{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# New Horizons launch and trajectory\n",
    "\n",
    "Main data source: Guo & Farquhar \"New Horizons Mission Design\" http://www.boulder.swri.edu/pkb/ssr/ssr-mission-design.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from astropy import time\n",
    "from astropy import units as u\n",
    "\n",
    "from poliastro.bodies import Sun, Earth\n",
    "from poliastro.twobody import Orbit\n",
    "from poliastro.plotting import plot, OrbitPlotter\n",
    "from poliastro import iod\n",
    "from poliastro import ephem\n",
    "from poliastro.util import norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parking orbit\n",
    "\n",
    "Quoting from \"New Horizons Mission Design\":\n",
    "\n",
    "> It was first inserted into an elliptical Earth parking orbit\n",
    "of **perigee altitude 165 km** and **apogee altitude 215 km**. [Emphasis mine]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$[0,~7.8198896,~0] \\; \\mathrm{\\frac{km}{s}}$"
      ],
      "text/plain": [
       "<Quantity [ 0.        , 7.81988961, 0.        ] km / s>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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r4ZqgyxCRCPtm1nKWrPSurFypElx+OQwbFnBRMaQgSiDD1RsSSUrOwetjZux/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\nxphO+S8vhLDpJUnQ+QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc8a1f25898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_p = Earth.R + 165 * u.km\n",
    "r_a = Earth.R + 215 * u.km\n",
    "\n",
    "a_parking = (r_p + r_a) / 2\n",
    "ecc_parking = 1 - r_p / a_parking\n",
    "\n",
    "parking = Orbit.from_classical(Earth, a_parking, ecc_parking,\n",
    "                               0 * u.deg, 0 * u.deg, 0 * u.deg, 0 * u.deg,  # We don't mind\n",
    "                               time.Time(\"2006-01-19\", scale='utc'))\n",
    "\n",
    "plot(parking)\n",
    "parking.v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hyperbolic exit\n",
    "\n",
    "Hyperbolic excess velocity:\n",
    "\n",
    "$$ v_{\\infty}^2 = \\frac{\\mu}{-a} = 2 \\varepsilon = C_3 $$\n",
    "\n",
    "Relation between orbital velocity $v$, local escape velocity $v_e$ and hyperbolic excess velocity $v_{\\infty}$:\n",
    "\n",
    "$$ v^2 = v_e^2 + v_{\\infty}^2 $$\n",
    "\n",
    "### Option a): Insert $C_3$ from report, check $v_e$ at parking perigee"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$16.718065 \\; \\mathrm{\\frac{km}{s}}$"
      ],
      "text/plain": [
       "<Quantity 16.718065140158593 km / s>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_3_A = 157.6561 * u.km**2 / u.s**2  # Designed\n",
    "\n",
    "a_exit = -(Earth.k / C_3_A).to(u.km)\n",
    "ecc_exit = 1 - r_p / a_exit\n",
    "\n",
    "exit = Orbit.from_classical(Earth, a_exit, ecc_exit,\n",
    "                            0 * u.deg, 0 * u.deg, 0 * u.deg, 0 * u.deg,  # We don't mind\n",
    "                            time.Time(\"2006-01-19\", scale='utc'))\n",
    "\n",
    "norm(exit.v).to(u.km / u.s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quoting \"New Horizons Mission Design\":\n",
    "\n",
    "> After a short coast in the parking orbit, the spacecraft was then injected into\n",
    "the desired heliocentric orbit by the Centaur second stage and Star 48B third\n",
    "stage. At the Star 48B burnout, the New Horizons spacecraft reached the highest\n",
    "Earth departure speed, **estimated at 16.2 km/s**, becoming the fastest spacecraft\n",
    "ever launched from Earth.  [Emphasis mine]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative error of 3.20 %\n"
     ]
    }
   ],
   "source": [
    "v_estimated = 16.2 * u.km / u.s\n",
    "\n",
    "print(\"Relative error of {:.2f} %\".format((norm(exit.v) - v_estimated) / v_estimated * 100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So it stays within the same order of magnitude. Which is reasonable, because real life burns are not instantaneous."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XHikAiiUuETkL0zv+bVW9E/gTMBLTT69c06cPjBsHN196VtCulCsSE4QLzzsZ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\nP79Zi8eXJ1MEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc8a1f17f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "op = OrbitPlotter()\n",
    "op.plot(parking)\n",
    "op.plot(exit)\n",
    "plt.xlim(-8000, 8000)\n",
    "plt.ylim(-20000, 20000)\n",
    "plt.gcf().autofmt_xdate()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Option b): Compute $v_{\\infty}$ using the Jupyter flyby\n",
    "\n",
    "According to Wikipedia, the closest approach occurred at 05:43:40 UTC. We can use this data to compute the solution of the Lambert problem between the Earth and Jupiter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "nh_date = time.Time(\"2006-01-19 19:00\", scale='utc')\n",
    "nh_flyby_date = time.Time(\"2007-02-28 05:43:40\", scale='utc')\n",
    "nh_tof = nh_flyby_date - nh_date\n",
    "\n",
    "nh_r_0, v_earth = ephem.planet_ephem(ephem.EARTH, nh_date)\n",
    "nh_r_f, v_jup = ephem.planet_ephem(ephem.JUPITER, nh_flyby_date)\n",
    "\n",
    "(nh_v_0, nh_v_f), = iod.lambert(Sun.k, nh_r_0, nh_r_f, nh_tof)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The hyperbolic excess velocity is measured with respect to the Earth:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$158.31571 \\; \\mathrm{\\frac{km^{2}}{s^{2}}}$"
      ],
      "text/plain": [
       "<Quantity 158.3157101470779 km2 / s2>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_3_lambert = (norm(nh_v_0 - v_earth)).to(u.km / u.s)**2\n",
    "C_3_lambert"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative error of 0.42 %\n"
     ]
    }
   ],
   "source": [
    "print(\"Relative error of {:.2f} %\".format((C_3_lambert - C_3_A) / C_3_A * 100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which again, stays within the same order of magnitude of the figure given to the Guo & Farquhar report."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## From Earth to Jupiter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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c3NyNjiKEEBUindk2kpmYgCkjw2aX4gshKr+DLzxC/VsnUavT9VZpTzqzHYxH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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc89ce89160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from poliastro.plotting import BODY_COLORS\n",
    "\n",
    "nh_earth = Orbit.from_vectors(Sun, nh_r_0.to(u.km), v_earth.to(u.km / u.s), nh_date)\n",
    "nh_jup = Orbit.from_vectors(Sun, nh_r_f.to(u.km), v_jup.to(u.km / u.s), nh_flyby_date)\n",
    "nh = Orbit.from_vectors(Sun, nh_r_0.to(u.km), nh_v_0.to(u.km / u.s), nh_date)\n",
    "\n",
    "op = OrbitPlotter(num_points=1000)\n",
    "\n",
    "for ll in op.plot(nh_jup, label=\"Jupiter\"):\n",
    "    ll.set_color(BODY_COLORS[\"Jupiter\"])\n",
    "\n",
    "plt.gca().set_autoscale_on(False)\n",
    "\n",
    "for ll in op.plot(nh_earth, label=\"Earth\"):\n",
    "    ll.set_color(BODY_COLORS[\"Earth\"])\n",
    "\n",
    "for ll in op.plot(nh, label=\"New Horizons\"):\n",
    "    ll.set_color(\"0\")\n",
    "\n",
    "leg = plt.legend()\n",
    "leg.get_frame().set_facecolor('#fafafa')"
   ]
  }
 ],
 "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": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
