\\sqrt{G^{2} M^{2} m^{4} + 2 \\, E {\\ell}^{2} m}} + \\frac{{\\ell}^{2}}{\\sqrt{G^{2} M^{2} m^{4} + 2 \\, E {\\ell}^{2} m} {r}}\\right)$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\arcsin\\left(-\\frac{G M m^{2}}{\\sqrt{G^{2} M^{2} m^{4} + 2 \\, E {\\ell}^{2} m}} + \\frac{{\\ell}^{2}}{\\sqrt{G^{2} M^{2} m^{4} + 2 \\, E {\\ell}^{2} m} {r}}\\right)\n", "\\end{math}" ], "text/plain": [ "-arcsin(-G*M*m^2/sqrt(G^2*M^2*m^4 + 2*E*l^2*m) + l^2/(sqrt(G^2*M^2*m^4 + 2*E*l^2*m)*vr))" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "assume(G^2*M^2*m^3+2*E*l^2>0)\n", "phrt.unhold()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Solução em termos de $\\varphi$" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\varphi} = -\\arcsin\\left(-\\frac{G M m^{2}}{\\sqrt{G^{2} M^{2} m^{4} + 2 \\, E {\\ell}^{2} m}} + \\frac{{\\ell}^{2}}{\\sqrt{G^{2} M^{2} m^{4} + 2 \\, E {\\ell}^{2} m} {r}}\\right)$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\varphi} = -\\arcsin\\left(-\\frac{G M m^{2}}{\\sqrt{G^{2} M^{2} m^{4} + 2 \\, E {\\ell}^{2} m}} + \\frac{{\\ell}^{2}}{\\sqrt{G^{2} M^{2} m^{4} + 2 \\, E {\\ell}^{2} m} {r}}\\right)\n", "\\end{math}" ], "text/plain": [ "vp == -arcsin(-G*M*m^2/sqrt(G^2*M^2*m^4 + 2*E*l^2*m) + l^2/(sqrt(G^2*M^2*m^4 + 2*E*l^2*m)*vr))" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq_vp = vp ==phrt.unhold();eq_vp" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sin\\left({\\varphi}\\right) = \\sin\\left(-\\arcsin\\left(-\\frac{G M m^{2}}{\\sqrt{G^{2} M^{2} m^{4} + 2 \\, E {\\ell}^{2} m}} + \\frac{{\\ell}^{2}}{\\sqrt{G^{2} M^{2} m^{4} + 2 \\, E {\\ell}^{2} m} {r}}\\right)\\right)$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sin\\left({\\varphi}\\right) = \\sin\\left(-\\arcsin\\left(-\\frac{G M m^{2}}{\\sqrt{G^{2} M^{2} m^{4} + 2 \\, E {\\ell}^{2} m}} + \\frac{{\\ell}^{2}}{\\sqrt{G^{2} M^{2} m^{4} + 2 \\, E {\\ell}^{2} m} {r}}\\right)\\right)\n", "\\end{math}" ], "text/plain": [ "sin(vp) == sin(-arcsin(-G*M*m^2/sqrt(G^2*M^2*m^4 + 2*E*l^2*m) + l^2/(sqrt(G^2*M^2*m^4 + 2*E*l^2*m)*vr)))" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol_vp = sin(eq_vp.lhs()) == sin(eq_vp.rhs());sol_vp" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sin\\left({\\varphi}\\right) = \\frac{G M m^{2} {r} - {\\ell}^{2}}{\\sqrt{G^{2} M^{2} m^{4} + 2 \\, E {\\ell}^{2} m} {r}}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sin\\left({\\varphi}\\right) = \\frac{G M m^{2} {r} - {\\ell}^{2}}{\\sqrt{G^{2} M^{2} m^{4} + 2 \\, E {\\ell}^{2} m} {r}}\n", "\\end{math}" ], "text/plain": [ "sin(vp) == (G*M*m^2*vr - l^2)/(sqrt(G^2*M^2*m^4 + 2*E*l^2*m)*vr)" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol_vp = sol_vp.trig_simplify();sol_vp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Isolando o $r$" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{r} = \\frac{{\\ell}^{2}}{G M m^{2} - \\sqrt{G^{2} M^{2} m^{4} + 2 \\, E {\\ell}^{2} m} \\sin\\left({\\varphi}\\right)}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{r} = \\frac{{\\ell}^{2}}{G M m^{2} - \\sqrt{G^{2} M^{2} m^{4} + 2 \\, E {\\ell}^{2} m} \\sin\\left({\\varphi}\\right)}\n", "\\end{math}" ], "text/plain": [ "vr == l^2/(G*M*m^2 - sqrt(G^2*M^2*m^4 + 2*E*l^2*m)*sin(vp))" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol_r = solve(sol_vp,vr)[0];sol_r" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Solução de livro texto em termos da excentricidade $\\epsilon$ da órbita" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\epsilon$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\epsilon\n", "\\end{math}" ], "text/plain": [ "epsilon" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ep = var('epsilon', domain='real');ep" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\epsilon = \\sqrt{\\frac{2 \\, E {\\ell}^{2}}{G^{2} M^{2} m^{3}} + 1}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\epsilon = \\sqrt{\\frac{2 \\, E {\\ell}^{2}}{G^{2} M^{2} m^{3}} + 1}\n", "\\end{math}" ], "text/plain": [ "epsilon == sqrt(2*E*l^2/(G^2*M^2*m^3) + 1)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq_ep = ep == sqrt(1+2*l^2*E/(m*(G*m*M)^2));eq_ep" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Para incluir a excentricidade na solução, isolamos $E$ na expressão da excentricidade" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}E = \\frac{{\\left(G^{2} M^{2} \\epsilon^{2} - G^{2} M^{2}\\right)} m^{3}}{2 \\, {\\ell}^{2}}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}E = \\frac{{\\left(G^{2} M^{2} \\epsilon^{2} - G^{2} M^{2}\\right)} m^{3}}{2 \\, {\\ell}^{2}}\n", "\\end{math}" ], "text/plain": [ "E == 1/2*(G^2*M^2*epsilon^2 - G^2*M^2)*m^3/l^2" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "assume(ep>0)\n", "sub_E = solve(eq_ep,E)[0]\n", "forget(ep>0)\n", "sub_E" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "e substituimos na solução" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{r} = -\\frac{{\\ell}^{2}}{{\\left(\\epsilon \\sin\\left({\\varphi}\\right) - 1\\right)} G M m^{2}}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{r} = -\\frac{{\\ell}^{2}}{{\\left(\\epsilon \\sin\\left({\\varphi}\\right) - 1\\right)} G M m^{2}}\n", "\\end{math}" ], "text/plain": [ "vr == -l^2/((epsilon*sin(vp) - 1)*G*M*m^2)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol_r = sol_r.subs(sub_E).canonicalize_radical().factor();sol_r" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Faremos $\\varphi \\to \\varphi - \\pi/2$ pra deixar com a cara mais usual nos livros texto." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{r} = \\frac{{\\ell}^{2}}{{\\left(\\epsilon \\cos\\left({\\varphi}\\right) + 1\\right)} G M m^{2}}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{r} = \\frac{{\\ell}^{2}}{{\\left(\\epsilon \\cos\\left({\\varphi}\\right) + 1\\right)} G M m^{2}}\n", "\\end{math}" ], "text/plain": [ "vr == l^2/((epsilon*cos(vp) + 1)*G*M*m^2)" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol_r = sol_r.subs(vp=vp-pi/2).expand_trig();sol_r" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Deixando os dois lados sem dimensão" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{G M m^{2} {r}}{{\\ell}^{2}} = \\frac{1}{\\epsilon \\cos\\left({\\varphi}\\right) + 1}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{G M m^{2} {r}}{{\\ell}^{2}} = \\frac{1}{\\epsilon \\cos\\left({\\varphi}\\right) + 1}\n", "\\end{math}" ], "text/plain": [ "G*M*m^2*vr/l^2 == (1/(epsilon*cos(vp) + 1))" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol_r = sol_r*G*M*m^2/l^2;sol_r" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vejamos os gráficos das órbitas em coordenadas polares (polar=True)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "orbita_0 = plot(sol_r.rhs().subs(ep==0),(vp,0,2*pi),polar=True,aspect_ratio=1, color='red', axes=False, frame=True, title=r'Órbita circular ($\\epsilon=0$)')" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "orbita_0" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "centro = circle((0,0),.01, fill=True, color='black', axes=False)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "centro+orbita_0" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "scrolled": true }, "outputs": [], "source": [ "orbita_1 = plot(sol_r.rhs().subs(ep==1),(vp,-.07*pi,.07*pi), polar=True, color='red', axes=False, frame=True, title=r'Órbita parabólica ($\\epsilon=1$)')" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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ly2jLLCJSCYWmFFFoEklCPEjNmAEffADTp/ufC2M/e3r0KAlRw4f7TOfNmkVaZBGROIWmFFFoEqmh3bvhk09KQtQHH/g8UkVF0KgR9OtXukYqP9/Xi4jUMYWmFFFoEkmh4mKYO7d0kJo/32uq9t7bJ+JMrJHq3t1nPBcRSSOFphRRaBJJsy1bfBLOeIiaPt1fZAzQurUHqPgyfDh84xuRFldE6h+FphRRaBKJwPr1HqASa6TWr/dtXbrAiBFwyCG+DB6s/lEiUisKTSmi0CSSAeKzmsdD1LRp3tF82zbvBzVggAeoeJg66CA164lI0hSaUkShSSRD7dgB8+bB1KkeoqZOhUWLfFurVqVro4YPh/32i7S4IpK5FJpSRKFJJIt89ZXXRE2dWhKmvvrKt/XuXbo2qm9fjdYTEUChqdbMbCwwFmgA9FJoEslCIcDixaVro+bMgV27fLTe0KEwapQvI0dCmzZRl1hEIqDQlCKqaRKpZ7Zu9dF68dqoyZNhzRrf1rNnSYgaNQr69IEGDaItr4iknUJTiig0idRz8ffrTZ5cssRro/LyvAYqHqKGD4fmzaMusYikmEJTiig0ieSgLVt8pF5ikNq0yWud+vcvXRu1//4aqSeS5RSaUkShSUTYvdtH5iWGqI8/9m3t25f0iRo1CoYMgaZNoy2viFSLQlOKKDSJSLk2bizpEzV5so/a27rVA9OwYXDYYTB6tAcpTXcgktEUmlJEoUlEkrJjB3z0Ebz/vi8TJ8K6dd50169fSYg67DDo1Cnq0opIAoWmFFFoEpEaCQGWLvXwFA9Rixf7tu7dSwLU6NE+h5T6RYlERqEpRRSaRCRl1q0rCVDvvw+zZnl/qdatS0LUYYfBoEHQuHHUpRXJGQpNKaLQJCJps3mz94uKh6ipU/19envv7bOWx4PUyJGwzz5Rl1ak3lJoShGFJhGpM8XFPvFmYm3Ul1/6616GDYMjjvDl0EM1X5RICik0pYhCk4hEZvduWLgQ3n23ZFm3Dho2hMGDS0LU6NEaoSdSCwpNKaLQJCIZIwT45JPSIerzz70T+cCBJSHqsMO8n5SIJEWhKUUUmkQkY4UAn35aOkQtX+7bBgyAo4+Go46Cww/3V8KISLkUmmrJzMYCY4EGQC+FJhHJCsuXw4QJ8J//wDvvwMqV/vqXoUM9QB19tPeJUsdykf9SaEoR1TSJSNaK10S9805JiFq3zqczGDHCA9TRR/tIPb36RXKYQlOKKDSJSL0RgncsjweoCRN8dN5ee3ntU7w5b+hQzRMlOUWhKUUUmkSk3tq921/9Eq+Jevddnztq3329M/nRR8Oxx0L//t7EJ1JPKTSliEKTiOSMnTth5sySmqj33/fJNtu29fA0Zox/dukSdUlFUkqhKUUUmkQkZxUVweTJ8O9/+zJzpjfx9erlAWrMGDjySNDPRslyCk0potAkIhKzcaPXQMVD1LJlPtHmIYeUhKjhw30Gc5EsotCUIgpNIiLliI/Miweod96BTZu81umoo0qa83r29Mk3RTKYQlOKKDSJiCQh3h8qHqKmTIEdO6BbNzjhBF+OOUbvzJOMpNCUIgpNIiI1sGWLj8Z74w14/XVYvNinMRg92gPUiSdC376qhZKMoNCUIgpNIiIpsHQpvPaaB6h33vFReZ06lQSoY4/Vq14kMgpNKaLQJCKSYtu3w8SJJSFq4ULvUD5qVEmIGjhQtVBSZxSaUkShSUQkzZYt8/D0+uvw9tvetNe+PRx/vAeoMWOgVauoSyn1mEJTiig0iYjUoeJimDSppBZq7lyfjfzQQ+HUU33p1Uu1UJJSCk21ZGZjgbFAA6CXQpOISARWrfIA9dJL8NZb3hfqoINKAtTo0XpPntSaQlOKqKZJRCRDbN3qnchfeglefhlWr/bO4yec4AHqxBPVjCc1otCUIgpNIiIZKASYNcsD1Esv+RxRDRuWNOOdcoqa8SRpCk0potAkIpIFPv8cXnmlpBlv+/aSZrwzzvAw1bBh1KWUDKXQlCIKTSIiWSaxGe+ll2DNGmjbFk4/Hc4802cmb9o06lJKBlFoShGFJhGRLLZ7N0yfDs8/D889B0uW+KtcTj4ZzjrL+0Htu2/UpZSIKTSliEKTiEg9EQLMn18SoGbP9hqn447zGqhTT4U2baIupURAoSlFFJpEROqpzz6DF17wADVpks8HdfjhHqDOOAO6dIm6hFJHFJpSRKFJRCQHrFsHL77oAertt2HHDhg+HL75TV8UoOo1haYUUWgSEckxBQU+Eu+ZZ+DVV6GoCEaOhHPPhXPO8RcNS72SjtDUIBUnqYyZXWlmn5nZdjObaWaHVbH/EbH9tpvZp2b2gzLbLzazUM6yV3rvREREslZeHnzrW17rtH49/PWvPvru+uu9xunww+G++2Dt2qhLKhksraHJzM4FxgP/CwwCJgKvmVnXCvbvDrwa228Q8GvgXjM7u8yuhUCHxCWEsD0d9yAiIvVM8+ZwwQXwr395E96f/+zrxo2Djh3hqKPggQfgiy+iLqlkmLQ2z5nZNODDEMIVCesWAi+EEG4qZ/87gNNCCH0S1j0ADAghjIx9fTEwPoSwXy3KpeY5EREp7csvfRTeP//pfaBCgKOP9v5P55wDLVtGXUKphqxqnjOzJsAQ4M0ym94ERlVw2Mhy9n8DGGpmiW9v3NfMlpvZKjN72cwGVVGWpmbWIr4AzZO/ExERyQmtWsEll8Abb/jkmX/6k88J9YMfQPv2PgLv2Wd9ZnLJSelsnmsDNATWlVm/DmhfwTHtK9i/Uex8AB8DFwOnAecD24FJZtajkrLcBBQkLKuSugMREclNbdvC5Zd7jdPnn8Mdd8CqVV7j1L49XHopTJjgoUpyRto7ggNl2/+snHVV7f/f9SGEqSGEv4YQ5oQQJgLfBD4BrqrknLcDeQlL5yTLLiIiua59e7j2WvjgA1i4EK66yl/pctRR0K0b3HADzJ0bdSmlDqQzNG0AdrFnrVI79qxNiltbwf47gY3lHRBC2A18AFRY0xRCKAohFMYXYHPVxRcRESmjd2/45S9h6VKfPPPUU+HRR6F/fxgwAO65Rx3I67G0haYQQjEwExhTZtMYYHIFh00pZ//jgBkhhB3lHWBmBgwE1tS4sCIiItVhBqNGwR//CKtX+ySavXrBjTf6nE+nn+6dyouLoy6ppFC6m+fuBi41s++ZWR8zuwfoCjwAYGa3m9njCfs/AHQzs7tj+38PuAS4M76Dmd1iZseb2QFmNhB4FA9ND6T5XkRERPbUpInXOP3zn96BfPx4D1JnneVTGFxzjb8TT7JeWkNTCOEp4Frg58Bs4HDgpBDC8tguHfAQFd//M+Ak4MjY/j8Drg4hPJtw2v2Ah4CF+Ei7TsDhIYTpabsRERGRZLRqBWPHev+nuXPhu9+Fp56CQYN8+dOffHZyyUp6jYrmaRIRkXTauRNef937Pr30EjRtCued56Pzhg/3pj5Juayap0lERESARo3glFO8j9OKFfCTn/hUBocc4p3H77sPNm2KupSSBIUmERGRutKxI9x8M3z6qdc+9ehR8vqWiy+GyZN9JnLJSApNIiIida1BAzj+eJ9hfMUK+NnPYOJEOPRQ6NcP7r1XfZ8ykEKTiIhIlDp0gJtugsWL4d//hvx8+NGPoHNnn0hz0aKoSygxCk0iIiKZoEEDOPZYn7pg+XK47jr/c+/ecOKJ8Oqrem1LxBSaREREMk3HjvCLX3jT3eOPw/r1cPLJHqD+8AcoTMlgMKkmhSYREZFM1bQpfPvbPu/TpEkweLB3HO/c2SfNXLw46hLmlJwKTWY21swWAJoIU0REskf8tS1PPgnLlsHVV8Pf/w49e/p0Bu++q1F3dSCnQlMI4f4QQj4wPOqyiIiI1EjnzvCrX8HKlfDYY97/6cgjYeRInwtK/Z7SJqdCk4iISL2x117+mpaPPoJXXvGvzzoL+vSBRx6BoqKoS1jvKDSJiIhkMzM46SSYMAGmToW+ff0VLfvvD3fcoU7jKaTQJCIiUl+MGOETZi5cCKeeCj//OXTvDr/+NWzeHHXpsp5Ck4iISH3Tqxc89BAsXQrf+pZPX7D//nD77QpPtaDQJCIiUl917uzzOi1dCuefD7feqvBUCwpNIiIi9V3nznDffQpPtaTQJCIikivi4WnJEjjvPA9P3bvDnXfC9u1Rly7jKTSJiIjkmi5d4P77PTz9v/8HN97or2j52980z1MlFJpERERyVZcu8Kc/wfz5/oqWCy+EYcPgnXeiLllGUmgSERHJdb16wXPPwcSJ0KQJHHOMz/00b17UJcsoCk0iIiLiRo+GyZPh6afhk09gwACfKHPDhqhLlhEUmkRERKSEGZxzDixYAPfc4wGqZ09vxtu1K+rSRSqnQpOZjTWzBcD0qMsiIiKS0Zo0gauvhkWL/J12V14JQ4d6TVSOyqnQFEK4P4SQDwyPuiwiIiJZoV07fwHw1KnQsCEceqi/KHjjxqhLVudyKjSJiIhIDY0YAdOmwYMPwvPPQ34+PPUUhBB1yeqMQpOIiIgkp2FD7xi+cCEcdphPkHnaabByZdQlqxMKTSIiIlI9HTrAM8/4NAUzZ3qt0yOP1PtaJ4UmERERqZkzz/RRdt/8Jlx2mX+9fn3UpUobhSYRERGpuf32g0cf9X5OkyZBv37wyitRlyotFJpERESk9s44A+bO9dexnHIKXHEFbNsWdalSSqFJREREUqN9e69l+uMf4S9/gVGjYOnSqEuVMgpNIiIikjpmXss0dSps2QJDhsC//hV1qVJCoUlERERSb8AAmDEDjjrKm+5uvDHrX8Oi0CQiIiLpkZfn0xL87ndw551w+umweXPUpaoxhSYRERFJHzP48Y/h5Zfhvfd8UsxVq6IuVY0oNImIiEj6nXCCT0nw1Vf+SpYPP4y6RNWWU6HJzMaa2QJgetRlERERyTn9+vn76zp1giOO8JqnLJJToSmEcH8IIR8YHnVZREREclL79vCf/8Dw4V779NZbUZcoaTkVmkRERCQD7LOP93E68kifCPPVV6MuUVIUmkRERKTuNWvmr1454QSfkuDFF6MuUZUUmkRERCQaTZvC00/Dqaf6S3/feSfqElVKoUlERESi07gx/P3v3jH8zDNh/vyoS1QhhSYRERGJVtOm8Mwz0K2b93Favz7qEpVLoUlERESi17w5vPQSbNvmfZy2b4+6RHtQaBIREZHM0K2bv9x35kyfRTzDKDSJiIhI5hgxAu6+G+6/H154IerSlKLQJCIiIpnliiu8U/j3vgerV0ddmv9SaBIREZHMYgaPPOIj6665JurS/JdCk4iIiGSeVq1g/HgfVffyy1GXBlBoEhERkUx13nlw/PFw1VVQXBx1aXIrNJnZWDNbAEyPuiwiIiJSBTO46y5Yvtyb66IuTggh6jLUOTNrARQUFBTQokWLqIsjIiIilfn2t+Htt2HpUn9nXRIKCwvJy8sDyAshFKaiGDlV0yQiIiJZ6Oc/hzVr4J//jLQYCk0iIiKS2Xr0gGOPhQcfjLQYCk0iIiKS+b7/fZgyBebOjawICk0iIiKS+U4/Hdq1g8cfj6wICk0iIiKS+Ro3htNO85f6RkShSURERLLD0UfDokWwfn0kl1doEhERkewwapR/TpkSyeUVmkRERCQ7dO0KbdvC7NmRXD7tocnMrjSzz8xsu5nNNLPDqtj/iNh+283sUzP7QTn7nG1mC8ysKPZ5ZvruQERERDKCGXTqBKtXR3L5tIYmMzsXGA/8LzAImAi8ZmZdK9i/O/BqbL9BwK+Be83s7IR9RgJPAU8AA2Kf/zSzEem7ExEREckIHTrA2rWRXDqtr1Exs2nAhyGEKxLWLQReCCHcVM7+dwCnhRD6JKx7ABgQQhgZ+/opoEUI4cSEfV4HvgohnJ9kufQaFRERkWx0ySUwbx5Mm1bpbln1GhUzawIMAd4ss+lNYFQFh40sZ/83gKFm1riKfSo6J2bW1MxaxBegeRK3ICIiIplm333h668juXQ6m+faAA2BdWXWrwPaV3BM+wr2bxQ7X2X7VHROgJuAgoRlVWUFFxERkQy1dSvss08kl66L0XNl2/+snHVV7V92fXXPeTuQl7B0rmRfERERyVRffw177x3JpRul8dwbgF3sWQPUjj1riuLWVrD/TmBjFftUdE5CCEVAUfxrM6toVxEREclka9dCmzZV75cGaatpCiEUAzOBMWU2jQEmV3DYlHL2Pw6YEULYUcU+FZ1TRERE6ovFi6FHj0gunc6aJoC7gSfMbAYedi4HugIPAJjZ7UCnEMJ3Yvs/APzQzO4GHsY7fV8CJI6K+z3wnpndAPwLOB04Fhid5nsRERGRKG3YAKtWwcEHR3L5tIamEMJTZtYa+DnQAZgHnBRCWB7bpQMeouL7f2ZmJwH3AGOB1cDVIYRnE/aZbGbnAb8CfgksBc4NIVQ+9lBERESy2/vv++foaOpJ0jpPU6bSPE0iIiJZaNw4ePZZWLGiyl2zap4mERERkZQJAZ5/Hk45JbIiKDSJiIhI5ps6FZYvh3POiawICk0iIiKS+R56CLp3hyOPjKwICk0iIiKS2datgyefhMsvhwbRRReFJhEREclsd90FjRrB978faTEUmkRERCRzLVsG997rI+datoy0KApNIiIikrluuglatYLrr4+6JGmfETyjmNlYfNJMhUUREZFMN3my92V67DHYd9+oS6PJLTW5pYiISAbavh0GDYLmzWHKFGjYsFqHp2Nyy5yqaRIREZEs8dOfwqefwqxZ1Q5M6aLQJCIiIpnlX//yEXN33gn5+VGX5r/Ut0dEREQyx5IlcNFFcMYZcN11UZemFIUmERERyQxbtvhrUtq2hb/8BcyiLlEpap4TERGR6BUVwZlnej+mSZPAO3FnFIUmERERidauXXDhhTBxIrz+OvTrF3WJyqXQJCIiItEJAa68Ep57zpcIX8hbFYUmERERiUYIcPPN