Vector Elliptical Perihelion.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import ellipsefns\n",
    "#getfocus, getsemiminor, theoreticalx, theoreticaly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import initdat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "angle 0.0\n",
      "0.5\n",
      "(array([3.14159265, 0.        ]), 0.0, 50, 0.5, array([1., 1.]))\n"
     ]
    }
   ],
   "source": [
    "\n",
    "rad0=50\n",
    "ecc0=0.5\n",
    "theta0= 0. #math.pi/6. #math.pi/6.\n",
    "mass0=1.0\n",
    "initdateqellipse=initdat.InitialDataEqualMassConic(rad0,ecc0,theta0,mass0)\n",
    "print(initdateqellipse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "VERIFIED FOR THETA=-45,45,135,180,90,30,-30. VERIFIED FOR ECC =0.001, 0.1,0.5, 0.7, 0.9, 0.95 VERIFIED FOR RAD0=50,75 100 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import getxyuvtwoellipse_apper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "useperihelion=True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initdat 50 [3.14159265 0.        ] 0.5 [-1.  1.] [1.2246468e-16 0.0000000e+00]\n",
      "coordsep 50\n",
      "pi\n",
      "zero\n",
      "[-50.  50.]\n",
      "[0. 0.]\n",
      "(array([1., 1.]), array([[-25.        ,   0.        ,   0.        ,  -0.        ,\n",
      "         -0.12247449,   0.        ],\n",
      "       [ 25.        ,   0.        ,   0.        ,  -0.        ,\n",
      "          0.12247449,   0.        ]]), array([[ 0.0004, -0.    ,  0.    ],\n",
      "       [-0.0004, -0.    ,  0.    ]]))\n"
     ]
    }
   ],
   "source": [
    "xyuvaeqellipse=getxyuvtwoellipse_apper.getxyuveqtwoellipses(initdateqellipse,useperihelion)\n",
    "print(xyuvaeqellipse)\n",
    "masses,xvec,avec=xyuvaeqellipse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import RK4implicit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import OrbitDiffEq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1. 1.] [[-25.           0.           0.          -0.          -0.12247449\n",
      "    0.        ]\n",
      " [ 25.           0.           0.          -0.           0.12247449\n",
      "    0.        ]] 0.0\n",
      "[1. 1.] [[-25.           0.           0.          -0.          -0.12247449\n",
      "    0.        ]\n",
      " [ 25.           0.           0.          -0.           0.12247449\n",
      "    0.        ]] 0.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<OrbitDiffEq.OrbitDiffEq at 0x7f079409bd30>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "masses, xvec,avec=xyuvaeqellipse\n",
    "ODEeq= OrbitDiffEq.OrbitDiffEq(masses,xvec,avec,0.0)\n",
    "ODEeq.print2D()\n",
    "ODEeq.print2D()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([1., 1.]), array([[-25.        ,   0.        ,   0.        ,  -0.        ,\n",
      "         -0.12247449,   0.        ],\n",
      "       [ 25.        ,   0.        ,   0.        ,  -0.        ,\n",
      "          0.12247449,   0.        ]]), array([[ 0.0004, -0.    ,  0.    ],\n",
      "       [-0.0004, -0.    ,  0.    ]]))\n"
     ]
    }
   ],
   "source": [
    "print(xyuvaeqellipse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import timestep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "numsteps=6000*10\n",
    "dt=0.1\n",
    "outputevery=1\n",
    "nptimes, npstar1x, npstar2x, npstar1a, npstar2a= timestep.timestep(numsteps,dt,xyuvaeqellipse,outputevery)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.50000000e+01,  0.00000000e+00,  0.00000000e+00,\n",
       "        -0.00000000e+00, -1.22474487e-01,  0.00000000e+00],\n",
       "       [-2.49999980e+01, -1.22474484e-02,  0.00000000e+00,\n",
       "         3.99999973e-05, -1.22474477e-01,  0.00000000e+00],\n",
       "       [-2.49999920e+01, -2.44948948e-02,  0.00000000e+00,\n",
       "         7.99999787e-05, -1.22474448e-01,  0.00000000e+00],\n",
       "       ...,\n",
       "       [ 6.50765680e+01, -2.58921131e+01,  0.00000000e+00,\n",
       "         3.01846656e-02,  3.50405295e-02,  0.00000000e+00],\n",
       "       [ 6.50795863e+01, -2.58886090e+01,  0.00000000e+00,\n",
       "         3.01799302e-02,  3.50424134e-02,  0.00000000e+00],\n",
       "       [ 6.50826040e+01, -2.58851046e+01,  0.00000000e+00,\n",
       "         3.01751950e-02,  3.50442969e-02,  0.00000000e+00]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npstar1x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "t = np.linspace(0, 2*math.pi, 100)\n",
    "xax=-200+np.arange(0,400)\n",
    "plt.ylim(-200,200)\n",
    "plt.xlim(-200,200)\n",
    "plt.title(\"Elliptical Orbit, RK4, a=\"+str(rad0)+\", e=\"+ str(ecc0)+\", theta=\"+str(round(180*theta0/math.pi))+ \" degrees\")\n",
    "plt.plot(ellipsefns.getxtheory(theta0,ecc0,rad0,t,1),ellipsefns.getytheory(theta0,ecc0,rad0,t,1),'b')\n",
    "plt.plot(ellipsefns.getxtheory(theta0,ecc0,rad0,t,-1),ellipsefns.getytheory(theta0,ecc0,rad0,t,-1),'g')\n",
    "plt.plot(npstar1x[:,0],npstar1x[:,1],'y')\n",
    "plt.plot(npstar2x[:,0],npstar2x[:,1],'r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "%%html\n",
    "<a href=\"https://github.com/sdorsher/ManyBodyProblem/blob/master/EllipseSymmetry.png\">Elliptical orbits at thirty degrees with symmetry line</a>\n",
    "It is clear that the elliptical orbits have focuses, perhelions, and aphelions on the axis of symmetry from this plot. It is also clear that the orbits are symmetric with respect to eachother. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getfocus(a,ecc):\n",
    "    c=a*ecc\n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getsemiminor(a,ecc):\n",
    "    c=getfocus(a,ecc)\n",
    "    b=np.sqrt(a**2-c**2)\n",
    "    return b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getxtheory2(theta0,ecc0,rad0,t, sgn):\n",
    "    focus=getfocus(rad0,ecc0)\n",
    "    b=getsemiminor(rad0,ecc0)\n",
    "    xdim=rad0\n",
    "    ydim=b\n",
    "    xtheory=sgn*focus*np.cos(theta0)+xdim*np.cos(t)*np.cos(theta0)-ydim*np.sin(t)*np.sin(theta0)\n",
    "    return xtheory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getytheory2(theta0, ecc0, rad0, t, sgn):\n",
    "    focus = getfocus(rad0,ecc0)\n",
    "    b=getsemiminor(rad0,ecc0)\n",
    "    xdim=rad0\n",
    "    ydim=b\n",
    "    ytheory=sgn*focus*np.sin(theta0)+ydim*np.cos(theta0)*np.sin(t)+xdim*np.sin(theta0)*np.cos(t)\n",
    "    return ytheory\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "t = np.linspace(0, 2*math.pi, 100)\n",
    "xax=-200+np.arange(0,400)\n",
    "plt.ylim(-200,200)\n",
    "plt.xlim(-200,200)\n",
    "plt.title(\"Elliptical Orbit, RK4, a=\"+str(rad0)+\", e=\"+ str(ecc0)+\", theta=\"+str(round(180*theta0/math.pi))+ \" degrees\")\n",
    "plt.plot(ellipsefns.getxtheory(theta0,ecc0,rad0,t,1),ellipsefns.getytheory(theta0,ecc0,rad0,t,1),'b')\n",
    "plt.plot(ellipsefns.getxtheory(theta0,ecc0,rad0,t,-1),ellipsefns.getytheory(theta0,ecc0,rad0,t,-1),'g')\n",
    "plt.plot(npstar1x[:,0],npstar1x[:,1],'y')\n",
    "plt.plot(npstar2x[:,0],npstar2x[:,1],'r')\n",
    "plt.plot(xax, np.tan(theta0)*xax,'c')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Computed orbit and parametric description of ellipse evolve at different rates, since the parametric description of the ellipse doesn't obey keplers law of equal area in equal time (conservation of angular momentum). This is a problem for the fit below. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conservation of angular momentum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "import Lstability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.1183369646375074e-14, -2.0412414523192806)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "deltaL, Lavg=Lstability.Lstability(npstar1x,npstar2x,mass0)\n",
    "deltaL, Lavg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-6.365278674517562e-14"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "deltaL*Lavg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Orbit conserves angular momentum to a tolerance of deltaL. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conservation of Energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "import Estability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.9347771707844668e-14, -0.0050000000000002065)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "deltaE, Eavg = Estability.Estability(npstar1x, npstar2x, mass0)\n",
    "deltaE, Eavg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-9.673885853922734e-17"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "deltaE*Eavg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Orbit conserves energy to a relative error of deltaE. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Symmetry of the two stars orbits with respect to eachother "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "import orbitSymmetricTol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "allcancelsx, allcancelsa=orbitSymmetricTol.howSymmetric(npstar1x,npstar2x,npstar1a,npstar2a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1e-14"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "allcancelsx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Orbit is symmetric with respect to x and v up to a tolerance of allcancelsx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1e-14"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "allcancelsa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.50000000e+01,  0.00000000e+00,  0.00000000e+00,\n",
