{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "84fbc800-cb62-4f3b-86b3-3a7340867d8a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# this part just defines the f-function\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from math import pi, sqrt\n",
    "\n",
    "from matplotlib import animation, rc\n",
    "from IPython.display import HTML\n",
    "from scipy.integrate import solve_ivp\n",
    "\n",
    "# u0  u1   u2   u3   u4   u5   u6   u7\n",
    "# x1  y1   x2   y2   vx1  vy1  vx2  vy2\n",
    "\n",
    "def myfun( t, u ):\n",
    "    f = np.zeros((8,));\n",
    "    f[0] = u[4];\n",
    "    f[1] = u[5];\n",
    "    f[2] = u[6];\n",
    "    f[3] = u[7];\n",
    "    R1 = sqrt((u[0]**2) + (u[1]**2));\n",
    "    R2 = sqrt((u[2]**2) + (u[3]**2));\n",
    "    dx = u[0]-u[2];\n",
    "    dy = u[1]-u[3];\n",
    "    R12 = sqrt((dx**2) + (dy**2));\n",
    "    q1 = -G*Ms/(R1**3);\n",
    "    q2 = -G*Ms/(R2**3);\n",
    "    q12 = -G*Mp2/(R12**3);\n",
    "    q21 = -G*Mp1/(R12**3);\n",
    "    c=1.0; # coupling between planets\n",
    "    f[4] = u[0]*q1 + c*dx*q12;\n",
    "    f[5] = u[1]*q1 + c*dy*q12;\n",
    "    f[6] = u[2]*q2 - c*dx*q21;\n",
    "    f[7] = u[3]*q2 - c*dy*q21;\n",
    "    return(f);\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "24a9db41-1af7-46a8-bd54-6a8bf2c60f71",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# function to make a numpy N-by-1 column vector\n",
    "# c=eda_cvec(v1, v2, ...) from a list of several\n",
    "# array-like entities v1, v2, including a number\n",
    "# a list of numbers, a tuple of numbers, an N-by-0 np array\n",
    "# and a N-by-1 np array. The function\n",
    "# also insures that, if v is an np array, that\n",
    "# c is a copy, as contrasted to a view, of it\n",
    "# It promotes integers to floats, and integers\n",
    "# and floats to complex, by context.\n",
    "# This version concatenates many argments,\n",
    "# whereas c=eda_cvec1(v1) takes just one argiment.\n",
    "# I recommend always using eda_cvec(v1, v2, ...)\n",
    "def gda_cvec(*argv):\n",
    "    t = int;\n",
    "    Nt = 0;\n",
    "    for a in argv:\n",
    "        v = gda_cvec1(a);\n",
    "        N,M = np.shape(v);\n",
    "        Nt = Nt + N;\n",
    "        if( N==0 ):\n",
    "            continue; # skip vector of zero length\n",
    "        if (t==int) and isinstance(v[0,0],float):\n",
    "            t=float;\n",
    "        elif isinstance(v[0,0],complex):\n",
    "            t=complex;\n",
    "    w = np.zeros((Nt,1),dtype=t);\n",
    "    Nt = 0;\n",
    "    for a in argv:\n",
    "        v = gda_cvec1(a);\n",
    "        N,M = np.shape(v);\n",
    "        w[Nt:Nt+N,0:1] = v;  # patch 20230418 was #w[Nt:Nt+N,0] = v[0:N,0];\n",
    "        Nt = Nt + N;\n",
    "    return w;\n",
    "\n",
    "# function to make a numpy N-by-1 column vector\n",
    "# c=gda_cvec1(v) from entity v that is array-like,\n",
    "# including a number, a list of numbers, a tuple\n",
    "# of numbers, an N-by-0 np array and a N-by1 np array.\n",
    "# It promotes integers to floats, and integers\n",
    "# and floats to complex, by context. The function\n",
    "# also insures that, if v is an np array, that\n",
    "# c is a copy, as contrasted to a view, of it.\n",
    "# This version takes just one input argment.\n",
    "# whereas c=gda_cvec(v1,v2,...) concatenates\n",
    "# many argiments.\n",
    "def gda_cvec1(v):\n",
    "    if isinstance(v, int) or isinstance(v, np.int32):\n",
    "        w = np.zeros((1,1),dtype=int);\n",
    "        w[0,0] = v;\n",
    "        return w;\n",
    "    elif isinstance(v, float):\n",
    "        w = np.zeros((1,1),dtype=float);\n",
    "        w[0,0] = v;\n",
    "        return w;\n",
    "    elif isinstance(v, complex):\n",
    "        w = np.zeros((1,1),dtype=complex);\n",
    "        w[0,0] = v;\n",
    "        return w;\n",
    "    elif isinstance(v, np.ndarray):\n",
    "        s = np.shape(v);\n",
    "        if len(s) == 1:\n",
    "            return np.copy(np.reshape(v,(s[0],1)));\n",
    "        else:\n",
    "            [r,c]=s;\n",
    "            if( c==1 ):\n",
    "                return(np.copy(v));\n",
    "            elif(r==1):\n",
    "                return(np.copy(v.T));\n",
    "            else:\n",
    "                raise TypeError(\"gda_cvec: %d by %d ndarray not allowed\" % (r, c));\n",
    "    elif isinstance(v, list):\n",
    "        r = len(v);\n",
    "        t = int;\n",
    "        for vi in v:\n",
    "            if isinstance(vi,int) or isinstance(vi, np.int32): #patch v->vi 20230418\n",
    "                pass;\n",
    "            elif isinstance(vi,float):\n",
    "                t=float;\n",
    "            elif isinstance(vi,complex):\n",
    "                t=complex;\n",
    "                break;\n",
    "            else:\n",
    "                raise TypeError(\"gda_cvec: list contains unsupported type %s\" % type(vi));\n",
    "        w = np.zeros((r,1),dtype=t);\n",
    "        w[:,0] = np.array(v); # patch v -> np.array(v)\n",
    "        return w;\n",
    "    elif isinstance(v, tuple):\n",
    "        r = len(v);\n",
    "        t = int;\n",
    "        for vi in v:\n",
    "            if isinstance(vi,int) or isinstance(vi, np.int32): #patch v->vi 20230418\n",
    "                pass;\n",
    "            elif isinstance(vi,float):\n",
    "                t=float;\n",
    "            elif isinstance(vi,complex):\n",
    "                t=complex;\n",
    "                break;\n",
    "            else:\n",
    "                raise TypeError(\"gda_cvec: tuple contains unsupported type %s\" % type(vi));\n",
    "        w = np.zeros((r,1),dtype=t);\n",
    "        w[:,0] = np.array(list(v)); # patch v -> np.array(list(v));\n",
    "        return w;\n",
    "    else:\n",
    "        raise TypeError(\"gda_cvec: %s not supported\" % type(v));\n",
    "\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "d524cf53-73d7-4b86-8bb9-76595f4263d6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solar only\n",
      "[ 1.   0.1  1.  -0.1  0.   0.   0.   0. ]\n",
