docs/source/examples/Analyzing the Parker Solar Probe flybys.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analyzing the Parker Solar Probe flybys\n",
    "\n",
    "## 1. Modulus of the exit velocity, some features of Orbit #2\n",
    "\n",
    "First, using the data available in the reports, we try to compute some of the properties of orbit #2. This is not enough to completely define the trajectory, but will give us information later on in the process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from astropy import units as u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$150 \\; \\mathrm{d}$"
      ],
      "text/plain": [
       "<Quantity 150. d>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T_ref = 150 * u.day\n",
    "T_ref"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from poliastro.bodies import Earth, Sun, Venus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.3271244 \\times 10^{20} \\; \\mathrm{\\frac{m^{3}}{s^{2}}}$"
      ],
      "text/plain": [
       "<Quantity 1.32712442e+20 m3 / s2>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = Sun.k\n",
    "k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ T = 2 \\pi \\sqrt{\\frac{a^3}{\\mu}} \\Rightarrow a = \\sqrt[3]{\\frac{\\mu T^2}{4 \\pi^2}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.55249526 \\; \\mathrm{AU}$"
      ],
      "text/plain": [
       "<Quantity 0.55249526 AU>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_ref = np.cbrt(k * T_ref ** 2 / (4 * np.pi ** 2)).to(u.km)\n",
    "a_ref.to(u.au)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\varepsilon = -\\frac{\\mu}{r} + \\frac{v^2}{2} = -\\frac{\\mu}{2a} \\Rightarrow v = +\\sqrt{\\frac{2\\mu}{r} - \\frac{\\mu}{a}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$-8.0283755 \\times 10^{8} \\; \\mathrm{\\frac{J}{kg}}$"
      ],
      "text/plain": [
       "<Quantity -8.02837549e+08 J / kg>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "energy_ref = (-k / (2 * a_ref)).to(u.J / u.kg)\n",
    "energy_ref"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from poliastro.twobody import Orbit\n",
    "from poliastro.util import norm\n",
    "\n",
    "from astropy.time import Time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Time object: scale='tdb' format='iso' value=2018-09-28 00:00:00.000>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flyby_1_time = Time(\"2018-09-28\", scale=\"tdb\")\n",
    "flyby_1_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.72573132 \\; \\mathrm{AU}$"
      ],
      "text/plain": [
       "<Quantity 0.72573132 AU>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_mag_ref = norm(Orbit.from_body_ephem(Venus, epoch=flyby_1_time).r)\n",
    "r_mag_ref.to(u.au)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$28.967364 \\; \\mathrm{\\frac{km}{s}}$"
      ],
      "text/plain": [
       "<Quantity 28.96736351 km / s>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v_mag_ref = np.sqrt(2 * k / r_mag_ref - k / a_ref)\n",
    "v_mag_ref.to(u.km / u.s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Lambert arc between #0 and #1\n",
    "\n",
    "To compute the arrival velocity to Venus at flyby #1, we have the necessary data to solve the boundary value problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Time object: scale='tdb' format='iso' value=2018-08-11 00:00:00.000>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d_launch = Time(\"2018-08-11\", scale=\"tdb\")\n",
    "d_launch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "ss0 = Orbit.from_body_ephem(Earth, d_launch)\n",
    "ss1 = Orbit.from_body_ephem(Venus, epoch=flyby_1_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "tof = flyby_1_time - d_launch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from poliastro import iod"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "((v0, v1_pre),) = iod.lambert(Sun.k, ss0.r, ss1.r, tof.to(u.s))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$[9.5993373,~11.298552,~2.9244933] \\; \\mathrm{\\frac{km}{s}}$"
      ],
      "text/plain": [
       "<Quantity [ 9.59933726, 11.29855172,  2.92449333] km / s>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$[-16.980821,~23.307528,~9.1312908] \\; \\mathrm{\\frac{km}{s}}$"
      ],
      "text/plain": [
       "<Quantity [-16.98082099,  23.30752839,   9.13129077] km / s>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v1_pre"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$30.248465 \\; \\mathrm{\\frac{km}{s}}$"
      ],
      "text/plain": [
       "<Quantity 30.24846495 km / s>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm(v1_pre)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Flyby #1 around Venus\n",
    "\n",
    "We compute a flyby using poliastro with the default value of the entry angle, just to discover that the results do not match what we expected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from poliastro.threebody.flybys import compute_flyby"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$[648499.74,~2695078.4,~1171563.7] \\; \\mathrm{\\frac{km}{d}}$"
      ],
      "text/plain": [
       "<Quantity [ 648499.73735241, 2695078.44750227, 1171563.7170508 ] km / d>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V = Orbit.from_body_ephem(Venus, epoch=flyby_1_time).v\n",
    "V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "h = 2548 * u.km"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$8599.8 \\; \\mathrm{km}$"
      ],
      "text/plain": [
       "<Quantity 8599.8 km>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d_flyby_1 = Venus.R + h\n",
    "d_flyby_1.to(u.km)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "V_2_v_, delta_ = compute_flyby(v1_pre, V, Venus.k, d_flyby_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$27.755339 \\; \\mathrm{\\frac{km}{s}}$"
      ],
      "text/plain": [
       "<Quantity 27.75533877 km / s>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm(V_2_v_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Optimization\n",
    "\n",
    "Now we will try to find the value of $\\theta$ that satisfies our requirements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func(theta):\n",