8NBDPoHl6adHXaJKKTSJiIhI3QsBbrwRfvtbn1rgu9+NukRVUmgSERGRurV7N4wdCw88APfcA9deG3WJkqLQJCIiInVn2za4+GJ45hl49FH43veiLlHSFJpERESkbqxd6/2W5s6Fp5+Gs86KukTVklOhyczGAmPRpJ4iIiJ166OP4JRTYOdOeO89GDo06hJVW06FhxDC/SGEfGB41GURERHJGa+8AoceCm3awPTpWRmYIMdCk4iIiNSh3bvhttvg1FPh2GO9hqlz56hLVWM51TwnIiIidWTDBp/l+8034dZb4ac/hQbZXVej0CQiIiKp9dZbcNFFUFwMb7wBY8ZEXaKUyO7IJyIiIplj+3a47joPSX36wOzZ9SYwgWqaREREJBXmzoULLoBFi+Duu+Gaa7K+Oa6s+nU3IiIiUrd27fKQNGyYvxrlgw9g3Lh6F5hAoUlERERqat48n0rgxz+GK67wwNS/f9SlShuFJhEREameoiK45RYYPBgKC+H99/0dcnvtFXXJ0kp9mkRERCR5773ntUqffAI33QQ33wxNm0ZdqjqhmiYRERGp2urV3tH7iCOgeXOYOdMnrsyRwAQKTSIiIlKZHTvgzjuhVy/497/hscdg8uR63XepImqeExERkfK99RZcfbVPI3DllV6z1LJl1KWKTE7VNJnZWDNbAEyPuiwiIiIZa948OOkkn5iydWv48EP4wx9yOjBBjoWmEML9IYR8YHjUZREREck4q1fDpZfCgAHe0fvpp73j94ABUZcsI6h5TkREJNdt3gy/+x3cdRc0a+bTB/zgB9CkSdQlyygKTSIiIrlq2zZ46CH49a99vqVrr4Ubb4S8vKhLlpEUmkRERHLN9u0eln7zG/jiC/jOd+DWW6Fr16hLltFyqk+TiIhITtu+He67Dw480N8Pd9xx8PHHPo2AAlOVFJpERETqu6Ii+OMf4aCD4Jpr4JhjPCz95S++TpKi0CQiIlJfFRfDAw9Ajx7wwx/CkUfCggXw+OO+TqpFoUlERKS+2bLFR8AdcIBPSnnooTB/Pvz1rz6zt9SIOoKLiIjUFxs3+iSUf/iDj4a74AK4/nrIz4+6ZPWCQpOIiEi2++QT+P3vvY9SCD5B5Y9+BN26RV2yekWhSUREJBuFAP/5jzfDvfIKtGkD//M/MHYstG0bdenqJYUmERGRbFJUBP/4B4wfD3PmQN++8Mgj8K1vwV57RV26ek2hSUREJBusXw9/+pNPHbBunb9Q9847ffoAs6hLlxNyKjSZ2VhgLBo1KCIi2WL+fK9VeuIJaNAALrrI51rq3TvqkuUcCyFEXYY6Z2YtgIKCggJatGgRdXFERERKKy6GF17wmqUJE6BjR59n6fLLoXXrqEuXFQoLC8nzd+jlhRAKU3HOnKppEhERyWgrV/o74R55BNauhcMP9/5LZ50FTZpEXbqcp9AkIiISpV274K23fObuF1+EffaBb38brrjCO3lLxlBoEhERicKKFfDnP/vLclesgH794P77fULK5s2jLp2UQ6FJRESkruzYAS+95M1vr78Oe+8N55/vk1EOH65RcBlOoUlERCTdPvnEg9L//R988QWMGAEPPwzf/KZqlbKIQpOIiEg6bNkCzz0Hjz4K770HrVp5X6VLLvGmOMk6Ck0iIiKpsmsXvPMOPP64B6atW+Hoo+Hvf4czz9SM3VlOoUlERKS25s3zoPS3v8Hq1dCrF9x8s3fq1ktz6420zoxtZi3N7AkzK4gtT5jZflUcY2Z2q5mtNrNtZjbBzA4us88EMwtllifTeS8iIiKlrFvnM3UPHuzNbY895vMpTZ8OCxfCT36iwFTPpLum6e9AZ+CE2NcPAU8Ap1ZyzPXAdcDFwCfAT4F/m1mvEMLmhP0eBn6e8PW2FJVZRESkfNu2+VxKjz8Ob7wBDRvCqafCLbfAiSdqAsp6Lm2hycz64GHpkBDCtNi6y4ApsQC0qJxjDLgW+N8QwnOxdRcB64BvAQ8m7L41hLA2XeUXEREBfJqAd96BJ5/0fkqFhTByJNx3n49+a9Uq6hJKHUlnTdNIoCAemABCCFPNrAAYBewRmoDuQHvgzYRjiszs3dgxiaHpAjO7EA9UrwG/KFMT9V9m1hRomrBK4ztFRKRiu3bBxIkelJ59FjZsgJ494dpr4cILoUePqEsoEUhnaGoPfFHO+i9i2yo6BjwIJVoHJDYM/w34DFgL9AVuBwYAYyo4703ALVUXWUREclYIMHWqB6Wnn4Y1a7xP0iWXwLnnwsCBmnwyx1U7NJnZrVQdQIbFPkN5p6hgfaKy20sdE0J4OGHbPDNbDMwws8EhhA/LOd/twN0JXzcHVlVRBhERqe9CgFmz4KmnfFm+HDp08Ga3887zSSgVlCSmJjVN9wFVjVRbBvQHvlHOtrbsWZMUF++j1B5Yk7C+XSXHAHwI7AB6xP5cSgihCCiKf236ByAikrtCgLlz4ZlnvFZp8WJo0wbOOceD0ujR3sFbpIxqh6YQwgZgQ1X7mdkUIM/MhocQpsfWjQDygMkVHBZvchsDzIod0wQ4ArihkssdDDSmdNASERFxu3fDBx94R+5nn4WlSyEvz6cI+MMffALKxo2jLqVkuLT1aQohLDSz14GHzez7sdUPAS8njpwzs4+Bm0IIz4cQgpmNB34Sa3JbDPwE2IpPX4CZHQhcALyKh7d84C48ZE1K1/2IiEiW2bUL3n/fQ9Lzz8OqVdC2LZxxBtx/Pxx1lKYIkGpJ9zxNFwD3UjIa7kXgh2X26YXXPsX9FmgG/BFoCUwDjksYGVcMHANcA+wLrARewUfP7UrDPYiISLYoLvbpAZ57Dl54Adavh06dvEbp7LPV9Ca1YiFU1Se7/jGzFkBBQUEBLVq0iLo4IiJSG1u3wptveo3SSy9BQQEceKCHpLPOgmHDoEFaX4AhGaiwsJC8vDyAvBBCYSrOqXfPiYhI9tmwAV591Wfnfu01D04HHwzXXONBqX9/jXqTlFNoEhGR7LBokYekF1+EyZO9c/fw4f5i3LPP9pfkiqSRQpOIiGSmnTth0iRvcnvxRZ8aoFkzOPZYePBBOPlkn1NJpI4oNImISOYoKPAX4b74oje/ffUVtG/vL8W96y445hjYe++oSyk5SqFJRESitWxZSW3Su+/6C3L794exYz0sDR2qjtySERSaRESkbu3cCVOmeE3SK6/47NyNG/u8SXff7UGpW7eqzyNSxxSaREQk/datg9df96D0xhveDNe2LZxwAvzsZ3D88aApYCTD5VRoMrOxwFhA9bwiIum0axfMmOEh6dVX/c9mPmfSuHFw0kkwZIia3SSraHJL/WYjIpIaa9f6JJNvvum1SRs2QMuWXot00kn+2a5d1KWUHKHJLUVEJHMUFfm73d54w5ePPvL1gwfD5Zf7lADDh0Mj/Vcj9YO+k0VEJDkhwMcfl9QkTZgA27b5lADHHQc33ABjxnhfJZF6SKFJREQq9tVX8NZbJUFp5Upo0gQOPxx+8QtvcuvXT68skZyg0CQiIiV27oTp00tC0vTp/rqSPn38VSXHHQdHHKEJJiUnKTSJiOSyeJPb22/7MmECbNrkHbiPPRYuvdSDUpcuUZdUJHIKTSIiuWbFCg9I77zjn2vW+OSSI0f6dADHH++zcDdsGHVJRTKKQpOISH23YQP85z8ltUlLlngfpEGD4MIL/X1uo0fDPvtEXVKRjKbQJCJS32zZAu+9V1KTNHu2r+/Vy0e3/eY3/sqSVq0iLaZItlFoEhHJdsXFMHVqSU3StGneobtTJ69FGjcOjj4aOneOuqQiWU2hSUQk2xQXwwcfwLvv+vL++7B1q3fePuoo+P3vPSz17KmpAERSSKFJRCTTFRV57VE8JE2e7JNKNm/ufZFuucVD0sCB6rwtkkYKTSIimWbbNm9ui4ekKVM8OOXlwWGHwW23+VxJgwbpFSUidSin/rWZ2VhgLKDXaotI5vj6aw9G8ZA0bZo3wbVs6TNv3367h6QBA1STJBIhCyFEXYY6Z2YtgIKCggJatGgRdXFEJNds2QKTJpWEpOnTveN2mzYeko44wpd+/aCBfscTqYnCwkLy8vIA8kIIhak4Z07VNImIRKKw0Dtrx0PSjBmwaxe0a+fhaPx4/8zPV0gSyWAKTSIiqbZmjYek99+HiRNhzhx/f1uHDh6OLr7YP3v31ug2kSyi0CQiUhshwKJFpUPSp5/6tgMO8I7bV1zhIalHD4UkkSym0CQiUh07dsCHH5aEpPff99eUNGjgHbVPPtmD0qGHQseOUZdWRFJIoUlEpDKbN/vw/4kTPSBNnepTAuy1FxxyCPzgBz5X0siRoIElIvWaQpOISFwIsGyZTx4ZXz76yPsjtW7t4ei22/xz8GBo0iTqEotIHVJoEpHctX27N7VNnuzzJE2eDGvX+rZevWDUKLjySg9JvXppZJtIjlNoEpHcsWZNSTiaPBlmzvRJJJs1gxEj4Lvf9aB0yCE+Z5KISAKFJhGpn3buhLlzSwLSlCnw2We+rWtXD0fnn++f/ftD48bRlldEMp5Ck4jUDxs3+sza8ZA0bZq/nqRxY+9/dMYZHpBGjoROnaIurYhkIYUmEck+xcU+YeS0ab5MnQpLlvi2du08HN1yiwekIUO8+U1EpJYUmkQks8VHtE2dWhKSZs2CoiIfvTZwIJx4ovdJOuQQn1BSE0iKSBrkVGgys7HAWEBDYEQy1aZN8MEHJQFp2jRYv963HXCAB6Pzz/eQNHAgNG0aZWlFJIdYCCHqMtQ5M2sBFBQUFNBCk9GJRCfeWTuxFunjj33bfvvB8OEejkaM8D+3bRtpcUUkexQWFpKXlweQF0IoTMU5c6qmSUQiFAKsXFm6BmnmTJ9du1EjH8F21FFw441em9Sjh+ZFEpGMotAkIunx1Vceij74wEe1TZ1aMnFk164ejM4802uRBg9WZ20RyXgKTSJSe1u2eOfsDz6AGTP8Mz6arXlzGDbMJ46MN7W1bx9teUVEakChSUSqZ/t2H+4fD0czZsDChf5+tmbNYNAgOOkkD0rDhqmZTUTqDYUmEanYjh0wf37pGqS5c70Dd+PG3g/psMNg3DgPSPn53j9JRKQe0k83EXG7dsEnn5QOSLNne81SgwYeiIYNg0sv9c/+/TXcX0RyikKTSC4KAT79tHQT28yZ3jcJoGdPGDoUzj3XPwcNgn32ibbMIiIRU2gSqe/iAWnmTPjwQ19mzPDRbQDdunkw+ulPvQZp8GCfI0lEREpRaBKpT3btgsWLPRjFQ9KsWVBQ4Ns7d/ZQdO21HpCGDPF3tYmISJUUmkSy1c6dPnt2Yg3SrFnw9de+vXt3D0jXX++fgwcrIImI1IJCk0g2KC72UWyJNUhz5ngnbfBh/UOGwGmneTgaNAhatYq2zCIi9YxCk0im2b4dPvqopPboww99mH9xsY9i693bg9G553pQGjgQ9A5FEZG0y6nQZGZjgbGAZtqTzPDll15jNGuWD++fPdsnity50+c7OvhgD0gXX+yfAwZoFJuISEQshBB1GeqcmbUACgoKCmih39ClLoQAy5aVBKP4smKFb2/WzOc9GjjQlyFDoF8/2GuviAosIpLdCgsLycvLA8gLIRSm4pw5VdMkUieKi2HBgj0DUnwEW9u23ufovPP8c+BA75PUsGFkRRYRkaopNInUxqZN3ryWGI7mz/fXj5jBQQd5MLrhhpJapPbtfZuIiGQVhSaRZIQAK1eWDkezZnmTG3gzWr9+PvfRZZd5OOrXD5o3j6zIIiKSWgpNImXt2OHzH5VtXvvyS9/eurXXHp1zTkntUa9eelGtiEg9p5/ykts2bvTh/fFl9myYN8/7JQEceKCHonHj/HPQIOjYUc1rIiI5SKFJcsOOHfDJJx6M5swpCUmff+7b99rLh/cPHOjD+wcN8tFsGl0pIiIxCk1S/6xfXzoYzZnjo9nitUddu3oguugin/eof3/vsK3mNRERqURa/5cws5bAvcBpsVUvAleFEDZVcsxZwPeBIUBrYFAIYXaZfZoCdwLnA82At4ErQwirUnwLksmKi73vUdnao7VrfXuzZt4Ze+hQuOQSD0f9+kHLltGWW0REslK6f7X+O9AZOCH29UPAE8CplRyzDzAJeBp4uIJ9xsfOcR6wEbgLeNnMhoQQdtW+2JJRQoBVq7yv0dy5vsyZUzJzNsD++3ut0WWXeTgaMAAOOEBzH4mISMqkbUZwM+sDLAAOCSFMi607BJgC9A4hLKri+P2BzyhT02RmecB64NshhKdi6zoCK4GTQghvJFE2zQieqb78siQcJX7GJ4bcd1/o27ekWW3AAP/aZ30VEREBsm9G8JFAQTwwAYQQpppZATAKqDQ0VWII0Bh4M+G8q81sXuy8VYYmyQDbtnk/o7LhaPVq3964sb+Ytm9fOPlk/+zXz/sjNdCrA0VEpO6lMzS1B74oZ/0XsW21OW9xCOGrMuvXVXTeWB+opgmrNONgXdm5E5Ys2bP2aMkSb3YDb0br2xe++92ScNSjBzRpEm3ZRUREElQ7NJnZrcAtVew2LPZZXtufVbC+tio7701UXWapjbL9juKfCxdCUZHv066dB6KTTvLPvn19mP+++0ZbdhERkSTUpKbpPuDJKvZZBvQHvlHOtrZ4rVBNrQWamFnLMrVN7YDJFRxzO3B3wtfNAY20q6lk+x0NHVpSe9S3r4cmERGRLFXt0BRC2ABsqGo/M5sC5JnZ8BDC9Ni6EUAeFYebZMwEdgBjgH/GztsB6AtcX0GZi4CihLLV4vI5pKp+R40aeb+jxNoj9TsSEZF6Km19mkIIC83sdeBhM/t+bPVDwMuJI+fM7GPgphDC87GvWwFdgY6xXXrFQs7aEMLaEEKBmT0K3GVmG4Ev8Tmb5gJvpet+6rXt22HRIg9I8+eXLIn9jrp390B08cUlTWs9e6rfkYiI5Ix0z9N0AT65ZXyk24vAD8vs0wuvfYo7DfhzwtfxpsBfALfG/jwO2InXNMUnt7xYczRVYft2f5VIPBTFQ9KSJbB7t+/ToYP3M1K/IxERkVLSNk9TJqv38zQVFXnNUWIwqigcHXww5OeXfGq2bBERqQeybZ4mSbeiotI1R/GQtGQJ7IpVunXo4GHohBNKhySFIxERkWpRaMoGieGobM1RPBy1b++B6Pjj4brrPBjl50OrVtGWXUREpJ5QaMokW7d6s9rChR6O4p+LF+8Zjo47DsaNK6k5UjgSERFJK4WmKGzaVDoYxZdly0pGq3XsCH36wJgxcO21CkciIiIRU2hKlxBg3bo9g9GCBbB2re9j5kP5+/SBc87xz/iiF9CKiIhkFIWm2tq9G1asKB2O4n/etMn3adzY36WWnw+XXVYSjHr1gmbNIi2+iIiIJEehKVk7dnjH67LBaNEi74sEsPfePkN2fj6ccooHo/x8fyFt48bRll9ERERqRaGpMk88AS+84OFo8WLYudPXt2zpYWjIELjwQv9znz7QpYteHyIiIlJP5VRoMrOxwFgguWSzfLm/hPaYY+Cqq0qa1dq18/5IIiIikjM0I3h9nBFcREQkx6VjRnC1JYmIiIgkQaFJREREJAkKTSIiIiJJyKmO4GUVFqakiVNEREQyTDr+j8/VjuCdgFVRl0NERETSrnMI4fNUnChXQ5MBHYHNwHRgeA1P1RwPX51j56qJ2lw/24/P9uenZ5e9x+v56fnp+WXv8dV5fs2B1SFFYScnm+diD+9zADPbXdOhiFYyV9PmWpyjxtfP9uOz/fnp2WXv8Xp+en56ftl7fDWfX0rb6NQRHO7P8utn+/G1FWX59eyy+/jairr8UR9fW1GXP+rjayvq8kd9fCRysnkuVeKTZJLCibNyiZ5fzenZ1Y6eX+3o+dWOnl/tRPn8VNNUO0XAL2KfUn16fjWnZ1c7en61o+dXO3p+tRPZ81NNk4iIiEgSVNMkIiIikgSFJhEREZEkKDSJiIiIJEGhSURERCQJOR2azOxKM/vMzLab2UwzOyzJ4w41s51mNrvM+sZm9nMzWxo75xwzO6GS89xkZsHMxtfuTupeFM/OzG6NPa/EZW0Kb6vORPW9Z2adzOyvZrbRzLaa2WwzG5Ki26ozEX3/LSvn+y+YWdbNNxPR82tkZr+KXXebmX0aOybr/h+K6Pk1N7PxZrY89vwmm9mwFN5WnanO8zOzIyv4d9e7zH5nm9kCMyuKfZ5Zm+tWKISQkwtwLlAMXAr0AcYDW4CuVRyXBywF3gBml9l2Bz7T+EnAAcAVwDZgUDnnGQZ8BswBxkf9PLLh2QG3AvOA9glL26ifRxY9v5bAMuDP+OsL9geOAQ6M+plkyfNrW+Z771ggAEdG/Uyy5PndDGwATo59752DvwLjmqifSZY8v6eA+cDhwEGxn4cFQKeon0k6nx9wZOzfWc8y//4aJuwzEtgJ3AT0jn3uAEbU9u9tj/JE/QAj/IubBvypzLqFwO1VHPck8MvYN+zsMttWA2PLrHsB+GuZdfsCn8R+6E4g+0JTJM+uvOOycYnw+f0GmBj1/Wfr8yvnfOOBJcSmbsmWJcLvv5eBR8vs8yzwRNTPJNOfH9AMDwUnl9lnNvCrqJ9JOp8fJaFpv0rO+RTwWpl1rwP/qO3fW9kl66pFU8HMmgBDgDfLbHoTGFXJcd8FDsQn1SpPU2B7mXXbgNFl1t0PvBJCeCvZMmeKDHh2PcxsdayK9UkzOyDpwmeAiJ/facAMM3vazL4ws1lmdll1yh+1DPj+SyzHhcBjIfbTNxtE/PzeB44xs56xcw6IbX812fJHLcLn1whoWMU+Ga+mzy9mlpmtMbO3zeyoMttGlnPON+LnrOV1S8nJ0AS0wb8B15VZvw6v9tuDmfXAf1O/IISws4LzvgFcZ2Y9zKyBmY0BTgc6JJznPGAwXn2YjSJ7dvhvCt8Bjgcui11vspm1runNRCDK5xev9l+MP8MHgHvN7Ds1vZkIRPn8Ep0B7Af8pTqFzwBRPr87gH8AH5vZDmAWXsv+jxrfTd2L5PmFEDYDU4CfmVlHM2toZhcCI6j4ezQTVfv5AWuAy4GzgbOARcDbZnZ4wj7tqzhnTa5brlwNTXFlf0O0ctZhZg2BvwO3hBA+qeR81+D/IX2Mt53eh/cf2RU7Txfg98CFIYSyvzFkmzp9dgAhhNdCCM+GEObGaulOjm26qMZ3EZ06f374v/cPQwg/CSHMCiE8CDyMB6lsE8XzS3QJ3hywuprlzhRRPL9z8dq5b+G/OF4E/NjM9O83uef37dh1PsdfH3J17NwVfY9msqSeH0AIYVEI4eEQwochhCkhhCuBV4Af1+CcSV+3Irkamjbg32hlE2Y79kyiAM2BocB9sZEPO4GfAwNiXx8NEEJYH0I4A9gH6IZ3SNuCd/gGrx5sB8xMOM8RwNWxrxum8ibTJKpnt4cQwtfAXKBHre6obkX5/NYAC8qcfyHQtVZ3VLci//4zs254f8RHUnJHdSvK5/c74DchhCdjv/g8AdxDdtW6R/b8QghLQwhH4H1iu4QQhgONqeRnZAaq7vOryFRK/9xfW8U5U3Xd3AxNIYRiYCYwpsymMcDkcg4pBPoBAxOWB/BqwoF4s1Hi+beHED7H26HPBv4V2/R2OeeZAfwNGBhCyPjfGCJ8dnsws6b4KIg11b2PqET8/CYBvcqcvyewvLr3EZUM+f77LvAF/ttuVon4+e0N7C5z/l1k0f9DmfD9F0L4OoSwxsxa4s3sFf6MzDQ1eH4VGUTpn/tTyjnncfFzpvC6OT16Lj788Hv4f7z34Mm+W2z77cDjlRx/K3uOgBiBt7keAByGh6RPqbzX/wSyb/RcJM8OuBOvmese2/8l/IdSt6ifSZY8v2H4MNyf4EOWvwV8jfe1iPy5ZPrzi+3XAA+Zv4n6OWTb88P7f62iZMqBM4H1wB1RP5MseX7HAyfEfv6NwUfOTQMaR/1M0vn8gGvxPoQ9gINj2wNwVsI+o/DRhTfgtXQ3UPGUA+VeN9mlETkqhPBUrAPxz/GOdPOAk0II8d+6O1D9Zou9gF/h3/hb8FEh3w4hbEpJoTNEhM+uM96RtA3+w3YqcEjCdbNCVM8vhPBBbMK322PX/gy4NoTwt1rcTp2L+N/usbFzP1az0kcvwud3FT7k/o94s8hq4EHgtprdSTQifH55+L/dzsCX+HQNN4cQdtTwViJRg+fXBP+FuRM+WnA+PvXCqwnnnBwbZPUr/HtsKXBuCGFawj5VXTcpFktgIiIiIlKJrGlLFhEREYmSQpOIiIhIEhSaRERERJKg0CQiIiKSBIUmERERkSQoNImIiIgkQaFJREREJAkKTSIiIiJJUGgSERERSYJCk4iIiEgSFJpEREREkqDQJCIiIpKE/w9i2jYqaXg8jwAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "orbita_1" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "orbita_m = plot(sol_r.rhs().subs(ep==.8),(vp,-pi,pi),aspect_ratio=1, polar=True, color='red', axes=False, frame=True, title=r'Órbita elíptica ($\\epsilon<1$)')" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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ZqAGcC1wPnBpCGJLkMRWapHjr18N//1sQlHJzYffd/Yfq6af71TkiUvmtWuWn1196Cd57z0eTe/Ys+L/etGnUFUqGyZTQdCjFN6t8JoRwgZk9DbQKIRya//xrgYuBnYE1eHgaGEJ4rxTHVGiSAiF4o8mnn/awtHw5tG9fMHyvy5hF4i0vz+dAvfSSX5G3cSMccQScfz707u3LF0nWy4jQFAWFJgH8CpvBgz0sTZsGzZvDeefBWWf5fCUFJZHss3y5n74bPBg+/dQD02mneYA69FB16M9iCk0KTdlnzRqfEPr00z5fqWZN/yR5wQW+TIMmc4tIwty5Hp6efRZmzvQ5T+edB/37e08oySoKTQpN2SEE+Ppr+Ne/4MUXfZ7SgQd6UDr9dPVvEZGtC8G7+z/zjP8MycvzdfB+9ztvYaAmmlkh60KTmV0OXA5UAdorNMXcqlXw/PPw6KO+hMkuu0Dfvj7M3q5d1NWJSGW0erXPfXziCW9s27gx/Pa3Pvqk9gWxlnWhKUEjTTE3ebIHpcGDvZ/S8cfDpZd680mdfhORVPn2Ww9Pgwf7CHZi9OnEEzX6FEPJhibNepPMt24dvPACHHywT+J+9VX4/e9hzhzvx3LccQpMIpJae+0FDz4I33/v8yRXrfJJ47vsAn/9q69FKVlHoUky17JlcOut0KoVnH22B6OXXoL58/3+li2jrlBE4m677fzU/xdfwMSJHpzuvdd//px3HowdG3WFUoF0ek4yz3ffwf33+1Ut4D+w/vAHdekWkcywYoVffPLgg34V3gEHwJVXwsknQ7Vq0dYmZaLTc1K5hODduo87zsPRW2/BjTfCggXw2GMKTCKSOXbYAa66ylsVDBniQen006FNGx+FWrky6golTRSaJFobN8Jzz8Hee/tEy8T8gblzYcAA2HHHqCsUESle1apwyim+WPC4cd4P7rrroEUL/9C3dGnUFUqKKTRJNNav9+HtDh3g3HO9Y/eHH/oPnr59vTGliEhl0bmzf+CbM8fbFNx/v897uuwymD074uIkVRSapGKtW+ctA9q1g379/AqVsWN9Uc3DD9fyJiJSuTVvDv/4h1+wMmCAX+3brh2cc47P15RKLTahycwuN7MpwOioa5FirF4NDzzgDeIuv9xXHJ840ecD7LNP1NWJiKRWgwZ+im7ePPjnP+Gzz3yB8DPP9H5zUinFJjSFEB4OIXQEukddixSyciXcdZev5XT11T5v6bvvvO/SXntFXZ2ISHrVru0fFGfM8FH2kSP9Z98ZZ8CkSVFXJ6UUm9AkGWbNGrjzTu+xdOONcNJJMH26n/Nv3z7q6kREKlbNmt5RfMYMePxxXzNzr72gTx+/TyoFhSZJrU2bYNAgP4d/440+FD1zpi9HoLWbRCTb1agBF13kHyKffBK+/NJbqlx2GSxeHHV1sg0KTZIaIfiSJp06+eKWBx4IU6fCww/75bciIlKgenX/WTl9Otx+O7z4ovd5uvFGX+tOMpJCk5TfyJFwyCG+kGXjxjB6dMEPABERKVnt2nDNNd6W4A9/8OaYiSaZa9dGXZ0UodAkZTdtGpx6ql8Jl5sLQ4d6r6Vu3aKuTESkctlhBxg40KcznHoqXHutz/98+mmf9iAZQaFJSm/JErjkEr98dswYXyPum2/gmGPUZ0lEpDyaNfOJ4pMnQ/fucOGFsN9+PqIvkVNokuRt2OBDxu3awcsv+9Vx06b5St9Vq0ZdnYhIfLRvD6+8Al984XNGe/aE88+HH36IurKsFpvQpOaWafbf//r6cNdc4yFp5kzvu1SrVtSViYjEV8+ePk/0ySd9CsRuu3nvu3Xroq4sK8UmNKm5ZZrMnevn1486yhfP/eYbvyKuQYOoKxMRyQ5VqxZcadevH/zlL97j6b33oq4s68QmNEmKbdgAd9zhC+p+9RU8/zx8+qmPNomISMWrX98XAp4wwVu5HH88/OY3vkiwVAiFJvm1kSN9Pbgbb/T2/9OmwVlnaZK3iEgm2GMP+OADeO01X8Nzjz18jumGDVFXFnsKTVJgxQq49FI44ADvHTJmDNxzD9StG3VlIiJSmBn07g1TpvjP7QEDYN99YdSoqCuLNYUmca+95qfinnvOV+QeORI6d466KhER2Zq6deEf//APubVq+cTxq6+G1aujriyWFJqy3bJlvj7caadBjx7w3XdwxRVqISAiUpl07uzr2N15JzzyiC9p9emnUVcVOwpN2WzIkIJz4y+84H/feeeoqxIRkbKoVg3+/GefKN6sGRx6qJ+6W7ky6spiQ6EpG/30k0/sTiyBMnmyjzZporeISOW3227wySfw0EMweHDBKJSUW2xCk5pbJum993x0adgwn780ZAg0aRJ1VSIikkpVqvjVzxMm+ELqBx3kV0TrCrtyiU1oUnPLbVi71lfQPv54bycweTKcfbZGl0RE4qxNGxgxAm65xec77b8/TJ0adVWVVmxCk2zFpEm+8OMTT/iVce++C02bRl2ViIhUhGrVfJRp5Ej45Rf/4Pzww76mnZSKQlOcheDntLt2hc2b4euv4fe/1+iSiEg26trVl8K68EK/SvqEE3yOqyRNoSmuli+Hk0/2kHTRRR6Y9tor6qpERCRK223no0zvvONLZGmSeKkoNMXR2LE+/PrZZ/D22/Dgg97hW0REBHx+6/jx0LIlHHww3HWXn5GQrUpraDKzg83sbTP73syCmZ2cxGsOMbOxZrbWzGab2SXprDFWQoDHH/c2Ajvu6MOwv/lN1FWJiEgmat4cPv4YrrkGrrvOT9f9/HPUVWW0dI801QEmAFck82Qz2xV4D/gM6ALcDvzTzE5NW4VxsWoV9O0Ll1wC/fvD559Dq1ZRVyUiIpmsenUYONDb0Xz1lV80NGlS1FVlLAsVNHvezAJwSgjhja08507gxBBCh0L3PQbsHULYv4TX1ARqFrpre2Bhbm4uOTk5Kak9482eDSed5LdPPumtBEREREpj9myfCzt7Njz7rC8InCXy8vKoV68eQL0QQl5Jz8u0OU37A8OL3DcM6Gpm1Ut4zQ1AbqFtYfrKy0CffOKfDNauhdGjFZhERKRsWrf2tgTHHecrRvz1r5rnVESmhaYmwJIi9y0BqgE7lvCagUC9QlvztFWXaR59FI46Crp0gVGjvNO3iIhIWdWpAy+9BLffDrfe6iNPeSUOvGSdTAtNAEXPF1oJ9/udIawLIeQlNiD+KxNu2ACXXebbpZfC0KHQoEHUVYmISByYwQ03+NXXn34K++0H06dHXVVGyLTQtBgfbSqsEbARUAcu8P5LvXr53KVEh+9q1aKuSkRE4ub4433aB0CPHr4cS5bLtNA0EjiqyH1HA2NCCFplcMECX3RxwgT48ENvWikiIpIu7dv7PKcuXXw6yHPPRV1RpNLdp6mumXU2s875d+2a//cW+Y8PNLNnC73kMaClmd1rZh3M7LdAP+CedNZZKUya5AstrlwJX3zhzchERETSbYcdfBrIWWfBuef6XKcsXbcu3ed1ugIfF/r7vfm3zwAXAE2BFokHQwhzzOw44D7gcuB74A8hhNfSXGdmGzHCWwq0aOHfuM2aRV2RiIhkkxo14N//hjZt4P/+D77/3lebqFo16soqVIX1aaooZpYD5MamT9Nrr8E553iX79dfB+8jISIiEo2nnoLf/Q5OP937OdWoEXVF5VZZ+zRJYQ895N+Up5ziI0wKTCIiErX+/eGVV/yD/Ikn+ooUWSI2ocnMLjezKcDoqGtJiVtvhd//Hq680ife1ay5zZeIiIhUiN69/cP8F1/4BPEsWbMuNqEphPBwCKEj0D3qWsolBLjxRj9n/Pe/w733QpXY/DOJiEhcHH64L/g7YwYccggsXRp1RWmn38aZJAS49lq47Ta46y4PTyIiIpmqa1e/WGnZMjjiiNgHJ4WmTBEC/PGPcM893rDymmuirkhERGTbOnTwEacff4x9cFJoygQh+NylBx+Exx/3uUwiIiKVxe67+wLyMQ9OCk1RC8HX+PnnP30B3osvjroiERGR0suC4KTQFLW//Q3uvBPuuw8uuSTqakRERMqucHA68khfLzVGFJqidNddcPPNcPvtfnpORESkstt9d/joI1i0CE44AVavjrqilFFoisqgQXDddX6F3A03RF2NiIhI6nTsCO++C+PGQZ8+sHFj1BWlRGxCU6Vqbvnuu96C/pJL/PSciIhI3PTo4UuBvf8+XHRRLBb5jU1oqjTNLUeN8qVRTjjBl0kxi7oiERGR9DjmGHjmGXj6abj++qirKbdqUReQVaZNg+OPh332geefz7rVoUVEJAudfbZPDL/ySmjcGK66KuqKykyhqaL89JMHpkaN4K23oHbtqCsSERGpGH/8IyxeDH/+M7RuDSefHHVFZaLQVBHWr4fTToPcXPj6a2jQIOqKREREKtZtt8HMmXDOOb7Qb+fOUVdUarGZ05SxQvAO3198Aa+/Dq1aRV2RiIhIxatSxec3dejg83p/+CHqikpNoSndHnwQnnjCl0c58MCoqxEREYnOdtvBm2/C5s1+im7duqgrKhWFpnT66CP405/g6qvhwgujrkZERCR6O+/swWnChErX2FmhKV2+/x7OOgsOO8yXSRERERHXtaufiXnsMRg8OOpqkqbQlA4bN8KZZ0K1amotICIiUpz+/aFvX2/2/O23UVeTlNiEpozqCD5gAHz5Jbz8srcYEBERkS2ZwSOPQLt2cOqpkJcXdUXbFJvQlDEdwd980xfivfNOOOCASEsRERHJaNttB6++CkuW+NzfDF9qJTahKSMsWuT/6CefXKk7noqIiFSYdu18mZUhQ/xK8wym0JQqIUC/flCrFjz1lNaUExERSdYpp8DFF/vV5tOnR11NiRSaUuWxx2DYMBg0CBo2jLoaERGRyuUf/4BmzeDcc2HDhqirKZZCUyrMmOHr6VxyCRx7bNTViIiIVD5168J//gPffONLrmQghaby2rgRzj8fmjaFu++OuhoREZHKa7/94MYb4dZbYXT0F8MXpdBUXnfd5f+wzz7rKVlERETKbsAAX8y3f39f8D6DKDSVx4wZcMstcM010LNn1NWIiIhUftWr+wVVU6Zk3Bmc2ISmCm9uGQJccYWvoXPTTRVySBERkazQubMPSPztbzB1atTV/I+FDG8kVVpmlgPk5ubmkpOTk74DvfIKnHEGvP02/OY36TuOiIhINlqzBjp18ivqPvkkra188vLyqFevHkC9EEKJrcljM9JUoVau9JWZTz5ZgUlERCQdateGRx+FESPgxRejrgZQaCqbm2+GFSvg/vsjLkRERCTGjjwSevf2U3W//BJ1NQpNpTZxIjzwAPz1r9CyZdTViIiIxNs//gE//QS33x51JekPTWZ2mZnNMbO1ZjbWzA7aynMPNbNQzLZ7uutM2jXXQNu28Kc/RV2JiIhI/LVqBdde6+Fp5sxIS0lraDKzPsD9wG1AF+AzYKiZtdjGS9sDTQttM9JYZvI++giGD/e0W6NG1NWIiIhkh+uug5128saXEUrr1XNmNgr4JoRwaaH7vgPeCCHcUMzzDwU+BuqHEFaU8ZjpuXouBOjRw29HjdKCvCIiIhVp0CBveDlmDOy7b0p3HfnVc2ZWA9gXGF7koeHAtjpBjjOzH8zsQzM7bBvHqWlmOYkN2L7sVW/FG2945+877lBgEhERqWh9+0KHDnD99ZGVkM7TczsCVYElRe5fAjQp4TU/ABcDpwK9gWnAh2Z28FaOcwOQW2hbWI6ai7dxo7d1P+ooOPzwlO9eREREtqFaNZ8e89//wscfR1NCBRyj6Pk/K+Y+f2II0/CglDDSzHYB/gyMKGH/A4F7C/19e1IdnAYPhu++81sRERGJxkknebfw226Dw7Z6Iiot0jnStAzYxK9HlRrx69GnrfkKaFfSgyGEdSGEvMQGrCx1pVuzaZOvtnzaaSk/hyoiIiKlYOaTwT/8EEaOrPDDpy00hRDWA2OBo4o8dBTwZSl21QU/bReN11+H2bN95r6IiIhE65RTfG7TbbdV+KHTfXruXmCwmY0BRuLzlVoAjwGY2UBg5xDC+fl/vxKYC0wGagDn4vObTk1zncULwVdYPvRQ6No1khJERESkkCpVfJ7xuefCuHHQpUvFHTqdOw8hvARcCfwVGA8cDBwXQpiX/5SmeIhKqAHcA0zEezodCBwfQhiSzjpL9MUXfsXcNddEcngREREpRp8+0KYN3HlnhR42rX2aopDSPk0nnwwzZsC333qyFRERkczwz3/C1VfDvHnQrFm5dhV5n6ZKb9o0eOst+POfFZhEREQyzQUXQK1a8NhjFXZIpYGSPPAANG4MZ58ddSUiIiJSVE6ON7x8/HFYt65CDhmb0GRml5vZFGB0uXf2yy/wn//AxRdDzZrlL05ERERS74orYOlSePnlCjlcbEJTCOHhEEJHoHu5d/bKKx6c+vUrf2EiIiKSHrvv7it1PPVUhRwuNqEppZ5+Go44Alq02OZTRUREJEL9+sGIETBzZtoPpdBU1KxZ/uZfcEHUlYiIiMi2nHIK1KvnAx5pptBU1DPPwPbb+z+CiIiIZLbateH00+GFF7wpdRopNBUWArz0EvTuDdttF3U1IiIikowzzvAlz8aNS+thFJoKmzQJpk/3xCoiIiKVw2GHQcOGab+KTqGpsFdf9fOiRx4ZdSUiIiKSrGrV4NRTPTSl8RSdQlNhr74KJ56o3kwiIiKVzRlnwJw5MHZs2g4Rm9BU7uaWc+fClClw0kkprUtEREQqwCGH+NmioUPTdojYhKZyN7ccOtSH93RqTkREpPKpVs17LL7/ftoOEZvQVG5Dh0LPnp5SRUREpPLp1QtGjYIVK9Kye4UmgPXr4aOP4Nhjo65EREREyqpXL9i0CT78MC27V2gCGDMGVq3yYT0RERGpnFq2hPbtYdiwtOxeoQngs8+gTh3o0iXqSkRERKQ8Dj/cl0NLA4Um8NC0//4+iUxEREQqrwMOgGnTYNmylO9aoWnzZvjiCzjooKgrERERkfLq2dNvv/oq5btWaJozx2fZdy9bpwIRERHJIK1aQZMm8OWXKd91bEJTmZtbJhb303wmERGRys8M9t0Xxo9P+a5jE5rK3Nxy/Hho2hQaN05LXSIiIlLBOnWCiRNTvtvYhKYyGzcOOneOugoRERFJlU6dYNEi+OmnlO5WoWnCBIUmERGROOnUyW+//Talu83u0LR6tSfR9u2jrkRERERSZbfdoHp1mDw5pbvN7tA0Z47ftmkTbR0iIiKSOtWq+VV0s2endLfZHZpmzfLb1q2jrUNERERSa9ddCwZHUiS7Q9Ps2VCrll89JyIiIvHRurVGmlJqzhwfvjOLuhIRERFJpVatYO7clO4yNqGpTM0tly71rqEiIiISL02aQG4urFuXsl3GJjSVqbnljz/CTjulrygRERGJRqNGfvvjjynbZWxCU5ksW6bQJCIiEkeJ0LR0acp2md2hSSNNIiIi8ZT4/a7QlCI//wwNGkRdhYiIiKRa3bp+u2pVynaZvaEpBFi7FmrXjroSERERSbXttvPbNWtStsu0hyYzu8zM5pjZWjMba2YHbeP5h+Q/b62ZzTazS9JS2IYNfluzZlp2LyIiIhGqWdNbCq1enbJdpjU0mVkf4H7gNqAL8Bkw1MxalPD8XYH38p/XBbgd+KeZnZry4hKXICo0iYiI/M+CBQsYP348IYSoSykfMz+bVFlCE3AVMCiE8FQI4bsQwpXAAuDSEp5/CTA/hHBl/vOfAv4F/LmkA5hZTTPLSWzA9klVtmKF3y5fnuSXIiIiEm/ffPMNbdu2pUuXLgwcODDqcsqvRg1Yvz5lu0tbaDKzGsC+wPAiDw0Hepbwsv2Lef4woKuZVS/hNTcAuYW2hUkVuGSJ36Z4BWQREZHKauTIkazPDxkffPBBxNWkwMaNUL2k+FB66Rxp2hGoCiwpcv8SoKQ23E1KeH61/P0VZyBQr9DWPKnqWrXy2wMPTOrpIiIicXf66aez995707BhQ6677rqoyym/DRtSGpqqpWxPJSt6UtSKuW9bzy/ufr8zhHXA/3qkW7LryNWqldhBcs8XERGJuUaNGjF+/Pioy0idjRuhWuqiTjpHmpYBm/j1qFIjfj2alLC4hOdvBH5KaXWJCeApXJNGREREMkQIsGlT5Tg9F0JYD4wFjiry0FHAlyW8bGQxzz8aGBNC2JDSAqtV85n1Ck0iIiLxs3Gj31aSkSaAe4H+ZvZbM+tgZvcBLYDHAMxsoJk9W+j5jwEtzeze/Of/FugH3JPyysygTh345ZeU71pEREQilpvrtzk5KdtlWuc0hRBeMrOGwF+BpsAk4LgQwrz8pzTFQ1Ti+XPM7DjgPuBy4HvgDyGE19JS4I47+qK9IiIiEi+JlkL166dsl2mfCB5CeAR4pITHLijmvk+BfdJclttxR1+0V0REROIlEZpSuMZs9q49B74CskaaRERE4icxKNKwYcp2GZvQZGaXm9kUYHTSL9JIk4iISDwtXAhVq0KTklpDll5sQlMI4eEQQkege9IvatbM31QRERGJl0WLPDBVrZqyXcYmNJVJ69awYIF3DBUREZH4WLQImie3SEiyFJo2b4b586OuRERERFJp9mxo2TKlu1RoAn9jRUREJD6mToUOHVK6y+wOTS1a+LnOWbOirkRERERSZcUKWLwYdt89pbvN7tBUrRq0aweTJ0ddiYiIiKTKtGl+q9CUYp07Q5xWdBYREcl2U6f6bbt2Kd2tQlPnzjBhgk8IFxERkcpv7FgPTHXqpHS3Ck2dO8PKlTBnTtSViIiISCqMGgX77Zfy3cYmNJWpIzhAly5++803qS9KREREKtbatTBuHPTokfJdxyY0lakjOECjRrDrrvD55+kpTERERCrO+PHetFojTWlyyCHw6adRVyEiIiLlNWoU1KoFnTqlfNcKTeChaeJEWL486kpERESkPL76CvbZB2rUSPmuFZrAQ1MIOkUnIiJSmW3eDB9/DAcdlJbdKzQBtGoFu+yiU3QiIiKV2bffwpIlcPTRadm9QhOAGRx2GHzwQdSViIiISFkNHw61a8MBB6Rl9wpNCccf7/Oa5s2LuhIREREpi2HD4NBDoWbNtOxeoSmhVy9fi+6dd6KuRERERErr5599ms3xx6ftELEJTWVubplQrx4cfDC8/XZqCxMREZH0e+st2LQJevdO2yFiE5rK3NyysJNOgo8+UusBERGRyubVV30uU9OmaTtEbEJTSpx2GmzcCEOGRF2JiIiIJCs31yeBn3ZaWg+j0FRYs2Y+gezFF6OuRERERJL1zju+dEoaT82BQtOvnXWWn6JbvDjqSkRERCQZzz/vC/TusktaD6PQVNSpp/pVdM89F3UlIiIisi2LFsH778OFF6b9UApNRTVo4MN7Tz3lS6uIiIhI5nr6aV+g98wz034ohabi9O8PU6fCl19GXYmIiIiUZPNmGDQIzjgDcnLSfjiFpuIcdhi0bg1PPhl1JSIiIlKSTz6BOXN8sKMCxCY0lbu5ZWFVqsDFF/tVdEuWlL84ERERSb2HHoIOHaBnzwo5XGxCU0qaWxb2u99B9erw4IMp2Z2IiIik0KxZ8MYbcOWVYFYhh4xNaEq5HXbw4b5HHoFVq6KuRkRERAq7/35o2BDOO6/CDqnQtDVXXgl5efCvf0VdiYiIiCQsX+6/my+7DGrXrrDDKjRtTcuWPiP/vvt8eRURERGJ3uOP++K8l11WoYdNa2gys/pmNtjMcvO3wWa2wzZe87SZhSLbV+msc6v+/Gefma/16ERERKK3ahXcey+cfz40blyhh073SNPzQGfgmPytMzA4ide9DzQttB2XnvKSsM8+cPjhcMcdanYpIiIStYcfhhUr4C9/qfBDpy00mVkHPCj1DyGMDCGMBC4CfmNm7bfx8nUhhMWFtp/TVWdSbroJxo2D116LtAwREZGstnIl3HUX/Pa30KpVhR8+nSNN+wO5IYRRiTtCCF8BucC2GiocamZLzWy6mT1pZo1KeqKZ1TSznMQGbJ+S6gs7+GA49lgYMEBzm0RERKLy0EMenCIYZYL0hqYmwNJi7l+a/1hJhgLnAIcDVwPdgI/MrGYJz78BD2KJbWFZC96q226D6dN9jRsRERGpWLm5cPfdcNFF0KJFJCWUOjSZ2c3FTNQuunXNf3pxk4CshPv9BSG8FEJ4N4QwKYTwNnAssBtwfAkvGQjUK7Q1L+3XlJQuXXwxwFtugTVr0nIIERERKcFtt8G6dZGNMgFUK8NrHgJe3MZz5gKdgOKmte8EJL02SQjhBzObB7Qr4fF1wLrE3y2dXUH//ndv1/7ww35VnYiIiKTf7NnwwAMemJo1i6yMUoemEMIyYNm2nmdmI4F6ZtY9hDA6/7798NGgL5M9npk1BHYBfihtrSnXtq0vr/L3v8O550KTrZ1lFBERkZS4/nrYccfIByzSNqcphPAd3jrgSTPrYWY9gCeBd0II0xLPM7OpZnZK/p/rmtk9Zra/mbUys0OBt/GQ9nq6ai2Vv/3N16S79tqoKxEREYm/zz+HV16BgQOhTp1IS0l3n6ZzgG+B4fnbRKDoIjHt8dEngE3AXsCbwHTgmfzb/UMIK9Nca3IaNIA774TBg+Gzz6KuRkREJL42bIBLL4Vu3fwMT8QsxKxhY37bgdzc3FxycnLSc5DNm6FnT1i9Gr75BqqVZWqYiIiIbNVdd8ENN8CYMX5BVprk5eVRr149gHohhLySnqe158qiShXvFTFpEjzySNTViIiIxM/cuXDzzfDHP6Y1MJWGQlNZde3qk8IHDIB586KuRkREJD5CgCuugIYNfS5xhohNaDKzy81sCjC6wg56551Qvz7066d16URERFLllVfg3XfhwQehbt2oq/mf2ISmEMLDIYSOQPcKO2hODjz1FHz4ITz+eIUdVkREJLYWL4bLLoNTT4WTT466mi3EJjRF5uij4eKL4Zpr/PyriIiIlE0I/ju1alV49NGoq/kVhaZUuPtub0XQr59fWSciIiKl98wz8Pbb8MQTsNNOUVfzKwpNqZCTA4MGwUcfeZt3ERERKZ25c/1Kub594aSToq6mWApNqXLkkXDVVXDddd5PQkRERJKzfj306eNnbe6/P+pqSqTQlEoDB0KnTnDmmZBXYm8sERERKez662HcOHj5Zdhhh6irKZFCUyrVqAEvvghLl8Ill6gNgYiIyLa8+Sbcd5/PD+7WLepqtkqhKdXatvX2Ay+84O0IREREpHjz5sEFF3hrgT/8Iepqtik2oSmS5pYlOessH2m64goYNSrqakRERDLP+vU+naVePfjXv8As6oq2SQv2psv69XDYYX41wNix0KRJdLWIiIhkmksu8bD02Wew336RlqIFe6NWowa8+qrPazr9dA9RIiIiAo895lNZHnss8sBUGgpN6dS0qQenUaPgyiujrkZERCR6I0bA73/v229/G3U1paLQlG49e8Ijj3g7eDW+FBGRbDZzpq8pd9BB8I9/RF1NqVWLuoCs0L8/TJ8Of/oTtGqVsZ1ORURE0ubHH+GYY6BhQ3jlFahePeqKSk2hqaLccQfMmQNnnw2ffgpdu0ZdkYiISMVYvRp+8xtYtQpGjvTgVAnp9FxFqVIFnn0W9trLv3Hmzo26IhERkfTbuNFbC0yeDO++62dcKimFpopUuza89RbUqQNHH+2dw0VEROIqBG9a+d57fkpun32irqhcYhOaMqq55dY0agTDh8PKldCrF+TmRl2RiIhIetxxh18I9fjjcOyxUVdTbrEJTSGEh0MIHYHuUdeyTW3aeHCaOxdOOAHWrIm6IhERkdR66CH4y1/gppugX7+oq0mJ2ISmSmevvfzc7tix3vxyw4aoKxIREUmNJ57wPkxXX+2hKSYUmqLUsycMGeKjTn36KDiJiEjl98wzBeuv3n13pVhTLlkKTVHr1Qteew3eecevLlBwEhGRyurFF73Ld//+3tA5RoEJFJoywwkneHB6+2046ywFJxERqXyGDIFzz4XzzvM15arEL2LE7yuqrE44wdepe+stb4Cp4CQiIpXFc8/BGWf4HN1Bg2IZmEChKbOceKL3sXjzTV9qZfXqqCsSERHZukcf9dGl886DwYOhatWoK0obhaZMc9JJflXdiBHeAHP58qgrEhERKd4dd8Bll3kDy0GDoFq8V2eLTWiqNM0tk3HUUfDhh/Ddd3DIIfDDD1FXJCIiUiAEuP56uOEGbylw332xPSVXmIUQoq4hpcwsB8jNzc0lJycn6nLKZ8oUH22qWRM++ABat466IhERyXabN8Pll/tk73vvhT/9KeqKyi0vL4969eoB1Ash5JX0vPjHwsqsY0f44gsf7jzgAJg4MeqKREQkm61dC+ec480rBw2KRWAqDYWmTNeyJXz2GTRrBgcfDJ9+GnVFIiKSjZYt8+kjr78OL7/s/ZiyjEJTZdCoEXz8Mey7r3/D/vvfUVckIiLZZMYM2H9/mDbNfx+demrUFUVCoamyyMmB99+HCy/0dH/ddX5eWUREJJ0+/xx69PCpIl995eEpS6U1NJnZADP70sxWm9mKJF9jZnazmX1vZmvM7BMz2yOddVYa1asXTLy7+27o3Rt++SXqqkREJK5eeAGOOAI6dYIvv8z6C5LSPdJUA3gFeLQUr7kWuAq4AugGLAY+MLPtU19eJWTmE+/eftvbEhx4ICxYEHVVIiISJ5s3w//9n69QceaZMGwY1K8fdVWRS2toCiHcFEK4D/g2meebmQFXAreFEIaEECYBfYHtgLNLeE1NM8tJbEB2hKvjj/fUv2IFdO8OI0dGXZGIiMRBXh6cfDLcdhvcdRc8/TTUqBF1VRkh0+Y07Qo0AYYn7gghrAM+BXqW8JobgNxC28I015g59toLRo2CNm38yrp//tMbjomIiJTF5Mn+QXzECF+d4ppr/AyHAJkXmprk3y4pcv+SQo8VNRCoV2hrnp7SMlTjxn4lwxVXwB//6EOpmuckIiKl9dxzHphq1IDRo+HYY6OuKOOUOjTlT9IO29i6lrOuosMlVsx9/sQQ1oUQ8hIbsLKcx658qlf3FvYvvQTvvOPf9FOnRl2ViIhUBuvWeYfvc8+F007zK+R22y3qqjJSWUaaHgI6bGObVMZ6FuffFh1VasSvR5+kqDPO8E8HAN26efMxERGRksybBwcdBE89BY8/7vOXttsu6qoyVqmXIw4hLAOWpaEWgDl4cDoKGAdgZjWAQ4Dr0nTMeOnQwYPTRRdBnz5+Xvruu6F27agrExGRTPLGG9CvH2y/vS/Z1bW8J4niL919mlqYWWegBVDVzDrnb3ULPWeqmZ0CEHz14PuBv5jZKWa2J/A0sBp4Pp21xkrduvD88/DQQ742ULduWrdORETc6tVwySVwyil+EdHYsQpMSUr3RPC/4SNGtwB18/88Dij8r9Men8CdcBcenB4BxgA7A0eHELJvrlJ5mPk56jFjoEoVn+f0wAPqIi4iks0mTPCA9OyzfjpuyBBo2DDqqioNCzG7RD2/V1Nubm4uOTk5UZeTGdauheuv99DUq5efs25S0sWIIiISOyF4W5prr/VpHC+84LcCQF5eHvXq1QOol39RWbEyreWApEOtWnD//TB0KIwf7/2d3n476qpERKQizJvni71feSVcdplfHafAVCYKTdnkmGN8blOPHnDiidC3L/z8c9RViYhIOoTgp+D23BOmT4fhw709Ta1aUVdWacUmNJnZ5WY2BRgddS0ZrVEjeOst+Ne/4M03YY89/AoKERGJj/nzfTrGJZf42nGTJvlok5RLbEJTCOHhEEJHoHvUtWQ8M7jwQm+X37WrX0Fx1lmwLF2dJEREpEKE4D2X9twTvvsO3n8fnnwSNMc3JWITmqQMdt7ZR53+8x8ftu3YEV55JeqqRESkLGbN8mkYF10Ep5/uo0u9ekVdVawoNGU7MzjnHB91Ougg7yp+8sk+tCsiIplv3Tq47TYfXZo6Fd57z3v01au37ddKqSg0iWvSBF57zUeavv7aR53+8Q/YsCHqykREpCSffAKdO8PNN8Mf/gBTpmih3TRSaJItnXaanwfv18/7eXTtCiNHRl2ViIgU9uOPfgX0YYdBgwbwzTdw551Qp07UlcWaQpP8Wk6ON8IcPRpq1ICePeG3v4UlWjNZRCRSmzb5xO727b3f3pNPwmefef89STuFJinZvvt6E7RHH/X2BLvtBvfeq1N2IiJR+PRTX0v04ovhhBNg2jTo39+XypIKoXdatq5qVe/zMWMGnHceXHMNdOoEw4ZFXZmISHaYPdunThx6KFSvDl98Ac88AzvtFHVlWSc2oUnNLdOsQQN46CEYNw4aN/bLWo8+2pdlERGR1MvLg+uu8yVPvvrK28OMHOlTJiQSsQlNam5ZQTp1go8/9i7i8+fDPvvA+ef72kYiIlJ+iXlL7dr5h9W//MVPxZ1zjk7FRUzvvpSeGZx0kjdOe/RRb4zZvr2fulu+POrqREQqpxD8A+nee/u8pV69PCzddJOuissQCk1SdtWqwe9+BzNn+iehRx+FNm28v9PatVFXJyJSeXz0Eey/vy9r1aSJX7387LPQvHnUlUkhCk1SfnXrwl//6i38zzzTz8HvvrsvCqwr7URESvb1176Q7hFH+EjTf//rW7duUVcmxVBoktRp3BgeeaRgIeB+/fy0ncKTiMiWJk2CU0+F7t3h++9hyBCf7H3EEVFXJluh0CSp1749vPoqTJjgvZ4S4WnQIIUnEcluEyZ4+4C99oKxY+Hpp2HiRD8tZxZ1dbINCk2SPp06+Vp2Eyf6yFP//t4g86mnFJ5EJLuMHeuLoXfu7K1bBg3y/nd9+3o/PKkUFJok/fbaC15+Gb791oeiL77YL6V94glfnVtEJK5GjoTf/MY/OE6Z4k0pp03zpamqV4+6Oiml2IQmNbesBPbcE156ycNTjx7eabxVKxg4UK0KRCQ+Nm/21gEHHuiNKGfNguee88XQzz/frzyWSik2oUnNLSuRPfaAF1+EqVPhxBPhllugRQu46ipvmCkiUhmtWQOPP+5XD59yijeifPNNvzjm7LN1Gi4GYhOapBLabTf/ATNvHvzxj/Dvf3ufp/PO83lQIiKVwY8/Fnz4u+wyb0751VcwYoR/MFQX79jQv6REr3FjuPVWWLAA7rnHf9DsvTccfji8/rovKSAikmlmzPCQ1KIF3Hkn9OkD06f7BTD77Rd1dZIGCk2SOerW9RGnmTPhhRd8knjv3j76dNdd8NNPUVcoItlu0yZ45x049lgfLX/tNRgwwD/0PfSQ/7yS2FJoksxTvbp3Fv/iC79M97DDvON48+betmDChKgrFJFs89NP/uGtXTs44QRYtsynFMybBzfeCA0bRl2hVAALIURdQ0qZWQ6Qm5ubS05OTtTlSKr8+KOv+v3oo7BwoV++27evh6sdd4y6OhGJoxBg1Cife/nii35VXJ8+cMUV3j5FYiMvL4969eoB1Ash5JX0PIUmqVw2boS33/ZeJ+++6/cdf7wHqOOOg5o1o61PRCq/Zctg8GBvQDl5ss9ZuvRSX91gp52irk7SQKFJoSn+fvzRP/09+yyMGQMNGvjIU9++vtilliQQkWRt2uQL5Q4a5D2WwDt49+/v68GpXUCsZV1oMrPLgcvxeVrtFZqyzOTJ/slw8GBf/LJ9e28id955sMsuUVcnIplqzhwfuf73v71P3B57+IjSuedqVCmLZF1oStBIU5bbtAk++shHn157Ddau9Ynk55/vK4rXrRt1hSIStWXLfGmn556DL7/0nwtnnulhab/9NEqdhRSaFJpk5UoPTs88A598Attt58Hp/PM9SGm4XSR7rFrl3bmfew6GD/dJ3r16eafuk07SB6osp9Ck0CSFzZsH//mPB6gZM7x9wbnneoDq0CHq6kQkHTZsgA8+gOef93lKq1b5WnDnnAOnn67Tb/I/Ck0KTVKcxCXEzzzjk8hXrPBJ4+efr/YFInGwbp2foh8yxIPSsmXQsaMHpbPOgl13jbpCyUAZEZrMbABwPNAZWB9C2CGJ1zwN9C1y96gQQo8kj6nQJMlZt847+z7zDAwd6oHqkEP8FN4pp0DTplFXKCLJWLUK3n/fg9I770Benjeh7N3bg1KnTpqnJFuVKaHpFmAF0BzoV4rQ1Bi4sNDd60MIPyd5TIUmKb2lS32du9deg48/9n5Qe+/tcx6OPhoOOABq1Yq6ShFJWL7ce7YNGQLDhvlFH507e1Dq3dtHlxSUJEkZEZr+dxCzC4D7SxGadgghnFzGYyk0Sfn8/LOPPA0f7tvixVC7to9CJUJUhw76gSxSkUKAqVPhvfd8GzHCP9zsv3/B6HDr1lFXKZVUZQ9NJwPr8VGqT4EBIYSlJTy/JlC4DfT2wEKFJkmJEGDSJP8kO3y4/6Bet84nkh99tG9HHql1p0TSYc0aH/lNBKU5c3zE9/DDfSWAk0+GZs2irlJioDKHpj7AL8A8YFfg70A1YN8Qwrpinn8zcFPR+xWaJC3WrPHglBiFmjTJR5z23bdgFKpHD6hRI+pKRSqfEGD6dL/ibehQn9C9di20auUh6bjjvF1I7dpRVyoxk7bQVFJIKaJbCGFModdcQJKhqZjjNcUD1JkhhCHFPK6RJonOokX+A374cL9dtsz7vRx2WEGIattWp/JESvLDD/Dhh77997++IHe1anDQQQVBaffd9X9I0iqdoWlHYFvXZc8NIawt9JoLKGNoyn/9DOCpEMKdSTxXc5okGps3w7hxBaNQX3zhfWJatfLw1KuXn1bYYYeoKxWJzk8/weef+2m3//7Xl0ACv8LtyCN9nbeDD1azSalQlfb0XDGvbQgsAi4OITybxPMVmiQzrFwJn37qAWrYMD/tUKWKL9OQCFHduvmnapE4CsHXc/vsM98+/xymTPHHWrSAo47ykHT44dC4cbS1SlbLiNBkZi2ABsCJwDXAQfkPzQwh/JL/nKnADSGE182sLnAz8BrwA9AKuB1oAXQIIaxM4pgKTZKZ5s71U3jDhvmpiBUroF4971C8334+F6p7d6hfP+pKRcpm82YfOfr884KgtHChP9axIxx4oJ92O/BAaNlSp9wkY2RKaHqaXzeqBDgshPBJ/nMCcGEI4Wkzqw28AXQBdsCD08fA/4UQFiR5TIUmyXwbN8KYMT4KNXKkdylfvtwf2203D1D77edbp05QvXq09YoUZ9Ei+Ppr/17++mvfli/30dN99y0ISAccoG77ktEyIjRFQaFJKqUQfE28UaMKtvHjPVzVquW/gAqPRrVooU/pUrF+/NHDUSIgjRnjk7jBT6116+bfmwce6Ld16kRbr0gpKDQpNEllt2aNTywvHKTmzvXH6tf3juWdOxfcdugANWtuZYciSQgBFiyAb7/1bexYD0nz5vnj9et7QOrateB2550V4qVSU2hSaJI4WrLEf4FNmODb+PEwc6b/oqtWzeeN7L23b3vs4X/fZRf9QpPi5eZ6r7GJEwtC0rff+v0AOTkeyLt1KwhIrVvr+0liJ+tCk5ldDlwOVAHaKzRJ1vjlF/9FN358QZD69ltYvdofr1PHR6E6dizY2rf31d41Vyr+Nm3yEcrp0wu2adP8dkH+VNFq1fx7olMn2Gsv3zp1UuCWrJF1oSlBI00i+FVM8+f75d3ffee3iS0v/+dB1areQ6ptW18RPrG1betzpnSqr/LYvNlHIWfO3DIUTZ8Os2bB+vX+vFq1/N94t938do89PBy1b69/b8lqCk0KTSK/FgJ8/73/Mp0xY8tt1ixfVw98dKFZMw9VRbfmzX0Oy/bbR/ZlZJ3Vq31UaP583+bNK/jz/Pn+WCIYmfnl/O3bezjabbeCP++yi/cKE5EtKDQpNImUzqZN3lNn5kz/pTx37pbbwoUeuhJycjw8JUJU8+bQpIlfSdW4MTRq5Lf16ukUT0nWrfMRoiVLYPHiLW8XLiwIRcuWFbzGDJo29dHAli39tkULD0Rt20KbNj6iJCJJU2hSaBJJrfXr/Rd5Ylu0qOA28efFi71NQmE1ahQEqPr1fRmZxG3hreh99etn/i//EPx9+eWXgm3lSu9V9PPPW9+WLvUGp4WZeT+jxo09hCYCUeFt5521ILRIiiUbmrR+g4gkp0YNv3KqdeuSnxOCB4YlSzwUJEZREn9escK3efP8dvlyvy0atAofs25dX9V+W1v16n7qqTTbpk2+PuD69X5beCt63+rVBcFo1aqCP5dUO/g8oYYNoUEDD4ENGvik/Pr1PUgmRuYStzvtpGV1RDKY/neKSOqYeTBIhINkhOCBJBGoCoepFSs8oKxZU/K2fLm/ftMmnxBd0lb08U2bfDJ8jRoeuKpX3/LPhf9eq5Z/TXXrFmx16mz598Jb4j2oXTttb7WIVDyFJhGJlpkHkDp1/NSTiEiG0mUUIiIiIkmITWgys8vNbAowOupaREREJH5iE5pCCA+HEDoC3aOuRUREROIntnOa8vJKvGJQRERE5H+SzQxx7NO0M7Aw6jpERESk0mkeQlhU0oNxDE0GNANWJvH07fGA1TzJ52/NaFJzajCu+9F7XXH70ntdcfuK83udyn3pva64fcX1vU7lvkraz/bA92ErwSh2p+fyv9gSU2JhVrC0w8qtdQBNcl+by7uPmO8n8Ue912nel97rittXnN/rTKtJ73XF7ScT3+tU7msr+9nmvmMzETwDPKz9VJhM+9pS+R5l2vudae+R3uuK208q96X3uuL2Fdf3OpX7KvN+Ynd6rjQS69SxjbVmpPz0XlccvdcVR+91xdF7XXH0Xpcs20ea1gG35N9Keum9rjh6ryuO3uuKo/e64ui9LkFWjzSJiIiIJCvbR5pEREREkqLQJCIiIpIEhSYRERGRJCg0iYiIiCRBoUlEREQkCQpN+cxsrpmFItsdUdcVZ2ZW08zG57/XnaOuJ47M7C0zm29ma83sBzMbbGbNoq4rbsyslZkNMrM5ZrbGzGaZ2S1mViPq2uLIzAaY2ZdmttrMVkRdT9yY2WX538trzWysmR0UdU2ZQqFpS38Fmhbabo22nNi7C/g+6iJi7mPgDKA9cCrQBng10oriaXf85+nvgD2APwGXALdHWVSM1QBeAR6NupC4MbM+wP3AbUAX4DNgqJm1iLKuTKE+TfnMbC5wfwjh/ohLyQpmdixwL/6LfDLQJYQwPtKisoCZnQi8AdQMIWyIuJxYM7NrgEtDCK2jriWuzOwC/Of2DhGXEhtmNgr4JoRwaaH7vgPeCCHcEF1lmUEjTVu6zsx+yj9lNEBD6+lhZo2BJ4HzgNURl5M1zKwBcA7wpQJThagH/Bx1ESLJyv+dty8wvMhDw4GeFV9R5lFoKvAAcCZwGPAQcCXwSJQFxZH58tlPA4+FEMZEXE5WMLM7zWwV8BPQAjgp4pJiz8zaAL8HHou6FpFS2BGoCiwpcv8SoEnFl5N5Yh2azOzmYiZ3F926AoQQ7gshfBpCmBhCeAqfj9DPzBpG+1VUDqV4r38P5AADIy650irN93W+u/G5CUcDm4Bn88OrbEMZ3mvyJ9q/D7yS/7NEklCW91rSpui8HSvmvqwU6zlNZrYjnpy3Zm4IYW0xr90ZWAj0CCGMSkd9cZLsew28CJzAlv8Bq+K/zJ8LIfRNS4ExUs7v6+bAAqBnCGFkOuqLk9K+1/mB6WNgFHBBCGFzmkuMjbJ8X2tOU2rln55bDZweQni90P0PAJ1DCIdEVlyGqBZ1AekUQlgGLCvjy7vk3/6QonJiLdn32sz+ANxY6K5mwDCgD/6LRrahnN/XiRGmmikqJ9ZK817nf9D6GBgLXKjAVDrl/L6WFAghrDezscBRwOuFHjoKeDOaqjJLrENTssxsf6AH/gMvF+gG3Ae8FUKYH2VtcVP0/TSzX/L/OCuEsDCCkmLLzLoD3YHPgeVAa+BvwCxAo0wplD/C9AkwH/gzsFPiDGgIYXF0lcVT/uXvDfA5elUL9XmbGUL4pcQXSjLuBQab2Rj858TF+Pus+XkoNCWsw0c6bsI/gc/Dr+66K8qiRMppDdAbuAWog4+avg+cGUJYF2VhMXQ00DZ/Kxr+NX8s9f4GFD6VPy7/9jA8vEoZhRBeyp/Lm+hbOAk4LoQwL9rKMkOs5zSJiIiIpEqsr54TERERSRWFJhEREZEkKDSJiIiIJEGhSURERCQJCk0iIiIiSVBoEhEREUmCQpOIiIhIEhSaRERERJKg0CQiIiKSBIUmERERkSQoNImIiIgk4f8BoiC/h/LYWwcAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "centro + orbita_m" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "orbita_M = plot(sol_r.rhs().subs(ep==2),(vp,-sqrt(2)/3,sqrt(2)/3), polar=True, color='red', axes=False, frame=True, title=r'Órbita hiperbólica ($\\epsilon<1$)')" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "Graphics object consisting of 5 graphics primitives" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "orbita_0+centro+orbita_m+orbita_M+orbita_1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculando a Constante na Lei de Deslocamento de Wien" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A [lei do deslocamento de Wien](https://en.wikipedia.org/wiki/Wien%27s_displacement_law) é a lei da física que relaciona o comprimento de onda do pico de emissão de radiação eletromagnética de corpo negro e sua temperatura:\n", "$$\n", "{\\displaystyle \\lambda _{\\text{max}}={\\frac {b}{T}}}\n", "$$\n", "onde \n", "\n", "- $\\displaystyle \\lambda _{\\text{max}}$ é o comprimento de onda do pico de intensidade da radiação eletromagnética;\n", "\n", "- ${\\displaystyle T\\,}$ é a temperatura absoluta do corpo negro;\n", "\n", "- ${\\displaystyle b\\,}$ é a constante de proporcionalidade, chamada *constante de dispersão de Wien*.\n", "\n", "Vamos calcular a constante $b$ usando a lei de Planck para a radiação de um corpo negro \n", "$$\n", "{\\displaystyle u(\\lambda ,T)={2hc^{2} \\over \\lambda ^{5}}{1 \\over e^{hc/\\lambda kT}-1}.}\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "| Constantes | | Unidade |\n", "| :-----------------: | :------------------------- | :--------------- |\n", "| ${\\displaystyle h}$ | constante de Planck | J$\\cdot$s |\n", "| ${\\displaystyle c}$ | velocidade da luz no vácuo | m$\\cdot$s$^{-1}$ |\n", "| ${\\displaystyle e}$ | número de Euler | sem dimensão |\n", "| ${\\displaystyle k}$ | constante de Boltzmann | J$\\cdot$K$^{-1}$ |" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "var('h c k', domain='positive')\n", "la = var('la', latex_name = r'\\lambda', domain='positive')\n", "lam = var('lam', latex_name = r'\\lambda_{\\text{max}}', domain='positive')\n", "u(la ,T) = 2*h*c^2/(la^5)*1/(e^(h*c/(k*la*T))-1)" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{2 \\, c^{2} h}{{\\lambda}^{5} {\\left(e^{\\left(\\frac{c h}{T k {\\lambda}}\\right)} - 1\\right)}}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{2 \\, c^{2} h}{{\\lambda}^{5} {\\left(e^{\\left(\\frac{c h}{T k {\\lambda}}\\right)} - 1\\right)}}\n", "\\end{math}" ], "text/plain": [ "2*c^2*h/(la^5*(e^(c*h/(T*k*la)) - 1))" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "u(la,T)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{10 \\, c^{2} h}{{\\lambda_{\\text{max}}}^{6} {\\left(e^{\\left(\\frac{c h}{T k {\\lambda_{\\text{max}}}}\\right)} - 1\\right)}} + \\frac{2 \\, c^{3} h^{2} e^{\\left(\\frac{c h}{T k {\\lambda_{\\text{max}}}}\\right)}}{T k {\\lambda_{\\text{max}}}^{7} {\\left(e^{\\left(\\frac{c h}{T k {\\lambda_{\\text{max}}}}\\right)} - 1\\right)}^{2}} = 0$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{10 \\, c^{2} h}{{\\lambda_{\\text{max}}}^{6} {\\left(e^{\\left(\\frac{c h}{T k {\\lambda_{\\text{max}}}}\\right)} - 1\\right)}} + \\frac{2 \\, c^{3} h^{2} e^{\\left(\\frac{c h}{T k {\\lambda_{\\text{max}}}}\\right)}}{T k {\\lambda_{\\text{max}}}^{7} {\\left(e^{\\left(\\frac{c h}{T k {\\lambda_{\\text{max}}}}\\right)} - 1\\right)}^{2}} = 0\n", "\\end{math}" ], "text/plain": [ "-10*c^2*h/(lam^6*(e^(c*h/(T*k*lam)) - 1)) + 2*c^3*h^2*e^(c*h/(T*k*lam))/(T*k*lam^7*(e^(c*h/(T*k*lam)) - 1)^2) == 0" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "u0 = diff(u(lam,T),lam)==0;u0" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[{\\lambda_{\\text{max}}} = \\frac{c h e^{\\left(\\frac{c h}{T k {\\lambda_{\\text{max}}}}\\right)}}{5 \\, {\\left(T k e^{\\left(\\frac{c h}{T k {\\lambda_{\\text{max}}}}\\right)} - T k\\right)}}\\right]$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[{\\lambda_{\\text{max}}} = \\frac{c h e^{\\left(\\frac{c h}{T k {\\lambda_{\\text{max}}}}\\right)}}{5 \\, {\\left(T k e^{\\left(\\frac{c h}{T k {\\lambda_{\\text{max}}}}\\right)} - T k\\right)}}\\right]\n", "\\end{math}" ], "text/plain": [ "[lam == 1/5*c*h*e^(c*h/(T*k*lam))/(T*k*e^(c*h/(T*k*lam)) - T*k)]" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(u0,lam)" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{10 \\, c^{2} h}{e^{\\left(\\frac{c h}{T k {\\lambda_{\\text{max}}}}\\right)} - 1} + \\frac{2 \\, c^{3} h^{2} e^{\\left(\\frac{c h}{T k {\\lambda_{\\text{max}}}}\\right)}}{T k {\\lambda_{\\text{max}}} {\\left(e^{\\left(\\frac{2 \\, c h}{T k {\\lambda_{\\text{max}}}}\\right)} - 2 \\, e^{\\left(\\frac{c h}{T k {\\lambda_{\\text{max}}}}\\right)} + 1\\right)}} = 0$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{10 \\, c^{2} h}{e^{\\left(\\frac{c h}{T k {\\lambda_{\\text{max}}}}\\right)} - 1} + \\frac{2 \\, c^{3} h^{2} e^{\\left(\\frac{c h}{T k {\\lambda_{\\text{max}}}}\\right)}}{T k {\\lambda_{\\text{max}}} {\\left(e^{\\left(\\frac{2 \\, c h}{T k {\\lambda_{\\text{max}}}}\\right)} - 2 \\, e^{\\left(\\frac{c h}{T k {\\lambda_{\\text{max}}}}\\right)} + 1\\right)}} = 0\n", "\\end{math}" ], "text/plain": [ "-10*c^2*h/(e^(c*h/(T*k*lam)) - 1) + 2*c^3*h^2*e^(c*h/(T*k*lam))/(T*k*lam*(e^(2*c*h/(T*k*lam)) - 2*e^(c*h/(T*k*lam)) + 1)) == 0" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "u1 = (u0*lam^6).expand();u1" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}x = \\frac{c h}{T k {\\lambda_{\\text{max}}}}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}x = \\frac{c h}{T k {\\lambda_{\\text{max}}}}\n", "\\end{math}" ], "text/plain": [ "x == c*h/(T*k*lam)" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqx = x == c*h/(lam*T*k);eqx" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\lambda_{\\text{max}}} = \\frac{c h}{T k x}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\lambda_{\\text{max}}} = \\frac{c h}{T k x}\n", "\\end{math}" ], "text/plain": [ "lam == c*h/(T*k*x)" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eql = solve(eqx,lam)[0];eql" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{2 \\, c^{2} h x e^{x}}{e^{\\left(2 \\, x\\right)} - 2 \\, e^{x} + 1} - \\frac{10 \\, c^{2} h}{e^{x} - 1} = 0$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{2 \\, c^{2} h x e^{x}}{e^{\\left(2 \\, x\\right)} - 2 \\, e^{x} + 1} - \\frac{10 \\, c^{2} h}{e^{x} - 1} = 0\n", "\\end{math}" ], "text/plain": [ "2*c^2*h*x*e^x/(e^(2*x) - 2*e^x + 1) - 10*c^2*h/(e^x - 1) == 0" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "u2 = u1.subs(eql);u2" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}x = 5 \\, {\\left(e^{x} - 1\\right)} e^{\\left(-x\\right)}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}x = 5 \\, {\\left(e^{x} - 1\\right)} e^{\\left(-x\\right)}\n", "\\end{math}" ], "text/plain": [ "x == 5*(e^x - 1)*e^(-x)" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqx2 = solve(u2,x)[0];eqx2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercício" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Encontre uma solução numérica para a equação\n", "$$x = 5 \\, {\\left(e^{x} - 1\\right)} e^{\\left(-x\\right)}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "** `find_root(equação, min, max)`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(eqx2,x,(x,0,10))" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}x = 4.96511423174416$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}x = 4.96511423174416\n", "\\end{math}" ], "text/plain": [ "x == 4.96511423174416" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqx3 = x == find_root(eqx2,4,6);eqx3" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}T {\\lambda_{\\text{max}}} = \\frac{0.20140523527264692 \\, c h}{k}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}T {\\lambda_{\\text{max}}} = \\frac{0.20140523527264692 \\, c h}{k}\n", "\\end{math}" ], "text/plain": [ "T*lam == 0.20140523527264692*c*h/k" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eql2 = (eql*T).subs(eqx3);eql2" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [], "source": [ "from scipy.constants import c as nc\n", "from scipy.constants import h as nh\n", "from scipy.constants import k as nk" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [], "source": [ "constantes = {c:nc, k:nk, h:nh}" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{c : 299792458.0, k : 1.380649 \\times 10^{-23}, h : 6.62607015 \\times 10^{-34}\\right\\}$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{c : 299792458.0, k : 1.380649 \\times 10^{-23}, h : 6.62607015 \\times 10^{-34}\\right\\}\n", "\\end{math}" ], "text/plain": [ "{c: 299792458.0, k: 1.380649e-23, h: 6.62607015e-34}" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "constantes" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}T {\\lambda_{\\text{max}}} = 0.0028977719551852403$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}T {\\lambda_{\\text{max}}} = 0.0028977719551852403\n", "\\end{math}" ], "text/plain": [ "T*lam == 0.0028977719551852403" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eql2.subs(constantes)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Logo,\n", "$$b \\approx 2,89777\\, \\text{mm}\\cdot\\text{K}$$" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}6377929856000.104$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}6377929856000.104\n", "\\end{math}" ], "text/plain": [ "6377929856000.104" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "u(500/(10^9),4500).subs(constantes)" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(u(la/(10^9),4500).subs(constantes),0,3000, frame=True, axes=False)" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "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": [ "plot(u(la/(10^9),4500).subs(constantes),0,3000, color=colors.darkgreen,axes=False, frame=True, gridlines=True, axes_labels=[r'$\\lambda\\, (nm)$',r'$u(\\lambda)$'], legend_label='$T=4500$')" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [], "source": [ "lista_u = [u(la/(10^9),k).subs(constantes) for k in [3500, 4000, 4500, 5000, 5500]]" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\frac{1.1910429723971882 \\times 10^{29}}{{\\lambda}^{5} {\\left(e^{\\frac{4110.791078582668}{{\\lambda}}} - 1\\right)}}, \\frac{1.1910429723971882 \\times 10^{29}}{{\\lambda}^{5} {\\left(e^{\\frac{3596.9421937598345}{{\\lambda}}} - 1\\right)}}, \\frac{1.1910429723971882 \\times 10^{29}}{{\\lambda}^{5} {\\left(e^{\\frac{3197.2819500087417}{{\\lambda}}} - 1\\right)}}, \\frac{1.1910429723971882 \\times 10^{29}}{{\\lambda}^{5} {\\left(e^{\\frac{2877.553755007867}{{\\lambda}}} - 1\\right)}}, \\frac{1.1910429723971882 \\times 10^{29}}{{\\lambda}^{5} {\\left(e^{\\frac{2615.9579590980616}{{\\lambda}}} - 1\\right)}}\\right]$ " ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\frac{1.1910429723971882 \\times 10^{29}}{{\\lambda}^{5} {\\left(e^{\\frac{4110.791078582668}{{\\lambda}}} - 1\\right)}}, \\frac{1.1910429723971882 \\times 10^{29}}{{\\lambda}^{5} {\\left(e^{\\frac{3596.9421937598345}{{\\lambda}}} - 1\\right)}}, \\frac{1.1910429723971882 \\times 10^{29}}{{\\lambda}^{5} {\\left(e^{\\frac{3197.2819500087417}{{\\lambda}}} - 1\\right)}}, \\frac{1.1910429723971882 \\times 10^{29}}{{\\lambda}^{5} {\\left(e^{\\frac{2877.553755007867}{{\\lambda}}} - 1\\right)}}, \\frac{1.1910429723971882 \\times 10^{29}}{{\\lambda}^{5} {\\left(e^{\\frac{2615.9579590980616}{{\\lambda}}} - 1\\right)}}\\right]\n", "\\end{math}" ], "text/plain": [ "[(1.1910429723971882e+29)/(la^5*(e^(4110.791078582668/la) - 1)),\n", " (1.1910429723971882e+29)/(la^5*(e^(3596.9421937598345/la) - 1)),\n", " (1.1910429723971882e+29)/(la^5*(e^(3197.2819500087417/la) - 1)),\n", " (1.1910429723971882e+29)/(la^5*(e^(2877.553755007867/la) - 1)),\n", " (1.1910429723971882e+29)/(la^5*(e^(2615.9579590980616/la) - 1))]" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lista_u" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 5 graphics primitives" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(lista_u,0,3000, axes=False, frame=True, gridlines=True, axes_labels=[r'$\\lambda\\, (nm)$',r'$u(\\lambda)$'])" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.2", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }