{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comparing Hohmann and bielliptic transfers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from mpl_toolkits.axes_grid1.inset_locator import zoomed_inset_axes\n",
    "from mpl_toolkits.axes_grid1.inset_locator import mark_inset\n",
    "\n",
    "from astropy import units as u\n",
    "\n",
    "from poliastro.bodies import Earth\n",
    "from poliastro.twobody import Orbit\n",
    "from poliastro.maneuver import Maneuver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/juanlu/.miniconda3/envs/poliastro35/lib/python3.5/site-packages/astropy/units/quantity.py:841: RuntimeWarning: invalid value encountered in true_divide\n",
      "  return super(Quantity, self).__truediv__(other)\n"
     ]
    }
   ],
   "source": [
    "ZOOM = True\n",
    "\n",
    "R = np.linspace(2, 75, num=100)\n",
    "Rstar = [15.58, 40, 60, 100, 200, np.inf]\n",
    "\n",
    "hohmann_data = np.zeros_like(R)\n",
    "bielliptic_data = np.zeros((len(R), len(Rstar)))\n",
    "\n",
    "ss_i = Orbit.circular(Earth, 1.8 * u.km)\n",
    "r_i = ss_i.a\n",
    "v_i = np.sqrt(ss_i.v.dot(ss_i.v))\n",
    "for ii, r in enumerate(R):\n",
    "    r_f = r * r_i\n",
    "    man = Maneuver.hohmann(ss_i, r_f)\n",
    "    hohmann_data[ii] = (man.get_total_cost() / v_i).decompose().value\n",
    "    for jj, rstar in enumerate(Rstar):\n",
    "        r_b = rstar * r_i\n",
    "        man = Maneuver.bielliptic(ss_i, r_b, r_f)\n",
    "        bielliptic_data[ii, jj] = (man.get_total_cost() / v_i).decompose().value\n",
    "\n",
    "idx_max = np.argmax(hohmann_data)\n",
    "\n",
    "ylims = (0.35, 0.6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fe51586ff60>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HRwi7EOZZe0X06cPKXo0a0aQ7ZQo95tWs3bX57Td6v69aBUyY4OzeKBQKhXPxCGEHbFtn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\nosYuIiISEDV2ERGRgKixi4iIBOQ/4IsrV5ZFJuMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe5158d1198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "l, = ax.plot(R, hohmann_data, lw=2)\n",
    "for jj in range(len(Rstar)):\n",
    "    ax.plot(R, bielliptic_data[:, jj], color=l.get_color())\n",
    "ax.vlines([11.94, R[idx_max]], *ylims, color='0.6')\n",
    "\n",
    "if ZOOM:\n",
    "    ax_zoom = zoomed_inset_axes(ax, 4, loc=4, axes_kwargs={'axisbg': '0.97'})\n",
    "    ax_zoom.plot(R, hohmann_data, lw=2)\n",
    "    for jj in range(len(Rstar)):\n",
    "        ax_zoom.plot(R, bielliptic_data[:, jj], color=l.get_color())\n",
    "    ax_zoom.vlines([11.94, R[idx_max]], *ylims, color='0.6')\n",
    "\n",
    "    ax_zoom.set_xlim(11.0, 16.0)\n",
    "    ax_zoom.set_ylim(0.52, 0.545)\n",
    "    ax_zoom.set_xticks([])\n",
    "    ax_zoom.set_yticks([])\n",
    "    ax_zoom.grid(False)\n",
    "    ax_zoom.set_title(\"4x zoom\")\n",
    "    mark_inset(ax, ax_zoom, loc1=1, loc2=3, fc=\"none\", ec='0.3')\n",
    "\n",
    "ax.set_xlabel(\"R\")\n",
    "ax.set_ylabel(\"Relative change in velocity\")\n",
    "ax.set_ylim(*ylims)\n",
    "ax.set_xlim(2, 75)\n",
    "ax.set_title(\"Hohmann vs bielliptic transfers\")"
   ]
  }
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