    "    V_2_v, _ = compute_flyby(v1_pre, V, Venus.k, d_flyby_1, theta * u.rad)\n",
    "    ss_1 = Orbit.from_vectors(Sun, ss1.r, V_2_v, epoch=flyby_1_time)\n",
    "    return (ss_1.period - T_ref).to(u.day).value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two solutions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "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": [
    "theta_range = np.linspace(0, 2 * np.pi)\n",
    "plt.plot(theta_range, [func(theta) for theta in theta_range])\n",
    "plt.axhline(0, color=\"k\", linestyle=\"dashed\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-9.142672330001131"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "func(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.09811543934556"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "func(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import brentq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$38.598709 \\; \\mathrm{{}^{\\circ}}$"
      ],
      "text/plain": [
       "<Quantity 38.59870925 deg>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_opt_a = brentq(func, 0, 1) * u.rad\n",
    "theta_opt_a.to(u.deg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$279.3477 \\; \\mathrm{{}^{\\circ}}$"
      ],
      "text/plain": [
       "<Quantity 279.34770004 deg>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_opt_b = brentq(func, 4, 5) * u.rad\n",
    "theta_opt_b.to(u.deg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "V_2_v_a, delta_a = compute_flyby(v1_pre, V, Venus.k, d_flyby_1, theta_opt_a)\n",
    "V_2_v_b, delta_b = compute_flyby(v1_pre, V, Venus.k, d_flyby_1, theta_opt_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$28.967364 \\; \\mathrm{\\frac{km}{s}}$"
      ],
      "text/plain": [
       "<Quantity 28.96736351 km / s>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm(V_2_v_a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$28.967364 \\; \\mathrm{\\frac{km}{s}}$"
      ],
      "text/plain": [
       "<Quantity 28.96736351 km / s>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm(V_2_v_b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Exit orbit\n",
    "\n",
    "And finally, we compute orbit #2 and check that the period is the expected one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0 x 1 AU x 18.8 deg (HCRS) orbit around Sun (☉) at epoch 2018-09-28 00:00:00.000 (TDB)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss01 = Orbit.from_vectors(Sun, ss1.r, v1_pre, epoch=flyby_1_time)\n",
    "ss01"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two solutions have different inclinations, so we still have to find out which is the good one. We can do this by computing the inclination over the ecliptic - however, as the original data was in the International Celestial Reference Frame (ICRF), whose fundamental plane is parallel to the Earth equator of a reference epoch, we have change the plane to the Earth **ecliptic**, which is what the original reports use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0 x 1 AU x 25.0 deg (HCRS) orbit around Sun (☉) at epoch 2018-09-28 00:00:00.000 (TDB)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss_1_a = Orbit.from_vectors(Sun, ss1.r, V_2_v_a, epoch=flyby_1_time)\n",
    "ss_1_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0 x 1 AU x 13.1 deg (HCRS) orbit around Sun (☉) at epoch 2018-09-28 00:00:00.000 (TDB)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss_1_b = Orbit.from_vectors(Sun, ss1.r, V_2_v_b, epoch=flyby_1_time)\n",
    "ss_1_b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's define a function to do that quickly for us, using the [`get_frame`](https://docs.poliastro.space/en/latest/api/safe/frames.html#poliastro.frames.get_frame) function from poliastro.frames:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "from astropy.coordinates import CartesianRepresentation, CartesianDifferential\n",
    "from poliastro.frames import Planes\n",
    "from poliastro.frames.util import get_frame\n",
    "\n",
    "\n",
    "def change_plane(ss_orig, plane):\n",
    "    \"\"\"Changes the plane of the Orbit.\n",
    "\n",
    "    \"\"\"\n",
    "    ss_orig_rv = ss_orig.get_frame().realize_frame(\n",
    "        ss_orig.represent_as(CartesianRepresentation, CartesianDifferential)\n",
    "    )\n",
    "\n",
    "    dest_frame = get_frame(ss_orig.attractor, plane, obstime=ss_orig.epoch)\n",
    "\n",
    "    ss_dest_rv = ss_orig_rv.transform_to(dest_frame)\n",
    "    ss_dest_rv.representation_type = CartesianRepresentation\n",
    "\n",
    "    ss_dest = Orbit.from_coords(ss_orig.attractor, ss_dest_rv, plane=plane)\n",
    "    return ss_dest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0 x 1 AU x 3.5 deg (HeliocentricEclipticIAU76) orbit around Sun (☉) at epoch 2018-09-28 00:00:00.000 (TDB)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "change_plane(ss_1_a, Planes.EARTH_ECLIPTIC)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0 x 1 AU x 13.1 deg (HeliocentricEclipticIAU76) orbit around Sun (☉) at epoch 2018-09-28 00:00:00.000 (TDB)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "change_plane(ss_1_b, Planes.EARTH_ECLIPTIC)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Therefore, **the correct option is the first one**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$150 \\; \\mathrm{d}$"
      ],
      "text/plain": [
       "<Quantity 150. d>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss_1_a.period.to(u.day)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$82652115 \\; \\mathrm{km}$"
      ],
      "text/plain": [
       "<Quantity 82652114.57939689 km>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss_1_a.a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And, finally, we plot the solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from poliastro.plotting import StaticOrbitPlotter\n",
    "\n",
    "frame = StaticOrbitPlotter()\n",
    "\n",
    "frame.plot(ss0, label=Earth)\n",
    "frame.plot(ss1, label=Venus)\n",
    "frame.plot(ss01, label=\"#0 to #1\")\n",
    "frame.plot(ss_1_a, label=\"#1 to #2\");"
   ]
  }
 ],
 "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": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}