      "[ 0.          0.          0.          0.         -0.98518534 -0.09851853\n",
      " -0.98518534  0.09851853]\n",
      " \n",
      "Solar only\n",
      "[ 0.1  1.  -0.1  1.   0.   0.   0.   0. ]\n",
      "[ 0.          0.          0.          0.         -0.09851853 -0.98518534\n",
      "  0.09851853 -0.98518534]\n",
      " \n",
      "Interplanetary only, equal masses\n",
      "[ 1.   0.1  1.  -0.1  0.   0.   0.   0. ]\n",
      "[  0.   0.   0.   0.  -0. -25.   0.  25.]\n",
      " \n",
      "Interplanetary only, equal masses\n",
      "[ 0.1  1.  -0.1  1.   0.   0.   0.   0. ]\n",
      "[  0.   0.   0.   0. -25.  -0.  25.   0.]\n",
      " \n",
      "Interplanetary only, unequal masses (Mp2 bigger)\n",
      "[ 1.   0.1  1.  -0.1  0.   0.   0.   0. ]\n",
      "[  0.   0.   0.   0.  -0. -50.   0.  25.]\n",
      " \n"
     ]
    }
   ],
   "source": [
    "# this part checks the f-function\n",
    "\n",
    "G = 1.0;\n",
    "t = 0.0;\n",
    "\n",
    "# check:  Just the planet-sun forces\n",
    "Ms=1.0; Mp1=0.0; Mp2=0.0;\n",
    "#                x1   y1    x2    y2    vx1   vy1   vx2   vy2\n",
    "u = np.array( [  1.0, 0.1,  1.0, -0.1,  0.0,  0.0,  0.0,  0.0 ] );\n",
    "f = myfun( t, u );\n",
    "print('Solar only');\n",
    "print(u);\n",
    "print(f);\n",
    "print(' ');\n",
    "\n",
    "# check:  Just the planet-sun forces\n",
    "Ms=1.0; Mp1=0.0; Mp2=0.0;\n",
    "#                x1   y1    x2    y2    vx1   vy1   vx2   vy2\n",
    "u = np.array( [  0.1, 1.0,  -0.1, 1.0,  0.0,  0.0,  0.0,  0.0 ] );\n",
    "f = myfun( t, u );\n",
    "print('Solar only');\n",
    "print(u);\n",
    "print(f);\n",
    "print(' ');\n",
    "\n",
    "# check:  Just the planet-planet forces\n",
    "Ms=0.0; Mp1=1.0; Mp2=1.0;\n",
    "#                x1   y1    x2    y2    vx1   vy1   vx2   vy2\n",
    "u = np.array( [  1.0, 0.1,  1.0, -0.1,  0.0,  0.0,  0.0,  0.0 ] );\n",
    "f = myfun( t, u );\n",
    "print('Interplanetary only, equal masses');\n",
    "print(u);\n",
    "print(f);\n",
    "print(' ');\n",
    "\n",
    "# check:  Just the planet-planet forces\n",
    "Ms=0.0; Mp1=1.0; Mp2=1.0;\n",
    "#                x1   y1    x2    y2    vx1   vy1   vx2   vy2\n",
    "u = np.array( [  0.1, 1.0,  -0.1, 1.0,  0.0,  0.0,  0.0,  0.0 ] );\n",
    "f = myfun( t, u );\n",
    "print('Interplanetary only, equal masses');\n",
    "print(u);\n",
    "print(f);\n",
    "print(' ');\n",
    "\n",
    "# check:  Just the planet-planet forces\n",
    "Ms=0.0; Mp1=1.0; Mp2=2.0;\n",
    "#                x1   y1    x2    y2    vx1   vy1   vx2   vy2\n",
    "u = np.array( [  1.0, 0.1,  1.0, -0.1,  0.0,  0.0,  0.0,  0.0 ] );\n",
    "f = myfun( t, u );\n",
    "print('Interplanetary only, unequal masses (Mp2 bigger)');\n",
    "print(u);\n",
    "print(f);\n",
    "print(' ');\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "d979cbe1-6b82-4698-9d0b-ebfcdc1b7e2b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "u0:\n",
      "[ 1.50000000e+11  0.00000000e+00  1.42500000e+11  0.00000000e+00\n",
      "  0.00000000e+00  2.96722092e+04  0.00000000e+00 -3.04430443e+04]\n",