       "        -0.00000000e+00, -1.22474487e-01,  0.00000000e+00],\n",
       "       [-2.49999980e+01, -1.22474484e-02,  0.00000000e+00,\n",
       "         3.99999973e-05, -1.22474477e-01,  0.00000000e+00],\n",
       "       [-2.49999920e+01, -2.44948948e-02,  0.00000000e+00,\n",
       "         7.99999787e-05, -1.22474448e-01,  0.00000000e+00],\n",
       "       ...,\n",
       "       [ 6.50765680e+01, -2.58921131e+01,  0.00000000e+00,\n",
       "         3.01846656e-02,  3.50405295e-02,  0.00000000e+00],\n",
       "       [ 6.50795863e+01, -2.58886090e+01,  0.00000000e+00,\n",
       "         3.01799302e-02,  3.50424134e-02,  0.00000000e+00],\n",
       "       [ 6.50826040e+01, -2.58851046e+01,  0.00000000e+00,\n",
       "         3.01751950e-02,  3.50442969e-02,  0.00000000e+00]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npstar1x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Orbit is symmetric with respect to a to up to or better than a tolerance of allcancelsa"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Testing for precision in perihelion and aphelion recovery from knowledge of the initial angle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "import aeTest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f075c7aec40>]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "plt.plot( np.abs(npstar1x[:,1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def findPerapHelionThetaIsZero(npstar1x,ecc0,rad0,useperihelion):\n",
    "    apindex=np.argmin(np.abs(npstar1x[1:,1]))+1\n",
    "    print(apindex)\n",
    "    delta=math.floor(.2*apindex)\n",
    "    print(delta)\n",
    "    perindex=np.argmin(np.abs(npstar1x[delta:apindex-delta,1]))+delta\n",
    "    print(perindex)\n",
    "    print(apindex/perindex)\n",
    "    if np.abs(apindex/perindex-2.)>0.05: \n",
    "        perindex=np.argmin(np.abs(npstar1x[apindex+delta:2*apindex+delta,1]))+delta+apindex\n",
    "        print(perindex)\n",
    "        apindex,perindex=perindex,apindex\n",
    "        print(apindex,perindex)\n",
    "        print(apindex/perindex)\n",
    "    #apindex3=np.argmin(np.abs(npstar1x[100:apindex2-100,1]))+100\n",
    "    #apindex4=np.argmin(np.abs(npstar1x[100:apindex3-100,1]))+100\n",
    "    #perindex=np.argmin(np.abs(npstar1x[100:apindex2-100,1]))+100\n",
    "    if useperihelion:\n",
    "        apindex,perindex=perindex,apindex\n",
    "    coordap=[npstar1x[apindex,0],npstar1x[apindex,1]]\n",
    "    coordper=[npstar1x[perindex,0],npstar1x[perindex,1]]\n",
    "    ra=np.sqrt(np.sum(np.array(coordap)**2))\n",
    "    rp=np.sqrt(np.sum(np.array(coordper)**2))\n",
    "    e=(ra-rp)/(ra+rp)\n",
    "    a=1./2.*(ra+rp)\n",
    "    deltae=np.abs(e-ecc0)/ecc0\n",
    "    deltaa=np.abs(a-rad0)/rad0\n",
    "    return apindex,perindex,coordap,coordper,ra,rp,e,a,deltae,deltaa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "22214\n",
      "4442\n",
      "17771\n",
      "1.2500140678633729\n",
      "44429\n",
      "44429 22214\n",
      "2.0000450166561627\n"
     ]
    }
   ],
   "source": [
    "if theta0==0:\n",
    "    apindex,perindex,coordap,coordper,ra,rp,e,a,deltae,deltaa=findPerapHelionThetaIsZero(npstar1x,ecc0,rad0,useperihelion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "if theta0!=0:\n",
    "    perindex,apindex,coordper,coordap,rp,ra,e,a,deltae,deltaa=aeTest.findPerApHelion(npstar1x,theta0,ecc0,rad0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recovered perihelion radius given by r_per, recovered aphelion radius given by r_ap, a is semimajor axis computed from the orbit, e is eccentricty computed from the orbit, delta a is relative error on the semimajor axis, and delta e is eccenticity relative error. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(22214,\n",
       " 44429,\n",
       " [74.99999996178201, -0.0016929680664632164],\n",
       " [-24.999999941777688, -0.002089640329429189],\n",
       " 74.99999998088961,\n",
       " 25.00000002910962,\n",
       " 0.4999999994678037,\n",
       " 50.00000000499962,\n",
       " 1.0643925740794202e-09,\n",
       " 9.999240546676447e-11)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "apindex,perindex,coordap,coordper,ra,rp,e,a,deltae,deltaa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f075c713bb0>]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nptimes[:perindex],npstar1x[:perindex,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Testing for symmetry within a given star's orbit about the line created by the initial angle with the origin that should pass thorugh the center of the ellipse, both focuses, and perihelion and aphelion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "pivotindex=perindex\n",
    "endindex = apindex\n",
    "if useperihelion:\n",
    "    pivotindex=apindex\n",
    "    endindex=perindex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "tosum1=list(range(0,endindex+1))\n",
    "tosum2=list(range(endindex+1,pivotindex+1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "44430"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(tosum1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(tosum2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(22214, 44429)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "apindex,perindex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "revtosum2=tosum2.reverse()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "xsum=np.zeros(endindex+1)\n",
    "ysum=np.zeros(endindex+1)\n",
    "for index in np.arange(0,pivotindex):\n",
    "    xsum[index]=npstar1x[index,0]+npstar1x[pivotindex+1-index,0]\n",
    "    ysum[index]=npstar1x[index,1]+npstar1x[pivotindex+1-index,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "xsum=xsum/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "ysum=ysum/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "b0=np.tan(theta0)\n",
    "plt.plot(xsum,ysum,label=\"Sum of data\")\n",
    "plt.plot(xsum,b0*xsum, color=\"green\", label=\"Line defining perhelion\")\n",
    "plt.xlabel(\"Symmetric X sum\")\n",
    "plt.ylabel(\"Symmetric Y sum\")\n",
    "plt.legend()\n",
    "plt.title(\"Sum of data reflection about perhelion\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xsum,ysum-np.tan(theta0)*xsum, color=\"green\", label=\"Residual\")\n",
    "plt.xlabel(\"Symmetric X sum\")\n",
    "plt.ylabel(\"Ysum-tan(theta)*Xsum\")\n",
    "plt.title(\"Residuals of data reflected about perihelion\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The residual improves substantially from .2 at perihelion with a timestep of dt=1 to .125 at perihelion with a timestep of dt=.3 to .02 at perihelion with a timestep of dt=.1. I think timestep makes all the difference between adjacent pairs of points in resolving perihelion. I think it is difficult to tell how symmetric the orbit is by this method when the limitation is in the resolution of the orbit with timestep. Interpolation would be necessary to get a good picture of orbital shape. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the interest of accomplishing further orbital evolutions, I think I'm going to let the precice numerical characterization of orbital shape question go (the predicted and actual orbits overlap quite nicely) and move on to evolving parabolic and hyperbolic orbits. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fit t as a function of the eccentric anomoly (angle from the center of the elipse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "def findEccentricAnomoly(coordap, coordper):\n",
    "    Ecenter=np.array(coordap)+np.array(coordper)\n",
    "    Ecenter/=2.\n",
    "    return Ecenter\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "ellipsecenter=findEccentricAnomoly(coordap,coordper)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.5000000e+01, -1.8913042e-03])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ellipsecenter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getEllipsecenter(ecc,rad,theta, useperihelion):\n",
    "    #ind of use perihelion\n",
    "    rp=rad*(1-ecc)\n",
    "    ra=-rad*(1+ecc)\n",
    "    rcent=(rp+ra)/2\n",
    "    #print(rp,ra,rcent)\n",
    "    rcentx=rcent*np.cos(theta)\n",
    "    rcenty=rcent* np.sin(theta)\n",
    "    return [rcentx,rcenty]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.5000000e+01, -1.8913042e-03])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.array(coordap)+np.array(coordper))/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-25.0, -0.0]"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "getEllipsecenter(ecc0,rad0,theta0, True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-90.0"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arctan2(-1.,0)/math.pi*180"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getEang(npstar2x,ecc,rad,theta, useperihelion):\n",
    "    ellipsecenter=getEllipsecenter(ecc,rad,theta, useperihelion)\n",
    "    #print(ellipsecenter)\n",
    "    #print(npstar1x)\n",
    "    #print(npstar1x[:,0])\n",
    "    xfortan=npstar2x[:,0]-ellipsecenter[0]\n",
    "    yfortan=npstar2x[:,1]-ellipsecenter[1]\n",
    "    #print(\"xy\",xfortan,yfortan)\n",
    "    Eang=np.arctan2(yfortan,xfortan)\n",
    "    Eangtheta=2*np.arctan2(np.sqrt(1-ecc)*np.sin(theta/2.),np.sqrt(1+ecc)*np.cos(theta/2.))\n",
    "    Eang-=Eangtheta\n",
    "    #if useperihelion:\n",
    "    #    Eang-=math.pi\n",
    "    print(len(Eang))\n",
    "    for i in np.arange(len(Eang)):\n",
    "        #if xfortan[i]<0:\n",
    "        #    Eang[i]+=math.pi\n",
    "        if Eang[i]<0:\n",
    "            Eang[i]+=2*math.pi\n",
    "    print(xfortan,yfortan,Eang/math.pi*180)\n",
    "    print(\"Eang\",Eang)\n",
    "    return xfortan, yfortan,Eang"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3.1412939168636456"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arctan2(-6.69327422*10**-6, -0.02240526)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "def xofeccanom(rad,Eang,ecc):\n",
    "    return rad*(np.cos(Eang)+ecc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "def yofeccanom(rad, Eang, ecc):\n",
    "    b=getsemiminor(rad,ecc)\n",
    "    return b*np.sin(Eang) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tofEccAnom(npstar2x, rad,ecc,theta,mass, useperihelion):\n",
    "    xE0,yE0,Eang=getEang(npstar2x,ecc,rad,theta, useperihelion)\n",
    "    b=getsemiminor(rad,ecc)\n",
    "    #fitval=rad*b*(Eang-ecc*np.sin(Eang))\n",
    "    sgn=-1\n",
    "    if useperihelion:\n",
    "        sgn*=-1\n",
    "    # added a factor of 2 in front of fitval\n",
    "    fitval=rad**(1.5)*mass**(-.5)*(Eang-sgn*ecc*np.sin(Eang))\n",
    "    fitval*=2\n",
    "    print(Eang, ecc,rad,mass,fitval)\n",
    "    return fitval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "def residualtEang(pars,nptimes,npstar2x):\n",
    "    residual=np.abs(nptimes-tofEccAnom(npstar2x,pars['rad'],pars['ecc'],pars['theta'],pars['mass'],pars['useperihelion']))\n",
    "    #print(nptimes, residual)\n",
    "    return residual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "endindex=apindex\n",
    "if useperihelion:\n",
    "    endindex=perindex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "44429"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "endindex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "44428\n",
      "[50.         49.999998   49.999992   ... 49.99997067 49.99998399\n",
      " 49.99999331] [ 0.          0.01224745  0.02449489 ... -0.04690014 -0.0346527\n",
      " -0.02240526] [0.00000000e+00 1.40345423e-02 2.80690841e-02 ... 3.59946256e+02\n",
      " 3.59960291e+02 3.59974325e+02]\n",
      "Eang [0.00000000e+00 2.44948973e-04 4.89897935e-04 ... 6.28224730e+00\n",
      " 6.28249225e+00 6.28273720e+00]\n"
     ]
    }
   ],
   "source": [
    "xE0,yE0,Eang0=getEang(npstar2x[0:endindex-1,:],ecc0,rad0,theta0, useperihelion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "nptimesoneorbit=nptimes[0:endindex-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f075c4ada90>]"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Eang0, xE0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f075c474a90>]"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Eang0, yE0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f075c44f4f0>]"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xE0,yE0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f075c3a3280>]"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nptimesoneorbit,xE0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f075c3761c0>]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nptimesoneorbit,yE0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f075c414880>]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nptimesoneorbit,yE0/xE0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arctan(0./1.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yE0[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50.0"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xE0[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f075c4dd220>]"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nptimesoneorbit,np.arctan2(yE0,xE0)*180/math.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "44428\n",
      "[50.         49.999998   49.999992   ... 49.99997067 49.99998399\n",
      " 49.99999331] [ 0.          0.01224745  0.02449489 ... -0.04690014 -0.0346527\n",
      " -0.02240526] [0.00000000e+00 1.40345423e-02 2.80690841e-02 ... 3.59946256e+02\n",
      " 3.59960291e+02 3.59974325e+02]\n",
      "Eang [0.00000000e+00 2.44948973e-04 4.89897935e-04 ... 6.28224730e+00\n",
      " 6.28249225e+00 6.28273720e+00]\n",
      "[0.00000000e+00 2.44948973e-04 4.89897935e-04 ... 6.28224730e+00\n",
      " 6.28249225e+00 6.28273720e+00] 0.5 50 1.0 [0.00000000e+00 8.66025407e-02 1.73205083e-01 ... 4.44255130e+03\n",
      " 4.44263791e+03 4.44272451e+03]\n"
     ]
    }
   ],
   "source": [
    "Eangtest=tofEccAnom(npstar2x[0:endindex-1,:],rad0,ecc0,theta0,masses[0], useperihelion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4442.724509064325"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(Eangtest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nptimes[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "nptimesoneorbit=nptimes[0:endindex-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "tpredoneorbit=Eangtest[0:endindex-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "Eangoneorbit=Eang0[0:endindex-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f075c5570d0>]"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nptimesoneorbit,npstar2x[0:endindex-1,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f075c839760>]"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nptimesoneorbit,Eangoneorbit/math.pi*180)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f075e927640>]"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nptimesoneorbit,tpredoneorbit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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wKiwlCxGpdDKzot5Os1dlc+WRnbj+GFU77S0lCxGpVGKrnYZdOoDDuzZLdkiVgpKFiFQKP6p26tCYJwar2qk0lZgszKwr8Heghbv3NrM+wGnufm/CoxMRiUNBtdOcrGyuOrIz1x3TRdVOpSyeq/lP4FYgF8DdpxLmxxYRSbY3v13KaU9+wZrN2xl2yQBuPL6bEkUCxFMNVcfdJ+wyjeDOBMUjIhKXbTvyuGvkdF6duJQBHRrz13P706KBqp0SJZ5kscbMOgEOYGa/BFYkNCoRkWLMXLGJq1+ezLzVm1XtVEbiSRZXAs8A3c1sGbAAuCChUYmIFMLdeWn8Iu4dPZOGtavz0qUDObRL02SHlRJKTBbuPh84xszqAlXcPTvxYYmI/Nj6LTu46fWpjJ25iiO7NePhs/rSpF7NZIeVMopMFmZ2QxHlALj7IwmKSUTkR76et5brX5nC2i3b+eMpPbn0kDR2aUeVBCvuzqJ+mUUhIlKInXn5PP7RXJ78JJMOTery7EWH0Lt1w2SHlZKKTBbufndZBiIiEmvJuq1cO3wy3y7ewFk/a8OQ03pRt6aeI06WeB7Ke6KQ4o3ARHd/u/RDEpFUN3rqCm55cyru8Pjgfgzq1zrZIaW8eNJ0LaA78FpYP5OoR1RfMzvS3a9LUGwikmKyc3K5+50MXp+0lL5tG/HXwf1p10TzYpcH8SSLPsAh7p4HYGZ/Bz4HDgWmJTA2EUkh3yxcx/WvTGH5hm1cdWRnrj2mi+bFLkfiSRb7APWIqp4A6gKN3T3PzLYnLDIRSQk7dubz2Ng5PP3pPFrvU5vXfnsQP2vfONlhyS7iSRYPAVPMbBxgwM+B+8JzF2MTGJuIVHKZWdlc98oUpi/bxNnpbbjz1F7UUyN2uRTPQ3nPmdkYYEAous3dl4flmxIWmYhUWu7Oi18v4r4xM6lToypPX/AzTui9b7LDkmLEm8KrAKvD/p3NrLO7f5a4sESkslq1KYebXp/KZ3NWc0S3Zjx0Zh+aawDAci+errMPAucAM4D8UOyAkoWI7JZRU5dzx4jp5OTmMXRQLy44sL2exK4g4rmzOB3o5u5qzBaRPbJ283bufHsGo6etoG+bhjxyTj86NauX7LBkN8TTL20+UH13D2xmtcxsgpl9Z2YzzOzuUN7BzP5nZplm9oqZ1QjlNcN6ZtieFnOsW0P5bDM7fndjEZHkGTNtBcc9+hkfZqzipuO78cbvDlaiqIDiubPYStQb6iPg+7sLd7+mhPdtB45y981mVh34wszeBW4AHnX34Wb2NHAZ0bStlwHr3b2zmQ0GHgTOMbOeRDPz9QJaAWPNrGvBcx8iUj6t27KDO9+ezqipK9ivdUMePqsv3fbVkHMVVTzJYmR47RZ3d2BzWK0eXg4cBZwXyocBQ4iSxaCwDPA68KRFlZmDgOGhGmyBmWUS9cz6endjEpGy8d70ldwxYhobt+Vy43FdueLwTnrAroKLp+vssD09uJlVBSYBnYGngHnABncvmJZ1KVAw6EtrYEk4504z2wg0CeXjYw4b+57Yc10OXA7Qrl27PQ1ZRPbC+i07uGvkDEZ+t5xerRrw0mUD6dGyQbLDklIQT2+oLsD9QE+icaIAcPeOJb03VBX1M7NGwFtEY0wlhLs/QzSjH+np6Z6o84hI4aK7iels2LqD64/pyu+P1N1EZRJPNdQLwF3Ao8CRwCXE1zD+PXffYGafAAcBjcysWri7aAMsC7stA9oCS82sGtAQWBtTXiD2PSKSZFmbcrjz7Rm8N2MlPVs24MVLB9Czle4mKpt4vvRru/tHgLn7IncfApxc0pvMrFm4o8DMagPHAjOBT4Bfht0uAgqGOR8Z1gnbPw7tHiOBwaG3VAegCzAhjrhFJIHcneETFnP0I5/yyewsbj6hO29fdYgSRSUVz53FdjOrAsw1s6uI/qqPp99bS2BYaLeoArzq7qPMLAMYbmb3ApOB58L+zwEvhQbsdUQ9oHD3GWb2KpAB7ASuVE8okeRasGYLt745lfHz13Fgx8bcf0YfOjStm+ywJIEs+uO9mB3MDiC6I2gEDAUaAH929/HFvS+Z0tPTfeLEickOQ6TSyc3L55+fz+exsXOpWa0Kt5/Ug3MOaKunsCsJM5vk7umFbYunN9Q3YXEzUXuFiKSgqUs3cPMb05i5YhMn9t6Xu0/rpTGdUojGAhaRYm3ZvpPHxs7huS8W0LReTY0Qm6KULESkUO7OBxmruHvkDJZvzOHcAe245cTuNKy926P/SCWgZCEiP7Fk3VaGjJzBR7Oy6L5vfZ44tz/paZq9LpXF81BeB+BqIC12f3c/LXFhiUgy7NgZNWD/9eO5VDHj9pN6cPEhaXq4TuK6sxhB1K31HX6Yz0JEKpmv563lj29PJzNrMyf02pc7T+1Jq0a1kx2WlBPxJIscd38i4ZGISFKs2byd+0bP5M3Jy2jbuDYvXHwAR3ZvnuywpJyJJ1k8bmZ3AR/w4yHKv01YVCKScPn5zsvfLObBd2exLTePK4/sxFVHdqF2jarJDk3KoXiSxX7Ar4iGFo+dVvWoRAUlIok1efF6hoycwXdLN3Jgx8bce3pvOjfXXBNStHiSxVlAR3ffkehgRCSxVmdv56H3ZvHapKU0r1+TR8/py+n9WusJbClRPMliOtFQH1mJDUVEEiU3L58Xv17EYx/OIWdnHlcc3pGrj+pCvZrqPS/xiedfSiNglpl9w4/bLNR1VqQC+CpzDXeNnMHcrM0c3rUZd57aU3Ngy26LJ1nclfAoRKTULduwjT+NzmDMtJW0a1yHf16YzjE9mqvKSfZIPAMJfmpmLYADQtEEd1eVlEg5lZObxzOfzedv4zIB+L9ju/Kbn3ekVnX1cpI9F88T3GcDfwbGAQb81cxucvfXExybiOwGd+fDjFUMHZ3BknXbOHm/ltx2cg9a68E6KQXxVEPdDhxQcDdhZs2AsYCShUg5MWdVNkNHZfD53DV0bVGP//56IAd3bprssKQSiSdZVNml2mktuzkHt4gkxtrN23l07Bz++7/F1KtZjTtP6cmvDmqvsZyk1MWTLN4zs/eBl8P6OcCYxIUkIiXZsTOfF79eyOMfzWXrjjwuPCiNa4/uwj51ayQ7NKmkik0WFnWbeIKocfvQUPyMu7+V6MBE5KcK5pi4f8xMFq7dypHdmnH7yT309LUkXLHJwt3dzMa4+37Am2UUk4gUImP5JoaOyuDr+Wvp0rwewy4dwOFdmyU7LEkR8VRDfWtmB8TMxS0iZSgrO4dHPpjDKxOX0Kh2dYYO6sW5A9pRTe0SUobiSRYDgfPNbBGwhaj7rLt7n4RGJpLicnLzeP7LBTz1cSY78vK57JAOXH1UFxrW0bSmUvaKTBZm1sHdFwDHl2E8IinP3RkzbSX3vzuTpeu3cWzPFtx2Ug86NK2b7NAkhRV3Z/E68DPgeXc/uoziEUlpU5duYOioDL5ZuJ7u+9bX8xJSbhSXLKqY2W1AVzO7YdeN7v5I4sISSS0rN+bw0PuzePPbZTStV4MHztiPs9LbUrWKxnGS8qG4ZDEYOD3so355IgmwbUc0jtPTn84jL9/57eGduPLITtSvpXYJKV+KTBbuPht40Mymuvu7ZRiTSKWXn++M/G45D743ixUbczhpv3255YQetGtSJ9mhiRQqnlFnlShEStGkResZOiqDKUs20Lt1Ax4f3J8BHRonOyyRYmmaLJEysnT9Vh54dxajpq6gef2aPHxWX87o35oqapeQCkDJQiTBNm/fyd8+yeTZLxZQxeCao7twxc87UldTmkoFUtxzFmcU90Z31/AfIsXIy3dem7iEhz+Yw5rN2/lF/9bcdHw3Wml+CamAivvT5tTwszlwMPBxWD8S+AqNFSVSpC8z1zB0VAazVmaT3n4fnr0onX5tGyU7LJE9VlxvqEsAzOwDoKe7rwjrLYF/lUl0IhXMvNWbuX/MTMbOzKLNPrV56rz9OWm/fTXvtVR48VSati1IFMEqoF2C4hGpkDZs3cFjY+fy7/GLqFW9Kjef0J1LDknTvNdSacSTLD4qZPKjsYkLSaTiyM3L56WvF/H4R3PJzsll8IB23HBsV5rWq5ns0ERKVTzPWVxlZr8Afh6KNPmRpDx3Z+zMLO4fM5P5a7ZwWJem3H5yD7rv2yDZoYkkRLx9974Fst19rJnVMbP67p5d3BvMrC3wItACcKIk87iZNQZeAdKAhcDZ7r4+zMr3OHASsBW42N2/Dce6CLgjHPpedx+2Ox9SpDRlLN/EvaMz+GreWjo1q8sLFx/AEd2aqV1CKrUSk4WZ/Qa4HGgMdAJaA08DJY1EuxP4P3f/1szqA5PM7EPgYuAjd3/AzG4BbgFuBk4EuoTXQODvwMCQXO4C0omSziQzG+nu63f3w4rsjazsHP7y/hxenbSEhrWrc/dpvThvYDuqaxIiSQHx3FlcCQwA/gfg7nPNrHlJbwqN4ivCcraZzSRKNIOAI8Juw4BxRMliEPCiuzsw3swahZ5XRwAfuvs6gJBwTuCHNhSRhNp1EqJLD+nANZqESFJMPMliu7vvKLjFNrNqRH/hx83M0oD+RAmnRUzvqpVE1VQQJZIlMW9bGsqKKt/1HJcT3QHRrp06a8nec3c+yFjFn0bPZPG6rZqESFJaPMni0zCvRW0zOxb4PfBOvCcws3rAG8B17r4ptl7X3d3MdivxFMXdnwGeAUhPTy+VY0rqmrMqm3veyeCLzDV0aV6Pf182kEO7aBIiSV3xJItbgMuAacAVwBh3/2c8Bzez6kSJ4j8xw4OsMrOW7r4iVDNlhfJlQNuYt7cJZcv4odqqoHxcPOcX2V0bt+by6Ng5vDR+EXVrVGXIqT254MD2VFO7hKS4eJLF1e7+OPB9gjCza0NZkULvpueAmbvMqjcSuAh4IPx8O6b8KjMbTtTAvTEklPeB+8xsn7DfccCtccQtEre8fOe/ExbzyAez2bgtl3MHtOP/jutG47o1kh2aSLkQT7K4iKhLa6yLCynb1SHAr4BpZjYllN1GlCReNbPLgEXA2WHbGKJus5lEXWcvAXD3dWY2FPgm7HdPQWO3SGn4et5a7n5nBrNWZjOwQ2PuOrUXPVvpeQmRWMWNOnsucB7QwcxGxmyqD5T4Ze3uXwBFdTz/Sbfb0AvqyiKO9TzwfEnnFNkdS9dv5b4xMxkzbSWtG2kcJ5HiFHdn8RVR19emwF9iyrOBqYkMSiSRtu3I4+/jMvnHZ/Mxg+uP6coVh3fUOE4ixShu1NlFRNVEB5VdOCKJ4+58mLGKu9/JYNmGbZzatxW3nthd80uIxCGeJ7iz+eG5ihpAdWCLu6tSVyqMRWu3MGTkDD6ZvZquLeox/PIDObBjk2SHJVJhxDOQYP2C5dDDaRBwYCKDEiktObl5/G3cPJ7+dB7Vqxh3nNyDiw5O0xAdIrtptyYBDo3QI8zsLqLnL0TKrY9mrmLIOzNYsm4bp/Vtxe0n96BFg1rJDkukQoqnGip2Lu4qRAP65SQsIpG9tHjtVu4ZNYOxM7Po3Lwe//3NQA7upKevRfZGPHcWp8Ys7yQaVnxQQqIR2Qs5uXn849P5/G1cJlWrGLed1J1LDumgKieRUhBPm8UlZRGIyN74fO5q7hgxnUVrt3JKn5bcfnIPWjZULyeR0hJPNVRHoqe1DyTqFfU1cL27z09wbCIlWrN5O/eOymDElOV0aFqX//x6IId0VpWTSGmLpxrqv8BTwC/C+mCiuSQGJiookZK4O69OXMJ9Y2axdcdOrjm6C78/opMerBNJkHiSRR13fylm/d9mdlOiAhIpSWbWZm57axoTFqxjQFpj7jujN52b1y/5jSKyx+JJFu+G6U+HE1VDnQOMCdOdokH9pKwUPDPx93GZ1KlRjQfP3I+zftaWKlU0lpNIosWTLApGhb1il/LBRMmjY6lGJFKIr+at4Y63pjN/zRZO79eKO07pSdN6NZMdlkjKiKc3VIeyCESkMBu35vKnMRm8OnEp7ZvU4aXLBnBYl2bJDksk5cTTG6oqcDKQFrv/LhMaiZS6D2as5I4R01m7ZQe/O6IT1x7dRQ3YIkkSTzXUO0RPbE8D8hMbjgis3bydIe9k8M53y+nRsgHPX3wAvVs3THZYIiktnmTRxt37JDwSSXnuzjtTVzBk5Ayyc3L5v2O78tsjOukJbJFyIN7eUMe5+wcJj0ZS1qpNOdz+1nTGzlxF37aN+PMv+9C1hbrDipQX8SSL8cBbZlYFyCWaKtU1n4WUBnfntYlLGTo6gx0787n9pB5cemgHqqo7rEi5Ek+yeIRotrxpYYhykVKxYuM2bn5jGp/NWc3ADo158Mw+pDWtm+ywRKQQ8SSLJcB0JQopLe7OiCnLuPPtGezMc4YO6sX5A9vr4TqRciyeZDEfGGdm7wLbCwrVdVb2xNrN27n9rem8N2Ml6e334S9n96V9E91NiJR38SSLBeFVI7xE9sgHM1Zy21vT2LRtJ7ec2J3fHNZRbRMiFUQ8T3DfDWBm9cL65kQHJZXLppxc7h6ZwRvfLqVnywb8+9d96b6v+keIVCTxPMHdG3gJaBzW1wAXuvuMBMcmlcCXmWu46bXvWJW9nauP6szVR3WhRjU9NyFS0cRTDfUMcIO7fwJgZkcA/wQOTlxYUtHl5ObxwLuz+NdXC+nYrC5v/O5g+rVtlOywRGQPxZMs6hYkCgB3H2dmapGUIs1csYlrXp7M3KzNXHxwGjef0J3aNTSmk0hFFldvKDP7I1FVFMAFRD2kRH4kP9954auFPPjuLBrWqc6Llw7g5101QqxIZRBPsrgUuBt4k2j+is9Dmcj3sjblcOPrU/lszmqO6dGcB8/sQxPNNyFSacTTG2o9cE0ZxCIV1EczV3HT61PZsn0nQ0/vzQUD22GmLrEilUmJ3VLM7EMzaxSzvo+ZvZ/QqKRC2LYjjz+OmM5lwybSokEtRl19KL86sL0ShUglFE81VFN331Cw4u7rzax54kKSiiBj+SauGT6ZzKzNXHZoB/5wQjdqVlMjtkhlFU+yyDezdu6+GMDM2hO1XUgKcnee/1KN2CKpJp5kcTvwhZl9SjQ8+WHA5QmNSsqlDVt3cONr3zF2ZpYasUVSTDwN3O+Z2f7AgaHoOndfk9iwpLyZtGgdV/93Mqs3b+ePp/Tk0kPS1DYhkkLiGnfB3de4+6jwiitRmNnzZpZlZtNjyhqHBvO54ec+odzM7AkzyzSzqSE5FbznorD/XDO7aHc/oOyd/Hzn6U/ncfY/xlO1qvH6bw/mskM7KFGIpJgik4WZxVNFVZx/ASfsUnYL8JG7dwE+CusAJwJdwuty4O8hhsbAXcBAYABwV0GCkcRbu3k7lw77hgfencVxPVsw6urD6KshO0RSUnF3FhP25sDu/hmwbpfiQcCwsDwMOD2m/EWPjAcamVlL4HjgQ3dfF573+JCfJiBJgAkL1nHSE5/zVeZa7hnUi7+dvz8Na1dPdlgikiTF3T0kop6hhbuvCMsrgRZhuTXRjHwFloayosp/wswuJzS8t2vXrhRDTi35+c7fxmXyyIdzaNe4Ds/9/gB6t26Y7LBEJMmKSxbNzOyGojbu7Ux57u5mVmpdcN39GaIRcklPT1fX3j2wOns7N7w6hc/nruHUvq247xe9qV9LdxMiUnyyqArUo3TvMFaZWUt3XxGqmbJC+TKgbcx+bULZMuCIXcrHlWI8EnyVuYZrX5nCpm253H/Gfgw+oK0asUXke8UlixXufk8pn28kcBHwQPj5dkz5VWY2nKgxe2NIKO8D98U0ah8H3FrKMaW0vHzniY/m8sTHc+nQtC4vXjqAHi01i52I/FjC2izM7GWiu4KmZraUqFfTA8CrZnYZsAg4O+w+BjgJyAS2ApcAuPs6MxsKfBP2u8fdd200lz2UtSmHa4dP4ev5azmjf2uGnt6bujX3thOciFRG5l549b6ZNa6oX8zp6ek+ceLEZIdRrn0+dzXXvzKFLdvzuGdQL85Kb1vym0SkUjOzSe6eXti2Iv+MrKiJQoq3My+fx8bO5alxmXRpXo+Xf7M/XVrUT3ZYIlLOqc4hhazYuI1rX57ChIXrOCe9LUNO66XpTkUkLkoWKeKTWVnc8OoUtu/M57Fz+nF6/0IfVxERKZSSRSWXm5fPw+/P5h+fzaf7vvV56vz96dSsXrLDEpEKRsmiElu6fitXvzyZyYs3cP7AdvzxlJ7Uqq5qJxHZfUoWldQHM1Zy0+tTyct3njyvP6f0aZXskESkAlOyqGR27Mzn/ndn8sKXC+ndugFPnbc/7ZvUTXZYIlLBKVlUIovXbuWql79l6tKNXHxwGree1F3zYotIqVCyqCTGTFvBza9PxQyevuBnnNB732SHJCKViJJFBZeTm8efRs/kpfGL6Nu2EU+e25+2jeskOywRqWSULCqweas3c83Lk5mxfBO/OawDNx3fnRrV4popV0RktyhZVEDuzivfLOHudzKoWb0Kz16YzjE9W5T8RhGRPaRkUcFs2LqDW9+cxrvTV3JwpyY8cnY/9m1YK9lhiUglp2RRgYyfv5brX5nC6uzt3HJidy4/rCNVqmiCIhFJPCWLCiA3L5/Hxs7hb+PmkdakLm/+/mD6tGmU7LBEJIUoWZRzi9Zu4ZrhU/huyQbOTm/DXaf20gRFIlLm9K1TTrk7r05cwj3vZFC1ivHUeftzcp+WyQ5LRFKUkkU5lLUph1venMbHs7I4qGMTHj67L60b1U52WCKSwpQsypmR3y3njyOmk5Obx12n9uSig9LUiC0iSadkUU6s37KDO96ezuipK+jXthF/Obuv5p0QkXJDyaIc+HjWKm5+Yxobtu7gpuO7ccXPO1Ktqp7EFpHyQ8kiidZt2cE978xgxJTldN+3PsMuGUDPVg2SHZaIyE8oWSSBuzPyu+Xc/U4G2Tm5XHN0F648spOGExeRckvJoowt27CNO96axiezV9OvbSMePLMP3fatn+ywRESKpWRRRvLznZfGL+Kh92aR73DnKT256OA0qqqnk4hUAEoWZWDmik3cMWI6kxat57AuTbnvF/tpzgkRqVCULBIoOyeXRz+cy7CvF9KwdnX+clZfzti/NWa6mxCRikXJIgHcnXemruDeURms3rydcwe04w/Hd6NRnRrJDk1EZI8oWZSyzKzN3Pn2dL6at5b9WjfkmQvT6de2UbLDEhHZK0oWpWTrjp389eNMnv18PrWrV2Xo6b05b0A7NWCLSKWgZLGXCp6ZeODdWazYmMOZ+7fh1pO607RezWSHJiJSapQs9sLkxeu5Z1QGkxdvoHfrBjxxbn8OSGuc7LBEREqdksUeWLFxGw+9N5u3Ji+jWf2a/PmXfThz/zYaHVZEKi0li92wbUce//hsHk9/Oo98hyuP7MTvjuhMPc1cJyKVnL7l4pCfH7VLPPhe1C5xcp+W3HJCdz1YJyIpQ8miBN8uXs8972QwZUnULvH44P4M6KB2CRFJLRUmWZjZCcDjQFXgWXd/IJHnW75hGw+9N4sRU5arXUJEUl6FSBZmVhV4CjgWWAp8Y2Yj3T2jtM+ldgkRkZ+qKN+AA4BMd58PYGbDgUFAqSaL75Zs4Lf/nqR2CRGRXVSUZNEaWBKzvhQYGLuDmV0OXA7Qrl27PTpJWpO6dG5eT+0SIiK7qCjJokTu/gzwDEB6errvyTEa1qnOS5cNLHlHEZEUUyXZAcRpGdA2Zr1NKBMRkTJQUZLFN0AXM+tgZjWAwcDIJMckIpIyKkQ1lLvvNLOrgPeJus4+7+4zkhyWiEjKqBDJAsDdxwBjkh2HiEgqqijVUCIikkRKFiIiUiIlCxERKZGShYiIlMjc9+j5tXLNzFYDi/biEE2BNaUUTmWg6/FTuiY/puvxUxXxmrR392aFbaiUyWJvmdlEd09Pdhzlha7HT+ma/Jiux09VtmuiaigRESmRkoWIiJRIyaJwzyQ7gHJG1+OndE1+TNfjpyrVNVGbhYiIlEh3FiIiUiIlCxERKZGSRQwzO8HMZptZppndkux4EsnMnjezLDObHlPW2Mw+NLO54ec+odzM7IlwXaaa2f4x77ko7D/XzC5KxmcpDWbW1sw+MbMMM5thZteG8pS8JmZWy8wmmNl34XrcHco7mNn/wud+JUwZgJnVDOuZYXtazLFuDeWzzez4JH2kUmNmVc1sspmNCuupcU3cXa+o3aYqMA/oCNQAvgN6JjuuBH7enwP7A9Njyh4CbgnLtwAPhuWTgHcBAw4E/hfKGwPzw899wvI+yf5se3g9WgL7h+X6wBygZ6pek/C56oXl6sD/wud8FRgcyp8GfheWfw88HZYHA6+E5Z7h/1JNoEP4P1Y12Z9vL6/NDcB/gVFhPSWuie4sfjAAyHT3+e6+AxgODEpyTAnj7p8B63YpHgQMC8vDgNNjyl/0yHigkZm1BI4HPnT3de6+HvgQOCHhwSeAu69w92/DcjYwk2ju95S8JuFzbQ6r1cPLgaOA10P5rtej4Dq9DhxtZhbKh7v7dndfAGQS/V+rkMysDXAy8GxYN1LkmihZ/KA1sCRmfWkoSyUt3H1FWF4JtAjLRV2bSnnNQnVBf6K/plP2moTqlilAFlHSmwdscPedYZfYz/b95w7bNwJNqETXI3gM+AOQH9abkCLXRMlCCuXR/XLK9as2s3rAG8B17r4pdluqXRN3z3P3fkRz3g8Auic3ouQys1OALHeflOxYkkHJ4gfLgLYx621CWSpZFapSCD+zQnlR16ZSXTMzq06UKP7j7m+G4pS+JgDuvgH4BDiIqLqtYIbN2M/2/ecO2xsCa6lc1+MQ4DQzW0hUTX0U8Dgpck2ULH7wDdAl9GyoQdQgNTLJMZW1kUBB752LgLdjyi8MPYAOBDaGqpn3gePMbJ/QS+i4UFbhhLrk54CZ7v5IzKaUvCZm1szMGoXl2sCxRO04nwC/DLvtej0KrtMvgY/DndhIYHDoGdQB6AJMKJMPUcrc/VZ3b+PuaUTfDx+7+/mkyjVJdgt7eXoR9XCZQ1Q3e3uy40nwZ30ZWAHkEtWZXkZUn/oRMBcYCzQO+xrwVLgu04D0mONcStRAlwlckuzPtRfX41CiKqapwJTwOilVrwnQB5gcrsd04M5Q3pHoiy0TeA2oGcprhfXMsL1jzLFuD9dpNnBisj9bKV2fI/ihN1RKXBMN9yEiIiVSNZSIiJRIyUJEREqkZCEiIiVSshARkRIpWYiISImULCRlmVkTM5sSXivNbFnMeo2Y/W7b5X1fJTCmNDM7L1HHF9lT6jorApjZEGCzuz9cyLbN7l6vjOI4ArjR3U8pi/OJxEt3FiLFMLMHgNrhbuM/oWxz+HmEmX1qZm+b2Xwze8DMzg/zQEwzs05hv2Zm9oaZfRNeh4Tyw2PuZCabWX3gAeCwUHZ9GMzvz+F9U83siphzf2Zmo8OcCE+bWZWw/7/MbHqI4fqkXDipdKqVvItI6nL3W8zsKo8G1CtMX6AH0XDv84Fn3X2ARZMnXQ1cRzR+0KPu/oWZtSMa/qMHcCNwpbt/GQYwzCGaM+P7Owszu5xoKJEDzKwm8KWZfRDOPYBoboRFwHvAGcACoLW79w7vb1R6V0NSmZKFyN75xsMQ5mY2Dyj4Ip8GHBmWjwF6RsNPAdAgJIcvgUfCHcub7r40Zp8CxwF9zKxg7KGGRGMJ7QAmuPv8cO6XiYYs+QjoaGZ/BUbHxCOyV5QsRPbO9pjl/Jj1fH74/1UFONDdc3Z57wNmNppoDKovrfDpNQ242t1/NBhhaNvYtcHR3X29mfUlmoTpt8DZRGNViewVtVmIlCw3DF++pz4gqpICwMz6hZ+d3H2auz9INOpxdyCbaFrXAu8Dvys4v5l1NbO6YduAMEpyFeAc4AszawpUcfc3gDuIps4V2Wu6sxAp2TPAVDP71qMhqXfXNcBTZjaV6P/cZ0R/9V9nZkcS3YXMIJrTOx/IM7PvgH8RtXekAd+GYdRX88O0nd8ATwKdiYbJfgvYD3ghJBCAW/cgXpGfUNdZkQpIXWylrKkaSkRESqQ7CxERKZHuLEREpERKFiIiUiIlCxERKZGShYiIlEjJQkRESvT/bdKXdcMYEfIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2HdEkr75UZ7edn7yzhxc3HiElph+PzBvJpIxY+gUFsL+miaWF5fxy5V6WbS3nz7dNYIgX/X1pkvchFcdPsfXIcR66JtPqUDxCaFAAN01I5fkNZdQ1tZMQGWJ1SMoDnero5t4XClhXUs89V2TwvTmZhAb9o7eelRTFovEprNlby4Ovbef6P6zn+bsnMz4txrqgL4KOyfuQlbt6Vnleq0M1n/vqpEF0dhteL9R6NuqfdXXb+fbLW/m0tJ5f3TiWHy4YdUaC723myESWf+tyYsKCuf3pTeypPOHmaC+NJnkfsmpPDVlJUQyOC7c6FI8xLDGCKUNieXnzEb09oPonP3+vmNXFtfzXojHcPDHtvO9Piw3j7/dMJiIkkHueK6C+2fNnhmuS9xGNLR0UHG7k6lEDrA7F49w6eTBHG0+xrrTe6lCUB1m1p5pn15dx17R0vjZl8AV/LrV/GE/enkdDSwff+vtWuj2886BJ3kd8WFyD3cAcTfL/5JrRA4kLD+blTUesDkV5iNqmNh5aupMxKVE8Mm/kRX9+TEo0P71+DBsPNvLs+kMuiNB5NMn7iPyiGpKiQxmd7F+1ai5EcKCNG3JS+HBvDQ1ecHqtXO9n7xZzqqOb3y3JueQpkV+ZkMrsrAH86oN9lNY2OzlC59Ek7wPaOrtZV1LP7KwBflmr5kLcPDGNzm7DW9srrQ5FWWxdSR3Ld1Ry/8yhfZpqLCL8YvEYwoID+NFbuzx20Z0meR/waUk9pzq7dTz+S4wYEMn4tBhe23LUY/8Ylet1ddt5bPkeMuLD+dfpQ/u8v8TIUP5jTiYbDzby3q5qJ0TofJrkfUB+UQ2RIYFMGeIfd4C6VDfnpbGvpomd5d4x9U0539LCcg7WtfCD+VnnnCp5sb46aRBZSVH8fEURpzq6nbJPZ9Ik7+W67YYP99YwPTOB4ED9z/llrh2XRGiQjdcKdM68P2rr7Obx1SXkDophdlai0/YbYBP+c+EoKk+08bfPypy2X2fRrODlth89Tn1zhw7VXICo0CDmj0li+fZKj+xxKdd6YcNhqk+28fDckU6/djV5SBwzMhP4y9oDNLV1OnXffaVJ3svlF9UQaBNmZDqvZ+LLbp6YRlN7F+/v0XvA+pO2zm7+svYglw+Ld9mw5veuzuR4ayfPfFrmkv1fKk3yXi6/qJopQ+KI7hdkdSheYXJGLIPjwnhti9aZ9ydvbqugvrmd+2f0/WLruWSnRjNn1ACeWneQE62e05vXJO/FDtY1c6CuRYdqLoKI8JUJqWw42MCRhlarw1Fu0G03PLn2IGNTo5k61LWTE747ewRN7V28uMlzbj2pSd6L5RfVADBbk/xFuXFCKjZBi5b5ifyiag7Vt3DflUNdvo5kVHIU00ck8Oz6Q7R1esZ1nz4neRFJE5E1IlIkIntE5DuO7bEiki8iJY5/+/c9XNVbflENo5OjSInpZ3UoXiUpuh9XjkhgaWG5x9cdUX3313WHGBQbxtwxA93S3n3Th1Df3MGyrRVuae98nNGT7wK+Z4wZBUwBHhCRUcAjwIfGmOHAh47nyknqm9spPHKM2Vnai78UN+elUXWijfVatMynFVWepPDwMW6fOpgAm3tWg08dEsfY1Gj+uu6gR3Qi+pzkjTFVxpitjsdNQDGQAiwCnnO87Tng+r62pf7ho+JajEHH4y/RrKxEokIDWaY3+vZpL246TEigjZsmpLqtTRHh3iuHcKi+5fMhVSs5dUxeRNKBHGATMMAYc3qeWjWg2ciJVhXVkBLTTwuSXaKQwAAWjkvm/T3VNLd3WR2OcoGmtk7e2lbBwnHJxIQFu7XteWOSSInpx/Mbytza7tk4LcmLSATwBvBdY8zJ3q+ZnmIhZz1vEZF7RaRARArq6uqcFY5PO9XRzaeldczOStSCZH2wODeVtk7753fUUr7lrW0VtHZ0c9tF1Ip3lgCb8C+TB/HZgQZKa5vc3n5vTknyIhJET4J/yRizzLG5RkSSHK8nAbVn+6wx5kljTJ4xJi8hIcEZ4fi8dSV1tHXauXqUey4k+arcQTGkx4V5zAUy5TzGGF7ceIQxKVGMS422JIYlE9MIDrDxwgZrp1M6Y3aNAE8DxcaY3/R6aTlwh+PxHcDbfW1L9cgvqiEyNJDJQ2KtDsWriQiLc3vmzJcf0znzvmRH+Qn21TTxL5MGW3a2GxcRwoKxSbyxtYIWC4cEndGTnwZ8DbhKRLY7fuYDvwSuFpESYLbjueqjbrvho721zMxMJChAlzn01Q05KUDPqb3yHW8UlhMSaOPacdbe1P5rUwfT3N7Fmxb+fgX2dQfGmE+Bc/2vclZf96/OtPXIMRpatCCZs6TFhjE5I5ZlWyt4YOYwvcbhA9q7unlnZyVzRg8kKtTach85aTGMTo7ihQ2HuXXyIEt+v7Qr6GVWF9UQFCDMyNTrF85yY24qB+tb2H70uNWhKCdYs7eW462d3JibYnUoiAi3TRnMvpomtln0+6VJ3svkF9UwZUgckRb3UHzJvOyBhATa9AKsj1haWEFCZAiXD4u3OhQArh2bRL+gAF636D4GmuS9SGltMwfrW5ijQzVOFRkaxDWjB7J8RyXtXZ5Rb0Rdmobmdj7eV8sNOSkEesg1q8jQIBaMTeKdHVW0drj/AqxnHAV1QU6vnpulpQycbnFuCidOdbJm71ln+iovsXxHJV12w4257lvheiFumZhGc3sXK3a6f02GJnkvkl9UzZiUKJK1IJnTXT4snoTIEN7QIRuv9tb2SkYlRZE5MNLqUM6QN7g/Q+LDLbn1pCZ5L1HX1M62o8e5OksXQLlCYICN68cns2ZvLY0tHVaHoy7B0cZWdhw9znXjk60O5Z+ICF/JS2NL2TEO1DW7tW1N8l7iw+IaLUjmYjdOSKXLbnhnR6XVoahLsMJRnmJBtrVz48/lxgkpBNjE7b15TfJeIt9RkCwrybNOQ33JyIFRjEqK0sqUXurdnZWMS4shLTbM6lDOKjEylJmZibxRWEFnt91t7WqS9wKtHV18WlrP1aMG6GIdF1ucm8KO8hOWF5VSF6esvoXdFSdZONYze/Gn3ZyXSn1zO+tK3FeMUZO8F1i7v572LrtOnXSD68YnYxN0zryXOT1UM99Dh2pOm5GZSP+wILf+fmmS9wL5RTVEhQYyMUMLkrlaYmQoVwxP4K1tFdg94K4+6sK8u7OKCYP7e/zMs+BAGwvHJZNfVMPJtk63tKlJ3sN1ddv5aG8NV43UgmTusjg3hcoTbWw81GB1KOoCHKhrprjqpMdecP2iG3JSaO9y330MNGt4uMLDxzjW2qm1491ozqiBRIQE8qYO2XiFFTurEPH8oZrTxqfFkBEf7rYhG03yHi6/qIbgABvTtSCZ2/QLDmDumIGs3F3NqQ4tc+DpVuysYuLgWAZGh1odygURERbnpLDpUKNb7mOgSd6DGWPIL65hytA4IkL6XBVaXYTFuSk0t3exqqja6lDUlzjc0MK+mibmjvGuM93r3XgfA03yHqy0tpnDDa26AMoCUzLiSI4OtfRmD+r8Ttdz8ra/kbTYMCZlxLJsWwU9t8B2HU3yHmzV6V9gLUjmdjabsCgnhXUl9dQ2tVkdjjqH/KIaRg6M9NgFUF9mcU4KB+ta2Fl+wqXtaJL3YPlFNYxNjfaasUZfszgnhW67Yfl2LXPgiY61dLClrNHrevGnzctOIjjQ5vIV1prkPVTNyTa2Hz2uC6AsNHxAJNkp0Tpk46E+2luL3YvrOUX3C+LqUQN4Z2eVS8scaJL3UKfHGueM9q4LSr5mcW4KeypPsq9ayxx4mvyiGgZEhTAmOdrqUC7Z4pwUGls6+GSf68ocuDzJi8hcEdknIqUi8oir2/MVq4pqSI8LY3hihNWh+LWF45IJsAnLtmnRMk/S1tnN2pI6ZmcNwGbz3npOV45IIC482KW/Xy5N8iISAPwBmAeMAr4qIqNc2aYvONnWyYYD9cwZPVALklksPiKE6SMSeHtbJd1a5sBjbDjQQGtHt9cO1ZwWFNBT5mB1ca3Lyhy4uic/CSg1xhw0xnQArwCLnN1IQVkjX3t6Ey3t7r9/oit8vK+Ozm6j4/EeYnFuCtUn29h4UMsceIpVRTWEBwcwdWic1aH02aLxyXR02Xl/l2vWZLg6yacAvSvklzu2fU5E7hWRAhEpqKu79HGpdSX1vL/bNxau5BfVEB8RTM6g/laHooDZWQOIDAnUypQewm43fFhcw/TMBEICA6wOp8/Gp8WQMyjGZTf5tvzCqzHmSWNMnjEmLyHh0pbuTxjcn0GxYT4xbtre1c2avbXMzhpAgBePNfqS0KAA5mcnsXJ3lcv+ENWF21lxgtqmdq8fqjlNRFj2zcu4c1qGS/bv6iRfAaT1ep7q2OZUIsINOSl8dqCBqhOnnL17t9p4sJHm9i6f+QX2FYtzU2jt6GbVnhqrQ/F7+UXVBNiEmZmJVofiNK689ubqJL8FGC4iGSISDCwBlruiocW5KRgDb23z7oUrq/ZUExYcwLRh8VaHonqZmB5LSkw/lumcecvlF9UwMb0/MWHBVofiFVya5I0xXcC3gA+AYuA1Y8weV7Q1OC6cCYP7s2xructrQbiK3W7IL6ph+ogEQoO8f6zRl9hsPWeLn5bUUXtSyxxY5XBDC/trmrX09kVw+Zi8MeY9Y8wIY8xQY8zPXdnW4twUSmqb2VN50pXNuMyO8uPUNrUzZ7QO1XiiG3JTsBt4W8scWObzRYI6nHnBLL/w6kzXZicTHGDz2lkQq4pqCLAJV2XqL7AnGpoQwbi0GB2ysZA3FySzik8l+eiwIGZlJbJ8R4VLa0G4gjGG93dXM2VILNFhQVaHo85hcU4KxVUnKa7yzrNFb3aspYOCw8eYrVVZL4pPJXnouX9ifXMH60pcVwvCFfZWN3GovsVrbmHmrxaOSybQJlq0zAJr9tXSbTc68+wi+VySn5GZSP+wIK8bsnlvVxU2gWu0IJlHiw0PZkZmIm9tq9AyB252uiBZdor3FiSzgs8l+eDAnloQq4pqXFYLwtmMMazYVcWUIXHER4RYHY46j8W5KdQ2tbO+tN7qUPxGW2c3n+yvY5aXFySzgs8leYDFual0dNlZuavK6lAuyL6aJg7WtTBPh2q8wlUjE4kKDdQhGzfacNA3CpJZwSeT/LjUaIbEh/OGlwzZvLezZ6hmrg7VeIXQoAAWjE3m/d3VPlMUz9PlOwqSXeYDBcnczSeTvIiwODeFzYcaOdrYanU4X+r0UM2kjFgSInWoxlsszk3hVGe3zxTF82R2u2F1UQ1XjvCNgmTu5pNJHmDR+J5il295+Cl1SW0zB+paWKBDNV4lb3B/0mL76ZCNG/haQTJ389kknxYbxuSMWN7cVuHRZQ5W7KxCBK4Zo0M13qSnKF4q6w/UU31Cyxy40urTiwRH+k5BMnfy2SQPPafUB+tb2H70uNWhnJUxhnd3VjIpPZbEyFCrw1EX6YYcR1G87dqbdyUtSNY3Pp3k52UnERpk4/VCz6wzv7viJAfqWrg+J+X8b1YeJyM+nNxBMby51bPPFr3ZkYZW9tU06SrXPvDpJB8VGsT87CSWb6/0yFkQb26rIDjAxvwxOh7vrW7ITWVfTRNFWubAJfKLTxck0+HMS+XTSR7gq5MG0dzexYqdnjVnvqvbzvIdlVw1MlFr1Xixa7OTCAoQr1th7S3yi6rJHBDJoDgtSHapfD7J5w3uz7DECF7ecsTqUM6w/kAD9c3tOlTj5fqHB3PVyETe3l5Jl5cVxfN0x1s72FJ2jNmj9IJrX/h8khcRlkxMY9uR4+yrbrI6nM+9va2CqNBAZo68tPvaKs9xQ04q9c3tfKplDpzqo72nC5LpUE1f+HySh54yB8EBNl7e7Bm9+daOLt7fU82Cscm6uMMHzByZQHQ/7yuK5+lWF9eQGBnCWC1I1id+keRjw4OZM3oAb26roK2z2+pw+GBPNa0d3Vw/PtnqUJQThAQGsHBcEquKqmn2wAv83qi9q5tP9tUxe5QWJOsrv0jy0HMB9sSpTj7YY/0y9Jc3HyU9LoxJGbFWh6Kc5IacVNo6vaconqf77EADLR3dXK1TJ/usT0leRH4tIntFZKeIvCkiMb1ee1RESkVkn4hc0+dI+2jqkDgGx4Xx0kZrh2wO1jWz+VAjt0wchIj2UHxF7qAY0uPCdMjGSfKLaggLDmCqFiTrs7725POBMcaYscB+4FEAERkFLAFGA3OBP4qIpYPPNptw2+TBbC5rZHfFCcvieHXLUQJtwo0TdFaNLzld5mDjoQYqj5+yOhyvdrog2fQRCYQG6TWrvupTkjfGrDLGnB6E3AikOh4vAl4xxrQbYw4BpcCkvrTlDDdPTCMsOIC/fVZmSfsdXXaWFpYzKytRyxj4IC1z4BynC5LNGa1DNc7gzDH5rwMrHY9TgKO9Xit3bLNUdL8gbsxNZfn2Suqb293e/uriGhpaOlgycZDb21auNygujLzB/VmmZQ76ZNWeagJswsxMnR/vDOdN8iKyWkR2n+VnUa/3/BDoAl662ABE5F4RKRCRgro61998+85p6XR02/n7JvePzb+48TDJ0aFcOULnxvuqxbmplNY2s7tCyxxcqvyiGialx2pBMic5b5I3xsw2xow5y8/bACJyJ3AtcKv5R/elAkjrtZtUx7az7f9JY0yeMSYvIcH1yW9oQgTTRyTwwsbDdHS5b4VicdVJPjvQwO2XpROgU8J81oLsJIIDbCzb5plF8TzdofoWSmqbdajGifo6u2Yu8DBwnTGm9y2YlgNLRCRERDKA4cDmvrTlTHdNS6euqZ3lOyrd1uaz6w8RGmRjycS0879Zea3osCBmZSWyfHslnVrm4KLlF/VMcdYbhDhPX8fknwAigXwR2S4ifwYwxuwBXgOKgPeBB4wx1q9Ccpg+IoGspCj++HEp3XbXj502NLfz1vZKbsxN1VNQP7A4N5WGlg7Wlbh++NHX5BfVkJUURWp/LUjmLH2dXTPMGJNmjBnv+PnXXq/93Bgz1BiTaYxZ+WX7cTcR4Vszh3GwroWVu12/eOWlTUfo6LJz17R0l7elrDd9RAL9w7TMwcWqb26n8PAx5mgv3qn8ZsXrF80dM5ChCeE88VEpdhf25pvbu3hm/SGuGpnIsMRIl7WjPEdwoI2F45JZVVTDybZOq8PxGh8V12I3OlTjbH6b5ANswgMzh7G3uonVjhsTuMKLGw9zvLWTb181zGVtKM+zODeVji4tc3AxVhXVkBLTj9HJUVaH4lP8NskDXDcumcFxYfzPqv0uGZtv7ejir2sPcuWIBHIG9Xf6/pXnGpcazZCEcN4o1CGbC9Ha0cW6kjquHjVAy304mV8n+cAAG9+fO5J9NU0sLTx6/g9cpOc3HKahpYPvzNJevL8REb4yIY3NZY0cqGu2OhyPt66knvYuuw7VuIBfJ3mAeWMGkjsohv9ZtZ/WDueViW1obucPH5UyMzOBCYO12qQ/unFCCoE24dUtzu9A+Jr8ohqiQgO1MqsL+H2SFxF+uCCL2qZ2/vTxAaft9/HVJbR2dvPDBVlO26fyLomRoczKSuSNwnK3LrzzNl3ddj4sruGqkYkEBfh9SnI6PaLAhMGx3JCTwp8/OcD+mr7fInBP5Qn+vvkIt04epDNq/NySSYNoaOlw6cV9b7f5UCPHWju5ZrTe5s8VNMk7/GhBFhEhgXz/jZ19ugjb2W3n4aU76R8WzINXj3BihMobXTk8geToUI+59aQnem93Ff2CApihBclcQpO8Q1xECD9eOIptR47zp49LL3k/f/74AHsqT/Kz60fr6lZFgE34Sl4an5bWc7Sx9fwf8DPddsMHe2qYOTKBfsFaO94VNMn3cv34FBaNT+Y3+fv57ED9RX/+s9J6frt6PwvHJTN3TJILIlTe6GZHvaLXC/QC7BcVHj5GXVM78/TvxWU0yfciIvzihmwy4sN54KWtlNZe+Ph8WX0L3355Gxnx4fz34mwXRqm8TUpMP6aPSOC1gnK6tGjZGd7bVUVIoI2ZI3WoxlU0yX9BeEggT98xkQCbjdue2syh+pbzfqb8WCu3PrUJuzH85Wt5RIQEuiFS5U2WTEyj+mQba7Vo2efsdsP7u6uZPiJB/2ZcSJP8WaTHh/PC3ZPo6LZz/R/W88n+c/9hbjrYwPV/WM/Jtk5euHsywxIj3Bip8hazsgYQHxHCy5t1yOa0bUePU32yjXnZOqvGlTTJn0NWUhRv3T+NxMgQ7nhmM998sZDPDtRzqqObts5uCsoa+fdXt3PLkxsJDwnkzfsvY0xKtNVhKw8VFGDjpgmpfLS3lpqTbVaH4xFW7qoiKECYlaWrXF1Jz5G+xKC4MN759uX86eMDPPPpIVburj7j9X5BAdx35RD+bdZwwvV0U53HLRPT+PMnB3h1y1H+bdZwq8OxlDGGlburuWJ4AlGhQVaH49M0M51HaFAA/371CO6bPoRPS+opqW3GGMPQhAimDY/XX1B1wTLiw7lieDx/33SE+2cMJdCPV3fuqjhBxfFTfHe2f//Pzh00yV+gsOBA5oweyJzRVkeivNntU9O55/kC8otqmJftv9MGV+ysItAmWpDMDfy3K6GUBa4amUhKTD+e33DY6lAsY7cb3tlRyZUjEnTBoBtoklfKjQJswq1TBrHhYAMlTqiT5I0KDh+j8kQbi8YnWx2KX9Akr5Sb3ZKXRnCAjRc2+mdv/u3tFfQLCmC2zqpxC6ckeRH5nogYEYl3PBcR+b2IlIrIThHJdUY7SvmCuIgQrh2bxLKtFTS3O+8eBt6gs9vOe7uqmD1qgM5Ic5M+J3kRSQPmAL3L7M0Dhjt+7gX+1Nd2lPIlX5s6mOb2Lt7cWm51KG71aUk9x1o7WTROh2rcxRk9+d8CDwO96/MuAp43PTYCMSLiv1MJlPqC8WkxZKdE8/yGwxjj/PsLe6q3t1cQ3S+IK0ckWB2K3+hTkheRRUCFMWbHF15KAXqv3y53bDvbPu4VkQIRKair07oeyj+ICLdPHUxJbTMbDjRYHY5btHZ0saqohvnZSQQH6uVAdznvkRaR1SKy+yw/i4AfAD/uSwDGmCeNMXnGmLyEBP2/u/IfC8clEx8RzFOfHrI6FLdYXVxLa0c31+lQjVud98qHMWb22baLSDaQAewQEYBUYKuITAIqgLReb091bFNKOYQGBfC1Ken8dvV+Smubfb643RuF5SRFh+rNut3sks+ZjDG7jDGJxph0Y0w6PUMyucaYamA5cLtjls0U4IQxpso5ISvlO26bMoiQQBtP+3hvvvpEG+tK6rgxN5UAm1gdjl9x1cDYe8BBoBT4K3C/i9pRyqvFRYSwODeVZVvLaWhutzocl3ljazl2AzdNSLU6FL/jtCTv6NHXOx4bY8wDxpihxphsY0yBs9pRytfcfXkG7V12n10cZYxhaWE5k9JjSY8Ptzocv6OXuJWy2LDECK4amcgLGw7T1tltdThOV3j4GIfqW7gpT3vxVtAkr5QH+MYVGTS0dPDWNt+bn/B6QTlhwQEs8OOqm1bSJK+UB5g6JI7RyVE8ue4g3XbfWRzV2tHFil1VzM9O0jIGFtEkr5QHEBHunzGMg3UtrNztOxPR3t1RRXN7FzfnpZ3/zcolNMkr5SHmjRnIsMQInvioFLsP9OaNMTy/sYwRAyKYmN7f6nD8liZ5pTyEzSY8MHMoe6ub+HBvrdXh9NmO8hPsrjjJ16YMxrFgUllAk7xSHmTh2GQGxYbxxEclXl+47IUNhwkPDuD6nLOWrVJuokleKQ8SGGDj/hlD2VF+gnUl9VaHc8mOtXTwzs5KbshNIVJvdm8pTfJKeZjFuakkRYfy+w+9tzf/euFROrrs3DZlsNWh+D1N8kp5mODAnt58weFjfLzf+8pvd3XbeX7DYSalxzJyYJTV4fg9TfJKeaBbJg4iLbYfv35/n9fNtFm5u5ryY6e4+4oMq0NRaJJXyiMFB9p48OoRFFWdZMUu75k3b4zhybUHyYgP52q9UbdH0CSvlIe6blwKmQMi+U3+fjq77VaHc0E2HmxkV8UJvnFFBjYtKewRNMkr5aECbMJD12RyqL6F1wu844bfT649QFx4MDfmajEyT6FJXikPNisrkQmD+/Pb1ftpbu+yOpwvVVR5kjX76rh9ajqhQQFWh6McNMkr5cFEhB8tyKKuqZ0/rCm1Opwv9fjq/USGBnLnZelWh6J60SSvlIfLGdSfxbkpPL3uEGX1LVaHc1a7K06wqqiGuy/PIDpMFz95Ek3ySnmBR+aOJChA+NmKYqtDOavHV5cQFRrI1y/XaZOeRpO8Ul4gMSqUb101nNXFNXy8z7OKl+04epzVxTV844ohRGkJA4/T5yQvIt8Wkb0iskdEftVr+6MiUioi+0Tkmr62o5S/+/rl6QyJD+dHb+2mtcMzLsIaY/jZiiLiI4K5a1q61eGos+hTkheRmcAiYJwxZjTw/xzbRwFLgNHAXOCPIqKX25Xqg5DAAP57cTblx07xP6v2Wx0O0LO6dUvZMR68OlMLkXmovvbkvwn80hjTDmCMOX0euQh4xRjTbow5BJQCk/rYllJ+b/KQOG6dPIhn1h9i25FjlsbS1tnNf68sZuTASG6ZqHd+8lR9TfIjgCtEZJOIfCIiEx3bU4Cjvd5X7timlOqjR+aNZGBUKA8v3UlbZ7dlcTy59iBHG0/xwwVZBOjqVo913iQvIqtFZPdZfhYBgUAsMAV4CHhNLvIWMCJyr4gUiEhBXZ33VdxTyt0iQ4P478XZlNQ284v3rJltU1rbzBMflXLt2CSuGJ5gSQzqwpz39unGmNnnek1EvgksMz1FrzeLiB2IByqA3udvqY5tZ9v/k8CTAHl5ed5Vbk8pi8zITOTuyzN4+tNDXD4snjmjB7qtbbvd8INlu+gXHMBjC0e7rV11afo6XPMWMBNAREYAwUA9sBxYIiIhIpIBDAc297EtpVQvD8/NZExKFA+/sZOK46fc1u6zn5WxuayRH87PIiEyxG3tqkvT1yT/DDBERHYDrwB3mB57gNeAIuB94AFjjHWDh0r5oJDAAH6/JIfubsM9zxW4ZVrl7ooT/HJlMbOzBvCVPC1C5g3Ek24vlpeXZwoKCqwOQymvsmZfLXf/bQtzRg3kj7fmuqzE78m2ThY9sZ5THd2s/M4V9A8Pdkk76uKJSKExJu9sr+mKV6W83MzMRH4wP4v391Tz8/eKXXJf2K5uO9/6+zaONrbyuyXjNcF7kfNeeFVKeb67L8+g/Ngpnv70EP2CAviPazKdtm9jDD95p4i1++v45eJsJg+Jc9q+letpklfKB4gIjy0cRXtXN0+sKaXLbnj4msw+D90YY/jFe8W8sPEw9105hCWTBjkpYuUumuSV8hEiws+vz0ZE+PMnB6g8fopf3TT2km/g0dVt5yfvFPHCxsPcMXUwj8wb6eSIlTtoklfKh9hsws+vH0Nq/3786v197K9p4vdfzWHEgMiL2k9dUzv//up2Pi2t574rh/DIvJFc5DpH5SH0wqtSPkZEuH/GMJ65M4/65nau/d9P+dX7e2lq6zzvZ7u67bxWcJSrf/sJm8sa+dVNY3l0fpYmeC+mUyiV8mF1Te38fEURb22vJDI0kBtzU5mfncT4tBiCA3v6eMYYyhpayS+q5uXNRzlU30LOoBh+fdNYhiVe3BmAssaXTaHUJK+UH9hZfpyn1h1i5e4qOrsNgTYhMTIEm0043tr5+U3Cx6XF8M3pQ5gzaqDL5tsr5/uyJK9j8kr5gbGpMfz+qzmcaB3DpkMN7Cg/TvWJdowxRPULYuTASKYOjWNwXLjVoSon0ySvlB+JDgtizuiBbi1opqylF16VUsqHaZJXSikfpkleKaV8mCZ5pZTyYZrklVLKh2mSV0opH6ZJXimlfJgmeaWU8mEeVdZAROqAw5f48Xh6biKu/kGPyZn0ePwzPSZn8tbjMdgYk3C2FzwqyfeFiBScq3aDv9JjciY9Hv9Mj8mZfPF46HCNUkr5ME3ySinlw3wpyT9pdQAeSI/JmfR4/DM9JmfyuePhM2PySiml/pkv9eSVUkp9gSZ5pZTyYT6R5EVkrojsE5FSEXnE6nhcRUSeEZFaEdnda1usiOSLSInj3/6O7SIiv3cck50iktvrM3c43l8iIndY8V2cRUTSRGSNiBSJyB4R+Y5ju18eFxEJFZHNIrLDcTx+4tieISKbHN/7VREJdmwPcTwvdbye3mtfjzq27xORayz6Sk4hIgEisk1E3nU895/jYYzx6h8gADgADAGCgR3AKKvjctF3vRLIBXb32vYr4BHH40eA/+t4PB9YCQgwBdjk2B4LHHT829/xuL/V360PxyQJyHU8jgT2A6P89bg4vleE43EQsMnxPV8Dlji2/xn4puPx/cCfHY+XAK86Ho9y/C2FABmOv7EAq79fH47Lg8DfgXcdz/3mePhCT34SUGqMOWiM6QBeARZZHJNLGGPWAo1f2LwIeM7x+Dng+l7bnzc9NgIxIpIEXAPkG2MajTHHgHxgrsuDdxFjTJUxZqvjcRNQDKTgp8fF8b2aHU+DHD8GuApY6tj+xeNx+jgtBWaJiDi2v2KMaTfGHAJK6flb8zoikgosAJ5yPBf86Hj4QpJPAY72el7u2OYvBhhjqhyPq4EBjsfnOi4+e7wcp9Y59PRe/fa4OIYmtgO19PzP6gBw3BjT5XhL7+/2+fd2vH4CiMOHjgfwOPAwYHc8j8OPjocvJHnlYHrOK/1yTqyIRABvAN81xpzs/Zq/HRdjTLcxZjyQSk9vc6S1EVlHRK4Fao0xhVbHYhVfSPIVQFqv56mObf6ixjHcgOPfWsf2cx0XnzteIhJET4J/yRizzLHZ74+LMeY4sAaYSs+wVKDjpd7f7fPv7Xg9GmjAd47HNOA6ESmjZyj3KuB3+NHx8IUkvwUY7rhaHkzPxZLlFsfkTsuB0zNB7gDe7rX9dsdskinACcfwxQfAHBHp75hxMsexzSs5xkufBoqNMb/p9ZJfHhcRSRCRGMfjfsDV9FynWAPc5HjbF4/H6eN0E/CR48xnObDEMdskAxgObHbLl3AiY8yjxphUY0w6PbnhI2PMrfjT8bD6yq8zfuiZMbGfnrHHH1odjwu/58tAFdBJz5jg3fSMF34IlACrgVjHewX4g+OY7ALyeu3n6/RcOCoF7rL6e/XxmFxOz1DMTmC742e+vx4XYCywzXE8dgM/dmwfQk9SKgVeB0Ic20Mdz0sdrw/pta8fOo7TPmCe1d/NCcdmBv+YXeM3x0PLGiillA/zheEapZRS56BJXimlfJgmeaWU8mGa5JVSyodpkldKKR+mSV4ppXyYJnmllPJh/x9OPnNjl0VfeAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nptimesoneorbit,tpredoneorbit, label='times')\n",
    "plt.xlabel(\"T timesteps\")\n",
    "plt.ylabel(\"T computed from angle\")\n",
    "plt.title(\"Times using start parameters\")\n",
    "plt.show()\n",
    "plt.plot(nptimesoneorbit,tpredoneorbit-nptimesoneorbit, label='residual')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# THERE IS A SECOND HARMONIC IN THIS TIMING DATA!!! I have heard of orbital resonances. Is that what I am seeing?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Arctan function is giving tangent output. I'm done for today. I'm asking for help on this, either Steve or on a forum. Clearly something really weird is going on. This is a distinct problem from the retrograde motion I had before I fixed the center, which you can tell from the sharply spiked top as opposed to the curved top I had before. Now the center appears to be in the correct location but there is some problem related to tangent versus arctangent. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f075c26d7f0>"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(nptimesoneorbit,tpredoneorbit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Retrograde motion as seen from the center of mass. I'm not sure that makes sense. So there's a problem with the definition of the Eang. The problem might be with the ellipse center, which probably shouldn't be at x=-70, if it spans between +5 and -95. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "44428\n",
      "[50.         49.999998   49.999992   ... 49.99997067 49.99998399\n",
      " 49.99999331] [ 0.          0.01224745  0.02449489 ... -0.04690014 -0.0346527\n",
      " -0.02240526] [0.00000000e+00 1.40345423e-02 2.80690841e-02 ... 3.59946256e+02\n",
      " 3.59960291e+02 3.59974325e+02]\n",
      "Eang [0.00000000e+00 2.44948973e-04 4.89897935e-04 ... 6.28224730e+00\n",
      " 6.28249225e+00 6.28273720e+00]\n",
      "[0.00000000e+00 2.44948973e-04 4.89897935e-04 ... 6.28224730e+00\n",
      " 6.28249225e+00 6.28273720e+00] <Parameter 'ecc', value=0.5, bounds=[0:1.0]> <Parameter 'rad', value=50.0, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [0.00000000e+00 8.66025407e-02 1.73205083e-01 ... 4.44255130e+03\n",
      " 4.44263791e+03 4.44272451e+03]\n",
      "44428\n",
      "[50.         49.999998   49.999992   ... 49.99997067 49.99998399\n",
      " 49.99999331] [ 0.          0.01224745  0.02449489 ... -0.04690014 -0.0346527\n",
      " -0.02240526] [0.00000000e+00 1.40345423e-02 2.80690841e-02 ... 3.59946256e+02\n",
      " 3.59960291e+02 3.59974325e+02]\n",
      "Eang [0.00000000e+00 2.44948973e-04 4.89897935e-04 ... 6.28224730e+00\n",
      " 6.28249225e+00 6.28273720e+00]\n",
      "[0.00000000e+00 2.44948973e-04 4.89897935e-04 ... 6.28224730e+00\n",
      " 6.28249225e+00 6.28273720e+00] <Parameter 'ecc', value=0.5, bounds=[0:1.0]> <Parameter 'rad', value=50.0, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [0.00000000e+00 8.66025407e-02 1.73205083e-01 ... 4.44255130e+03\n",
      " 4.44263791e+03 4.44272451e+03]\n",
      "44428\n",
      "[50.         49.999998   49.999992   ... 49.99997067 49.99998399\n",
      " 49.99999331] [ 0.          0.01224745  0.02449489 ... -0.04690014 -0.0346527\n",
      " -0.02240526] [0.00000000e+00 1.40345423e-02 2.80690841e-02 ... 3.59946256e+02\n",
      " 3.59960291e+02 3.59974325e+02]\n",
      "Eang [0.00000000e+00 2.44948973e-04 4.89897935e-04 ... 6.28224730e+00\n",
      " 6.28249225e+00 6.28273720e+00]\n",
      "[0.00000000e+00 2.44948973e-04 4.89897935e-04 ... 6.28224730e+00\n",
      " 6.28249225e+00 6.28273720e+00] <Parameter 'ecc', value=0.5, bounds=[0:1.0]> <Parameter 'rad', value=50.0, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [0.00000000e+00 8.66025407e-02 1.73205083e-01 ... 4.44255130e+03\n",
      " 4.44263791e+03 4.44272451e+03]\n",
      "44428\n",
      "[50.         49.999998   49.999992   ... 49.99997067 49.99998399\n",
      " 49.99999331] [ 1.17033446e-06  1.22486187e-02  2.44960651e-02 ... -4.68989659e-02\n",
      " -3.46515281e-02 -2.24040848e-02] [3.60000000e+02 1.40343349e-02 2.80688766e-02 ... 3.59946256e+02\n",
      " 3.59960291e+02 3.59974325e+02]\n",
      "Eang [6.28318530e+00 2.44945352e-04 4.89894314e-04 ... 6.28224730e+00\n",
      " 6.28249225e+00 6.28273720e+00]\n",
      "[6.28318530e+00 2.44945352e-04 4.89894314e-04 ... 6.28224730e+00\n",
      " 6.28249225e+00 6.28273720e+00] <Parameter 'ecc', value=0.5, bounds=[0:1.0]> <Parameter 'rad', value=50.0, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [4.44288294e+03 8.66012604e-02 1.73203803e-01 ... 4.44255130e+03\n",
      " 4.44263791e+03 4.44272451e+03]\n",
      "44428\n",
      "[50.00000038 49.99999838 49.99999238 ... 49.99997105 49.99998437\n",
      " 49.99999369] [ 0.          0.01224745  0.02449489 ... -0.04690014 -0.0346527\n",
      " -0.02240526] [0.00000000e+00 1.40345422e-02 2.80690839e-02 ... 3.59946256e+02\n",
      " 3.59960291e+02 3.59974325e+02]\n",
      "Eang [0.00000000e+00 2.44948971e-04 4.89897932e-04 ... 6.28224730e+00\n",
      " 6.28249225e+00 6.28273720e+00]\n",
      "[0.00000000e+00 2.44948971e-04 4.89897932e-04 ... 6.28224730e+00\n",
      " 6.28249225e+00 6.28273720e+00] <Parameter 'ecc', value=0.5, bounds=[0:1.0]> <Parameter 'rad', value=50.000000759667046, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [0.00000000e+00 8.66025420e-02 1.73205086e-01 ... 4.44255141e+03\n",
      " 4.44263801e+03 4.44272461e+03]\n",
      "44428\n",
      "[50.00000037 49.99999837 49.99999237 ... 49.99997104 49.99998436\n",
      " 49.99999368] [ 0.          0.01224745  0.02449489 ... -0.04690014 -0.0346527\n",