      "done\n",
      "times:  1764611\n"
     ]
    }
   ],
   "source": [
    "# this part calculates the orbits\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from math import pi, sqrt, sin, cos\n",
    "from scipy.integrate import solve_ivp\n",
    "\n",
    "MYCASE = 0;\n",
    "if( MYCASE == 0 ):\n",
    "    q1 = 0.0;       # angle (with respect to x-axis in rads) of planet 1 (u0[0] = cos(q1)*Rp1; u0[1] = sin(q1)*Rp1) \n",
    "    q2 = 0.0;       # angle (with respect to x-axis in rads) of planet 2 (u0[2] = cos(q2)*Rp2; u0[3] = sin(q2)*Rp2)\n",
    "    fR = 0.95;      # planet 2 has this fraction of its normal radius (Rp2 = fR*Rp1)\n",
    "    sv2 = -1.0;     # sign of planet 2 velocity (sv2)\n",
    "    fv2 = 1.0;      # planet 2 has this fraction of its normal velocity  (u0[7] = fv2*sv2*Vp2)\n",
    "    fM2 = 1.0;      # planet 2 has this fraction of its normal mass  (Mp2 = fM2*Mp1)\n",
    "elif( MYCASE == 1 ):\n",
    "    q1 = 0.05;\n",
    "    q2 = -0.05;\n",
    "    fR = 0.95;\n",
    "    sv2 = 1.0;\n",
    "    fv2 = 1.0;\n",
    "    fM2 = 1.0;\n",
    "elif( MYCASE == 2 ):\n",
    "    q1 = 0.0;\n",
    "    q2 = 0.0;\n",
    "    fR = 0.99;\n",
    "    sv2 = -1.0;\n",
    "    fv2 = 1.0;\n",
    "    fM2 = 1.0;\n",
    "elif( MYCASE == 3 ):\n",
    "    q1 = 0.05;\n",
    "    q2 = -0.05;\n",
    "    fR = 0.95;\n",
    "    sv2 = -1.0;\n",
    "    fv2 = 1.0;\n",
    "    fM2 = 1.0;\n",
    "elif( MYCASE == 4 ):\n",
    "    q1 = 0.0;\n",
    "    q2 = 0.0;\n",
    "    fR = 1.001;\n",
    "    sv2 = 1.0;\n",
    "    fv2 = 2.11;\n",
    "    fM2 = 0.01;\n",
    "\n",
    "G = 6.67e-11; # units of m3⋅kg−1⋅s−2\n",
    "Ms = 1.98e30; # mass of sun in km\n",
    "Re = 150.0e9; # distance of earth from sun;\n",
    "\n",
    "Mp1 = 0.001*Ms; # mass of planet 1\n",
    "Mp2 = fM2*Mp1;  # mass of planet 2\n",
    "\n",
    "# assume circular orbits\n",
    "Rp1 = 150.0e9; # distance of planet 1 from sun;\n",
    "Rp2 = fR*Rp1; # distance of planet 2 from sun;\n",
    "k = 4*(pi**2)/(G*Ms); # Kepler's 3rd law consant\n",
    "Pp1 = sqrt(k*(Rp1**3)); # period in s via \n",
    "Pp2 = sqrt(k*(Rp2**3));\n",
    "Vp1 = (2.0*pi*Rp1)/Pp1; # orbital velocity in m/s\n",
    "Vp2 = (2.0*pi*Rp2)/Pp2; # orbital velocity in m/s\n",
    "\n",
    "# u0  u1   u2   u3   u4   u5   u6   u7\n",
    "# x1  y1   x2   y2   vx1  vy1  vx2  vy2\n",
    "\n",
    "# initial conditions\n",
    "\n",
    "u0 = np.zeros((8,));\n",
    "u0[0] = cos(q1)*Rp1;\n",
    "u0[1] = sin(q1)*Rp1;\n",
    "u0[2] = cos(q2)*Rp2;\n",
    "u0[3] = sin(q2)*Rp2;\n",
    "u0[4] = 0.0;\n",
    "u0[5] = Vp1;\n",
    "u0[6] = 0.0;\n",
    "u0[7] = fv2*sv2*Vp2;\n",
    "\n",
    "print('u0:');\n",
    "print(u0);\n",
    "\n",
    "Dt = 0.1*60.0*60.0;\n",
    "t0 = 0.0;     \n",
    "tmax = 20.0*Pp1\n",
    "t = np.arange(t0, t0+tmax, Dt);\n",
    "N,=np.shape(t);\n",
    "\n",
    "sol=solve_ivp(myfun, [t0, tmax], u0, method = 'DOP853', t_eval=t);\n",
    "print('done');\n",
    "\n",
    "# break out solution into Nx1 vectors\n",
    "t = gda_cvec(sol.t);\n",
    "tmax = np.max(t);\n",
    "N, i = np.shape(t);\n",
    "xp1 = gda_cvec(sol.y[0]);\n",
    "yp1 = gda_cvec(sol.y[1]);\n",
    "xp2 = gda_cvec(sol.y[2]);\n",
    "yp2 = gda_cvec(sol.y[3]);\n",
    "vp1x = gda_cvec(sol.y[4]);\n",
    "vp1y = gda_cvec(sol.y[5]);\n",
    "vp2x = gda_cvec(sol.y[6]);\n",
    "vp2y = gda_cvec(sol.y[7]);\n",
    "\n",
    "R1 = np.sqrt( np.power(xp1,2) + np.power(yp1,2) );\n",
    "R2 = np.sqrt( np.power(xp2,2) + np.power(yp2,2) );\n",
    "Dx = xp1 - xp2;\n",
    "Dy = yp1 - yp2;\n",
    "R12 = np.sqrt( np.power(Dx,2) + np.power(Dy,2) );\n",
    "\n",
    "vp1 = np.sqrt( np.power(vp1x,2) + np.power(vp1y,2) );\n",
    "vp2 = np.sqrt( np.power(vp2x,2) + np.power(vp2y,2) );\n",
    "\n",
    "# anguar velocity w = ( r x v ) / R2\n",
    "wp1 = (np.multiply(xp1,vp1y) - np.multiply(yp1,vp1x) )/(R1**2);\n",
    "wp2 = (np.multiply(xp2,vp2y) - np.multiply(yp2,vp2x) )/(R2**2);\n",
    "\n",
    "print('times: ',N);\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "4393d4fa-dfd3-404e-99ee-17430f1f455f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 46948 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this part plots the orbits in the (x,y) plane\n",
    "\n",
    "fig1 = plt.figure();\n",
    "ax = plt.subplot(1,1,1);\n",
    "plt.axis( [-2e8, 2e8, -2e8, 2e8] );\n",
    "plt.plot( 0.0, 0.0, 'ko', lw=1 );\n",
    "plt.plot( xp1/1000.0, yp1/1000.0, 'g-', lw=1 );\n",
    "plt.plot( xp2/1000.0, yp2/1000.0, 'r-', lw=1 );\n",
    "plt.xlabel('x (km)');\n",
    "plt.ylabel('y (km)');\n",
    "plt.show();\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "7e55b511-c48b-4cb8-9208-0bc6e50557a8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 122200 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this part plots the orbits in the 3d\n",
    "fig1 = plt.figure();\n",
    "ax1 = fig1.add_subplot(projection='3d');\n",
    "ax1.set_xlim(( -3e8, 3e8));\n",
    "ax1.set_ylim((-3e8, 3e8));\n",
    "ax1.set_zlim((0, tmax));\n",
    "ax1.plot(sol.y[0]/1000.0, sol.y[1]/1000.0, sol.t, 'k-' );\n",
    "ax1.plot(sol.y[2]/1000.0, sol.y[3]/1000.0, sol.t, 'r-' );\n",
    "ax1.set_xlabel('x (km)');\n",
    "ax1.set_ylabel('y (km)');\n",
    "ax1.set_zlabel('t (s)');\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "fbbe4b17-6441-4b56-bd55-8211c5c15d77",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 30192 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this part plots the sun-planet distance\n",
    "\n",
    "fig1 = plt.figure();\n",
    "ax = plt.subplot(1,1,1);\n",
    "plt.axis( [0, tmax, 0, 4e8] );\n",
    "plt.plot( t, R1/1000.0, 'r-', lw=1 );\n",
    "plt.plot( t, R2/1000.0, 'g-', lw=1 );\n",
    "plt.xlabel('t (s)');\n",
    "plt.ylabel('R (km)');\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "9297265c-c5f6-43be-840d-d3cbaeda2136",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 56808 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this part plots the inter-planet distance\n",
    "\n",
    "fig1 = plt.figure();\n",
    "ax = plt.subplot(1,1,1);\n",