      " -0.02240526] [0.00000000e+00 1.40345422e-02 2.80690839e-02 ... 3.59946256e+02\n",
      " 3.59960291e+02 3.59974325e+02]\n",
      "Eang [0.00000000e+00 2.44948971e-04 4.89897932e-04 ... 6.28224730e+00\n",
      " 6.28249225e+00 6.28273720e+00]\n",
      "[0.00000000e+00 2.44948971e-04 4.89897932e-04 ... 6.28224730e+00\n",
      " 6.28249225e+00 6.28273720e+00] <Parameter 'ecc', value=0.5000000074505806, bounds=[0:1.0]> <Parameter 'rad', value=50.0, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [0.00000000e+00 8.66025387e-02 1.73205079e-01 ... 4.44255130e+03\n",
      " 4.44263791e+03 4.44272451e+03]\n",
      "44428\n",
      "[51.14253001 51.14252801 51.14252201 ... 51.14250069 51.142514\n",
      " 51.14252332] [-5.34042313e-13  1.22474484e-02  2.44948948e-02 ... -4.69001362e-02\n",
      " -3.46526984e-02 -2.24052551e-02] [5.59653822e-14 1.37210090e-02 2.74420175e-02 ... 3.59947457e+02\n",
      " 3.59961178e+02 3.59974899e+02]\n",
      "Eang [9.76780186e-16 2.39476784e-04 4.78953559e-04 ... 6.28226826e+00\n",
      " 6.28250774e+00 6.28274721e+00]\n",
      "[9.76780186e-16 2.39476784e-04 4.78953559e-04 ... 6.28226826e+00\n",
      " 6.28250774e+00 6.28274721e+00] <Parameter 'ecc', value=0.5238503172967668, bounds=[0:1.0]> <Parameter 'rad', value=49.90457989778409, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [3.27929844e-13 8.03984217e-02 1.60796845e-01 ... 4.42986292e+03\n",
      " 4.42994332e+03 4.43002372e+03]\n",
      "44428\n",
      "[51.14253001 51.14252801 51.14252201 ... 51.14250069 51.142514\n",
      " 51.14252332] [-5.34042313e-13  1.22474484e-02  2.44948948e-02 ... -4.69001362e-02\n",
      " -3.46526984e-02 -2.24052551e-02] [5.59653822e-14 1.37210090e-02 2.74420175e-02 ... 3.59947457e+02\n",
      " 3.59961178e+02 3.59974899e+02]\n",
      "Eang [9.76780186e-16 2.39476784e-04 4.78953559e-04 ... 6.28226826e+00\n",
      " 6.28250774e+00 6.28274721e+00]\n",
      "[9.76780186e-16 2.39476784e-04 4.78953559e-04 ... 6.28226826e+00\n",
      " 6.28250774e+00 6.28274721e+00] <Parameter 'ecc', value=0.5238503172967668, bounds=[0:1.0]> <Parameter 'rad', value=49.90457989778409, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [3.27929844e-13 8.03984217e-02 1.60796845e-01 ... 4.42986292e+03\n",
      " 4.42994332e+03 4.43002372e+03]\n",
      "44428\n",
      "[51.14253041 51.14252841 51.14252241 ... 51.14250108 51.1425144\n",
      " 51.14252372] [-5.34042321e-13  1.22474484e-02  2.44948948e-02 ... -4.69001362e-02\n",
      " -3.46526984e-02 -2.24052551e-02] [5.59653777e-14 1.37210089e-02 2.74420173e-02 ... 3.59947457e+02\n",
      " 3.59961178e+02 3.59974899e+02]\n",
      "Eang [9.76780109e-16 2.39476783e-04 4.78953555e-04 ... 6.28226826e+00\n",
      " 6.28250774e+00 6.28274721e+00]\n",
      "[9.76780109e-16 2.39476783e-04 4.78953555e-04 ... 6.28226826e+00\n",
      " 6.28250774e+00 6.28274721e+00] <Parameter 'ecc', value=0.5238503172967668, bounds=[0:1.0]> <Parameter 'rad', value=49.90458065602871, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [3.27929825e-13 8.03984229e-02 1.60796848e-01 ... 4.42986302e+03\n",
      " 4.42994342e+03 4.43002382e+03]\n",
      "44428\n",
      "[51.14253003 51.14252803 51.14252203 ... 51.1425007  51.14251402\n",
      " 51.14252334] [-5.34042313e-13  1.22474484e-02  2.44948948e-02 ... -4.69001362e-02\n",
      " -3.46526984e-02 -2.24052551e-02] [5.59653817e-14 1.37210090e-02 2.74420175e-02 ... 3.59947457e+02\n",
      " 3.59961178e+02 3.59974899e+02]\n",
      "Eang [9.76780177e-16 2.39476784e-04 4.78953559e-04 ... 6.28226826e+00\n",
      " 6.28250774e+00 6.28274721e+00]\n",
      "[9.76780177e-16 2.39476784e-04 4.78953559e-04 ... 6.28226826e+00\n",
      " 6.28250774e+00 6.28274721e+00] <Parameter 'ecc', value=0.5238503176518945, bounds=[0:1.0]> <Parameter 'rad', value=49.90457989778409, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [3.27929841e-13 8.03984217e-02 1.60796845e-01 ... 4.42986292e+03\n",
      " 4.42994332e+03 4.43002372e+03]\n",
      "44428\n",
      "[51.18790693 51.18790493 51.18789893 ... 51.1878776  51.18789092\n",
      " 51.18790024] [-5.34969277e-13  1.22474484e-02  2.44948948e-02 ... -4.69001362e-02\n",
      " -3.46526984e-02 -2.24052551e-02] [5.46008166e-14 1.37088457e-02 2.74176908e-02 ... 3.59947504e+02\n",
      " 3.59961212e+02 3.59974921e+02]\n",
      "Eang [9.52964024e-16 2.39264494e-04 4.78528978e-04 ... 6.28226907e+00\n",
      " 6.28250834e+00 6.28274760e+00]\n",
      "[9.52964024e-16 2.39264494e-04 4.78528978e-04 ... 6.28226907e+00\n",
      " 6.28250834e+00 6.28274760e+00] <Parameter 'ecc', value=0.5248011162568158, bounds=[0:1.0]> <Parameter 'rad', value=49.90063115066929, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [3.19257399e-13 8.01572345e-02 1.60314471e-01 ... 4.42933804e+03\n",
      " 4.42941820e+03 4.42949836e+03]\n",
      "44428\n",
      "[51.18790693 51.18790493 51.18789893 ... 51.1878776  51.18789092\n",
      " 51.18790024] [-5.34969277e-13  1.22474484e-02  2.44948948e-02 ... -4.69001362e-02\n",
      " -3.46526984e-02 -2.24052551e-02] [5.46008166e-14 1.37088457e-02 2.74176908e-02 ... 3.59947504e+02\n",
      " 3.59961212e+02 3.59974921e+02]\n",
      "Eang [9.52964024e-16 2.39264494e-04 4.78528978e-04 ... 6.28226907e+00\n",
      " 6.28250834e+00 6.28274760e+00]\n",
      "[9.52964024e-16 2.39264494e-04 4.78528978e-04 ... 6.28226907e+00\n",
      " 6.28250834e+00 6.28274760e+00] <Parameter 'ecc', value=0.5248011162568158, bounds=[0:1.0]> <Parameter 'rad', value=49.90063115066929, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [3.19257399e-13 8.01572345e-02 1.60314471e-01 ... 4.42933804e+03\n",
      " 4.42941820e+03 4.42949836e+03]\n",
      "44428\n",
      "[51.18790733 51.18790533 51.18789933 ... 51.187878   51.18789132\n",
      " 51.18790063] [-5.34969285e-13  1.22474484e-02  2.44948948e-02 ... -4.69001362e-02\n",
      " -3.46526984e-02 -2.24052551e-02] [5.46008121e-14 1.37088456e-02 2.74176906e-02 ... 3.59947504e+02\n",
      " 3.59961212e+02 3.59974921e+02]\n",
      "Eang [9.52963946e-16 2.39264492e-04 4.78528974e-04 ... 6.28226907e+00\n",
      " 6.28250834e+00 6.28274760e+00]\n",
      "[9.52963946e-16 2.39264492e-04 4.78528974e-04 ... 6.28226907e+00\n",
      " 6.28250834e+00 6.28274760e+00] <Parameter 'ecc', value=0.5248011162568158, bounds=[0:1.0]> <Parameter 'rad', value=49.900631908855054, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [3.19257380e-13 8.01572357e-02 1.60314473e-01 ... 4.42933814e+03\n",
      " 4.42941830e+03 4.42949846e+03]\n",
      "44428\n",
      "[51.18790695 51.18790495 51.18789895 ... 51.18787762 51.18789094\n",
      " 51.18790025] [-5.34969278e-13  1.22474484e-02  2.44948948e-02 ... -4.69001362e-02\n",
      " -3.46526984e-02 -2.24052551e-02] [5.46008160e-14 1.37088457e-02 2.74176908e-02 ... 3.59947504e+02\n",
      " 3.59961212e+02 3.59974921e+02]\n",
      "Eang [9.52964014e-16 2.39264494e-04 4.78528978e-04 ... 6.28226907e+00\n",
      " 6.28250834e+00 6.28274760e+00]\n",
      "[9.52964014e-16 2.39264494e-04 4.78528978e-04 ... 6.28226907e+00\n",
      " 6.28250834e+00 6.28274760e+00] <Parameter 'ecc', value=0.5248011166260778, bounds=[0:1.0]> <Parameter 'rad', value=49.90063115066929, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [3.19257395e-13 8.01572344e-02 1.60314471e-01 ... 4.42933804e+03\n",
      " 4.42941820e+03 4.42949836e+03]\n",
      "44428\n",
      "[51.18972009 51.18971809 51.18971209 ... 51.18969076 51.18970408\n",
      " 51.18971339] [-5.35006317e-13  1.22474484e-02  2.44948948e-02 ... -4.69001362e-02\n",
      " -3.46526984e-02 -2.24052551e-02] [5.45460153e-14 1.37083601e-02 2.74167197e-02 ... 3.59947505e+02\n",
      " 3.59961214e+02 3.59974922e+02]\n",
      "Eang [9.52007561e-16 2.39256019e-04 4.78512028e-04 ... 6.28226910e+00\n",
      " 6.28250836e+00 6.28274762e+00]\n",
      "[9.52007561e-16 2.39256019e-04 4.78512028e-04 ... 6.28226910e+00\n",
      " 6.28250836e+00 6.28274762e+00] <Parameter 'ecc', value=0.5248394339111238, bounds=[0:1.0]> <Parameter 'rad', value=49.90044267908916, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [3.18909445e-13 8.01474780e-02 1.60294958e-01 ... 4.42931298e+03\n",
      " 4.42939313e+03 4.42947328e+03]\n",
      "44428\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[51.18972009 51.18971809 51.18971209 ... 51.18969076 51.18970408\n",
      " 51.18971339] [-5.35006317e-13  1.22474484e-02  2.44948948e-02 ... -4.69001362e-02\n",
      " -3.46526984e-02 -2.24052551e-02] [5.45460153e-14 1.37083601e-02 2.74167197e-02 ... 3.59947505e+02\n",
      " 3.59961214e+02 3.59974922e+02]\n",
      "Eang [9.52007561e-16 2.39256019e-04 4.78512028e-04 ... 6.28226910e+00\n",
      " 6.28250836e+00 6.28274762e+00]\n",
      "[9.52007561e-16 2.39256019e-04 4.78512028e-04 ... 6.28226910e+00\n",
      " 6.28250836e+00 6.28274762e+00] <Parameter 'ecc', value=0.5248394339111238, bounds=[0:1.0]> <Parameter 'rad', value=49.90044267908916, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [3.18909445e-13 8.01474780e-02 1.60294958e-01 ... 4.42931298e+03\n",
      " 4.42939313e+03 4.42947328e+03]\n",
      "44428\n",
      "[51.18972049 51.18971849 51.18971249 ... 51.18969116 51.18970447\n",