    "plt.axis( [0, tmax, 0, 4e8] );\n",
    "plt.plot( t, R12/1000.0, 'k-', lw=1 );\n",
    "plt.xlabel('t (s)');\n",
    "plt.ylabel('R12 (km)');\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "c4c36e3d-d698-4bc1-a411-0c80600da49f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 96288 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this part plots the velocities\n",
    "\n",
    "fig1 = plt.figure();\n",
    "ax = plt.subplot(1,1,1);\n",
    "vmin = min( np.min(vp1), np.min(vp2) );\n",
    "vmax = max( np.max(vp1), np.max(vp2) );\n",
    "plt.axis( [0, tmax, 0.99*vmin, 1.01*vmax] );\n",
    "plt.plot( t, vp1, 'g-', lw=1 );\n",
    "plt.plot( t, vp2, 'r-', lw=1 );\n",
    "plt.xlabel('t (s)');\n",
    "plt.ylabel('V (km)');\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "5ad6e1cf-914f-4724-a688-92b555fa2b47",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 39092 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this part plots the angular velocities\n",
    "\n",
    "fig1 = plt.figure();\n",
    "ax = plt.subplot(1,1,1);\n",
    "wmin = min( np.min(wp1), np.min(wp2) );\n",
    "wmax = max( np.max(wp1), np.max(wp2) );\n",
    "plt.axis( [0, tmax, 0.99*wmin, 1.01*wmax] );\n",
    "plt.plot( t, wp1, 'g-', lw=1 );\n",
    "plt.plot( t, wp2, 'r-', lw=1 );\n",
    "plt.xlabel('t (s)');\n",
    "plt.ylabel('w (rad/s)');\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "b619df6a-abaa-4031-bfab-775b4b39ef43",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N   1764611  Nframes  800  Nskip  2205\n"
     ]
    },
    {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "[encoded data, 10592 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this plot anomates the orbits\n",
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from math import pi, sqrt\n",
    "\n",
    "from matplotlib import animation, rc\n",
    "from IPython.display import HTML\n",
    "\n",
    "N, = np.shape(sol.t);\n",
    "Nframes = 800;\n",
    "Nskip = int(N/Nframes);\n",
    "print('N  ',N,' Nframes ', Nframes, ' Nskip ', Nskip );\n",
    "\n",
    "fig = plt.figure();\n",
    "ax = fig.subplots();\n",
    "\n",
    "ax.set_xlim(( -2.0*Re/1000.0, 2.0*Re/1000.0));\n",
    "ax.set_ylim(( -2.0*Re/1000.0, 2.0*Re/1000.0));\n",
    "ax.plot(0.0, 0.0, 'ko', lw=2);\n",
    "\n",
    "line1, = ax.plot([], [], 'ro', lw=2);\n",
    "line2, = ax.plot([], [], 'go', lw=2);\n",
    "\n",
    "def init():\n",
    "    line1.set_data([], []);\n",
    "    line2.set_data([], []);\n",
    "    return (line1,line2)\n",
    "\n",
    "def animate(i):\n",
    "    x1 = sol.y[0][i*Nskip]/1000.0;\n",
    "    y1 = sol.y[1][i*Nskip]/1000.0;\n",
    "    x2 = sol.y[2][i*Nskip]/1000.0;\n",
    "    y2 = sol.y[3][i*Nskip]/1000.0;\n",
    "    line1.set_data([x1], [y1]);\n",
    "    line2.set_data([x2], [y2]);\n",
    "    return (line1,line2)\n",
    "\n",
    "anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
    "                               frames=Nframes, interval=100, \n",
    "                               blit=True)\n",
    "\n",
    "HTML(anim.to_html5_video())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "3e2cdeb2-326f-4288-b6a2-e0e3e1a0ed86",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nzoom   11112  Nframes  800  Nskip  13\n"
     ]
    },
    {
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       "YXRhAAAAAQAAAABMYXZmNTguNDUuMTAw\n",
       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "[encoded data, 20768 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this plot anomates a portion of the orbits, centered on the posiion of planet 1\n",
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from math import pi, sqrt\n",
    "\n",
    "from matplotlib import animation, rc\n",
    "from IPython.display import HTML\n",
    "\n",
    "tstart = 2.08e8;\n",
    "tend = 2.12e8;\n",
    "tmax = np.max(sol.t);\n",
    "N, = np.shape(sol.t);\n",
    "Nstart = int(N*tstart/tmax);\n",
    "Nend = int(N*tend/tmax);\n",
    "Nzoom = Nend-Nstart+1;\n",
    "\n",
    "Nframes = 800;\n",
    "Nskip = int(Nzoom/Nframes);\n",
    "print('Nzoom  ',Nzoom,' Nframes ', Nframes, ' Nskip ', Nskip );\n",
    "\n",
    "fig = plt.figure();\n",
    "ax = fig.subplots();\n",
    "ax.set_xlim(( -1.0e8, 1.0e8));\n",
    "ax.set_ylim(( -1.0e8, 1.0e8));\n",
    "ax.set_xlabel('x2-x1');\n",
    "ax.set_ylabel('y2-y1');\n",
    "ax.plot(0.0, 0.0, 'ro', lw=2);\n",
    "\n",
    "line1, = ax.plot([], [], 'go', lw=2);\n",
    "\n",
    "def init():\n",
    "    line1.set_data([], []);\n",
    "    return (line1,)\n",
    "\n",
    "def animate(i):\n",
    "    x1 = sol.y[0][Nstart+i*Nskip]/1000.0;\n",
    "    y1 = sol.y[1][Nstart+i*Nskip]/1000.0;\n",
    "    x2 = sol.y[2][Nstart+i*Nskip]/1000.0;\n",
    "    y2 = sol.y[3][Nstart+i*Nskip]/1000.0;\n",
    "    line1.set_data([x2-x1], [y2-y1]);\n",
    "    return (line1,)\n",
    "\n",
    "anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
    "                               frames=Nframes, interval=30, \n",
    "                               blit=True)\n",
    "\n",
    "HTML(anim.to_html5_video())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "64127264-e411-424c-83f7-196e19dc3f28",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N   1764611  Nframes  800  Nskip  2205\n",
      "writing  planetanimation.gif\n",
      "done\n"
     ]
    },
    {
     "data": {
      "image/png": "[encoded data, 13268 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from math import pi, sqrt\n",
    "\n",
    "from matplotlib import animation, rc\n",
    "\n",
    "N, = np.shape(sol.t);\n",
    "Nframes = 800;\n",
    "Nskip = int(N/Nframes);\n",
    "print('N  ',N,' Nframes ', Nframes, ' Nskip ', Nskip );\n",
    "\n",
    "fig = plt.figure();\n",
    "ax = fig.subplots();\n",
    "\n",
    "ax.set_xlim(( -2.0*Re/1000.0, 2.0*Re/1000.0));\n",
    "ax.set_ylim(( -2.0*Re/1000.0, 2.0*Re/1000.0));\n",
    "ax.set_xlabel('x (km)');\n",
    "ax.set_ylabel('y (km)');\n",
    "ax.plot( 0.0, 0.0, 'ko' );\n",
    "\n",
    "line1, = ax.plot([], [], 'ro', lw=2);\n",
    "line2, = ax.plot([], [], 'go', lw=2);\n",
    "\n",
    "def init():\n",
    "    line1.set_data([], []);\n",