      " 51.18971379] [-5.35006325e-13  1.22474484e-02  2.44948948e-02 ... -4.69001362e-02\n",
      " -3.46526984e-02 -2.24052551e-02] [5.45460109e-14 1.37083600e-02 2.74167194e-02 ... 3.59947505e+02\n",
      " 3.59961214e+02 3.59974922e+02]\n",
      "Eang [9.52007483e-16 2.39256017e-04 4.78512024e-04 ... 6.28226910e+00\n",
      " 6.28250836e+00 6.28274762e+00]\n",
      "[9.52007483e-16 2.39256017e-04 4.78512024e-04 ... 6.28226910e+00\n",
      " 6.28250836e+00 6.28274762e+00] <Parameter 'ecc', value=0.5248394339111238, bounds=[0:1.0]> <Parameter 'rad', value=49.900443437272116, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [3.18909426e-13 8.01474792e-02 1.60294960e-01 ... 4.42931309e+03\n",
      " 4.42939323e+03 4.42947338e+03]\n",
      "44428\n",
      "[51.18972011 51.18971811 51.18971211 ... 51.18969078 51.1897041\n",
      " 51.18971341] [-5.35006317e-13  1.22474484e-02  2.44948948e-02 ... -4.69001362e-02\n",
      " -3.46526984e-02 -2.24052551e-02] [5.45460148e-14 1.37083601e-02 2.74167196e-02 ... 3.59947505e+02\n",
      " 3.59961214e+02 3.59974922e+02]\n",
      "Eang [9.52007552e-16 2.39256019e-04 4.78512028e-04 ... 6.28226910e+00\n",
      " 6.28250836e+00 6.28274762e+00]\n",
      "[9.52007552e-16 2.39256019e-04 4.78512028e-04 ... 6.28226910e+00\n",
      " 6.28250836e+00 6.28274762e+00] <Parameter 'ecc', value=0.5248394342809554, bounds=[0:1.0]> <Parameter 'rad', value=49.90044267908916, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [3.18909442e-13 8.01474779e-02 1.60294958e-01 ... 4.42931298e+03\n",
      " 4.42939313e+03 4.42947328e+03]\n",
      "44428\n",
      "[51.18979262 51.18979062 51.18978462 ... 51.18976329 51.1897766\n",
      " 51.18978592] [-5.35007798e-13  1.22474484e-02  2.44948948e-02 ... -4.69001362e-02\n",
      " -3.46526984e-02 -2.24052551e-02] [5.45438227e-14 1.37083407e-02 2.74166808e-02 ... 3.59947506e+02\n",
      " 3.59961214e+02 3.59974922e+02]\n",
      "Eang [9.51969292e-16 2.39255680e-04 4.78511350e-04 ... 6.28226911e+00\n",
      " 6.28250836e+00 6.28274762e+00]\n",
      "[9.51969292e-16 2.39255680e-04 4.78511350e-04 ... 6.28226911e+00\n",
      " 6.28250836e+00 6.28274762e+00] <Parameter 'ecc', value=0.5248409672669576, bounds=[0:1.0]> <Parameter 'rad', value=49.900435082380554, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [3.18895524e-13 8.01470875e-02 1.60294177e-01 ... 4.42931197e+03\n",
      " 4.42939212e+03 4.42947227e+03]\n",
      "44428\n",
      "[51.18979262 51.18979062 51.18978462 ... 51.18976329 51.1897766\n",
      " 51.18978592] [-5.35007798e-13  1.22474484e-02  2.44948948e-02 ... -4.69001362e-02\n",
      " -3.46526984e-02 -2.24052551e-02] [5.45438227e-14 1.37083407e-02 2.74166808e-02 ... 3.59947506e+02\n",
      " 3.59961214e+02 3.59974922e+02]\n",
      "Eang [9.51969292e-16 2.39255680e-04 4.78511350e-04 ... 6.28226911e+00\n",
      " 6.28250836e+00 6.28274762e+00]\n",
      "[9.51969292e-16 2.39255680e-04 4.78511350e-04 ... 6.28226911e+00\n",
      " 6.28250836e+00 6.28274762e+00] <Parameter 'ecc', value=0.5248409672669576, bounds=[0:1.0]> <Parameter 'rad', value=49.900435082380554, bounds=[0:inf]> <Parameter 'mass', value=1.0 (fixed), bounds=[-inf:inf]> [3.18895524e-13 8.01470875e-02 1.60294177e-01 ... 4.42931197e+03\n",
      " 4.42939212e+03 4.42947227e+03]\n"
     ]
    }
   ],
   "source": [
    "from lmfit import Minimizer,Parameters\n",
    "pfittEang = Parameters()\n",
    "pfittEang.add(name='theta', value=theta0, min=theta0-math.pi, max=theta0+math.pi, vary=True)\n",
    "pfittEang.add(name='rad', value=rad0, min=0, vary=True)\n",
    "pfittEang.add(name='ecc', value=ecc0, min=0, max=1.0, vary=True)\n",
    "pfittEang.add(name='mass', value=masses[0], vary=False)\n",
    "pfittEang.add(name='useperihelion', value=True, vary=False)\n",
    "\n",
    "minit = Minimizer(residualtEang, pfittEang, fcn_args=(nptimesoneorbit,npstar2x[:endindex-1,:]))\n",
    "\n",
    "outt = minit.leastsq()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<h2>Fit Statistics</h2><table><tr><td>fitting method</td><td>leastsq</td><td></td></tr><tr><td># function evals</td><td>17</td><td></td></tr><tr><td># data points</td><td>44428</td><td></td></tr><tr><td># variables</td><td>3</td><td></td></tr><tr><td>chi-square</td><td> 54905637.6</td><td></td></tr><tr><td>reduced chi-square</td><td> 1235.91756</td><td></td></tr><tr><td>Akaike info crit.</td><td> 316311.209</td><td></td></tr><tr><td>Bayesian info crit.</td><td> 316337.313</td><td></td></tr></table><h2>Variables</h2><table><tr><th> name </th><th> value </th><th> initial value </th><th> min </th><th> max </th><th> vary </th></tr><tr><td> theta </td><td> -2.0428e-14 </td><td> 0.0 </td><td> -3.14159265 </td><td>  3.14159265 </td><td> True </td></tr><tr><td> rad </td><td>  49.9004351 </td><td> 50 </td><td>  0.00000000 </td><td>         inf </td><td> True </td></tr><tr><td> ecc </td><td>  0.52484097 </td><td> 0.5 </td><td>  0.00000000 </td><td>  1.00000000 </td><td> True </td></tr><tr><td> mass </td><td>  1.00000000 </td><td> 1.0 </td><td>        -inf </td><td>         inf </td><td> False </td></tr><tr><td> useperihelion </td><td>  1.00000000 </td><td> True </td><td>        -inf </td><td>         inf </td><td> False </td></tr></table>"
      ],
      "text/plain": [
       "<lmfit.minimizer.MinimizerResult at 0x7f074bf89eb0>"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "outt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Eccentricity fit is still not great for eccentricity of 0.9 (0.99), but radius fit is pretty good. The chi square is enormous. Eccentricity of 0.5 looks somewhat better (ecc 0.51) but still has a large chisquared and generates a potentially helpful divide by zero warning in the fit. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4442.699999998631"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tfinal=nptimesoneorbit[endindex-2]\n",
    "tfinal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Updated Jupyter and python packages and angular momentum and energy conservation improved by many orders of magnitude, but the fit is about the same. deltaL and deltaE are now consistent with roundoff error. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.fft import fft"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.signal import blackman\n",
    "wndow=blackman(len(nptimesoneorbit))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "ftresiduals=fft(nptimesoneorbit-tpredoneorbit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "xf = np.linspace(0.0, 1.0/(2.0*dt), len(nptimesoneorbit)//2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f074ad250d0>]"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(xf[1:len(nptimesoneorbit)//2], 2.0/len(nptimesoneorbit) * np.abs(ftresiduals[1:len(nptimesoneorbit)//2]), '-b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "ftr=fft(np.sqrt(npstar1x[:endindex-1,0]**2+npstar1x[:endindex-1,1]**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f074ac9abb0>]"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(xf[1:len(nptimesoneorbit)//2], 2.0/len(nptimesoneorbit) * np.abs(ftr[1:len(nptimesoneorbit)//2]), '-b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fourier transform won't work. The period is one time the length of the signal. See the blip at the second bin? That's the second harmonic. I don't see higher harmonics. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f074ab8dca0>]"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(xf[1:50], 2.0/len(nptimesoneorbit) * np.abs(ftresiduals[1:50]), '-b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f074aa29460>]"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(np.arange(1,30), 2.0/len(nptimesoneorbit[:29]) * np.abs(ftresiduals[1:30]), '-b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "peaks=[4,8,13,17]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the FFT of the residuals of the predicted time versus the actual time for the parameters of the simulation, using the theoretically expected equation E-esinE up to some factors. Looks like it has some resonances with percoids of about four times the lowest frequency resolution, I’m going to have to think about that, but either that means there’s an issue related to the four fold symmetry of the orbit, or something is happening related to the fact that it’s an RK4. I forget whether the lowest frequency resolution comes from the step size or from the orbital period. I think it comes from the orbital period, which suggests that it has to do with the four fold orbital symmetry, though it would be nice to think it comes from the RK4. Maybe it makes sense that it should have higher moments in its residuals, since its not circular. But the residuals shouldn’t be this large, I don’t think. I am using 0.9 as the eccentricity. Maybe that’s part of the issue. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1/tfinal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f074a885580>]"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(xf[1:50], 2.0/len(nptimesoneorbit) * np.abs(ftr[1:50]), '-b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For e=0.5 and e=0.05 the fit looks the same on Ubuntu 20.04 as it does on a Macbook Pro running 10.15.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}