    "    line2.set_data([], []);\n",
    "    return (line1,line2)\n",
    "\n",
    "def animate(i):\n",
    "    x1 = sol.y[0][i*Nskip]/1000.0;\n",
    "    y1 = sol.y[1][i*Nskip]/1000.0;\n",
    "    x2 = sol.y[2][i*Nskip]/1000.0;\n",
    "    y2 = sol.y[3][i*Nskip]/1000.0;\n",
    "    line1.set_data([x1], [y1]);\n",
    "    line2.set_data([x2], [y2]);\n",
    "    return (line1,line2)\n",
    "\n",
    "anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
    "                               frames=Nframes, interval=100, \n",
    "                               blit=True)\n",
    "\n",
    "f = \"planetanimation.gif\" \n",
    "print('writing ',f);\n",
    "writergif = animation.PillowWriter(fps=30);\n",
    "anim.save(f, writer=writergif);\n",
    "print('done');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "56294b0b-ba6e-420e-bb84-84cc7607e02a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nzoom   11112  Nframes  800  Nskip  13\n",
      "writing  planetanimationzoom.gif\n",
      "done\n"
     ]
    },
    {
     "data": {
      "image/png": "[encoded data, 20768 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this plot anomates a portion of the orbits, centered on the posiion of planet 1\n",
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from math import pi, sqrt\n",
    "\n",
    "from matplotlib import animation, rc\n",
    "from IPython.display import HTML\n",
    "\n",
    "tstart = 2.08e8;\n",
    "tend = 2.12e8;\n",
    "tmax = np.max(sol.t);\n",
    "N, = np.shape(sol.t);\n",
    "Nstart = int(N*tstart/tmax);\n",
    "Nend = int(N*tend/tmax);\n",
    "Nzoom = Nend-Nstart+1;\n",
    "\n",
    "Nframes = 800;\n",
    "Nskip = int(Nzoom/Nframes);\n",
    "print('Nzoom  ',Nzoom,' Nframes ', Nframes, ' Nskip ', Nskip );\n",
    "\n",
    "fig = plt.figure();\n",
    "ax = fig.subplots();\n",
    "ax.set_xlim(( -1.0e8, 1.0e8));\n",
    "ax.set_ylim(( -1.0e8, 1.0e8));\n",
    "ax.set_xlabel('x2-x1');\n",
    "ax.set_ylabel('y2-y1');\n",
    "ax.plot(0.0, 0.0, 'ro', lw=2);\n",
    "\n",
    "line1, = ax.plot([], [], 'go', lw=2);\n",
    "\n",
    "def init():\n",
    "    line1.set_data([], []);\n",
    "    return (line1,)\n",
    "\n",
    "def animate(i):\n",
    "    x1 = sol.y[0][Nstart+i*Nskip]/1000.0;\n",
    "    y1 = sol.y[1][Nstart+i*Nskip]/1000.0;\n",
    "    x2 = sol.y[2][Nstart+i*Nskip]/1000.0;\n",
    "    y2 = sol.y[3][Nstart+i*Nskip]/1000.0;\n",
    "    line1.set_data([x2-x1], [y2-y1]);\n",
    "    return (line1,)\n",
    "\n",
    "anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
    "                               frames=Nframes, interval=30, \n",
    "                               blit=True)\n",
    "\n",
    "f = \"planetanimationzoom.gif\" \n",
    "print('writing ',f);\n",
    "writergif = animation.PillowWriter(fps=30);\n",
    "anim.save(f, writer=writergif);\n",
    "print('done');"
   ]
  },
  {
   "cell_type": "raw",
   "id": "a2277703-5927-48e9-99f2-1f50987f83b0",
   "metadata": {},
   "source": []
  }
 ],
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