{
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   "metadata": {},
   "source": [
    "Copyright (c) 2024 Massachusetts Institute of Technology\n",
    "\n",
    "SPDX-License-Identifier: MIT"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Transformations\n",
    "\n",
    "`astroforge` provides a number of utilies that can transform between coordinate frames and between compatible orbital parameters. We highlight a few of these transformations in this example, but the full list can be reviewed in the API documentation for `astroforge.coordinates._transformations`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Coordinate Conversions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Convert between the International Terrestrial Reference System (ITRS) and the Mean Equator Mean Equinox of Date system (MEMED) at a specific time defined as a Modified Julian Date (MJD)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 4394.69603967 -5881.50950936  3177.18312508]\n",
      "[-5413.11749016  4960.20830485  3177.18312508]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from astroforge.coordinates import ITRSToMEMED, MEMEDToITRS\n",
    "\n",
    "MJD = 60197.5\n",
    "\n",
    "x_itrs = np.array([-5413.11749016, 4960.20830485, 3177.18312508])  # just a random vector\n",
    "x_memed = ITRSToMEMED(MJD, x_itrs)\n",
    "x_itrs_2 = MEMEDToITRS(MJD, x_memed)\n",
    "\n",
    "print(x_memed)\n",
    "print(x_itrs_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Convert between ITRS and Latitude/Longitude/Altitude (degrees and km)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(23.511926934533797, 137.50000000001472, 1625.2463742566208)\n",
      "[-5413.11749016  4960.20830485  3177.18312508]\n"
     ]
    }
   ],
   "source": [
    "from astroforge.coordinates import ITRSToLatLonAlt, LatLonAltToITRS\n",
    "\n",
    "x_itrs = np.array([-5413.11749016, 4960.20830485, 3177.18312508])  # just a random vector\n",
    "x_latlonalt = ITRSToLatLonAlt(x_itrs)\n",
    "x_itrs_2 = LatLonAltToITRS(*x_latlonalt)\n",
    "\n",
    "print(x_latlonalt)\n",
    "print(x_itrs_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Convert between Keplerian elements and True Equator True Equinox of Date (TETED) carteisan coordinates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-371.69607966 7116.79717907  707.23699658]] [[-8.19634168  2.03599094  0.36358961]]\n",
      "{'inclination_rad': 0.10000000000000056, 'raan_rad': 0.19999999999999946, 'argp_rad': 0.3000000000000009, 'eccentricity': 0.4000000000000004, 'semi_major_axis_km': 10000.000000000005, 'eccentric_anomaly_rad': 0.7818320279930673, 'true_anomaly_rad': 1.1237047648504743, 'mean_anomaly_rad': 0.49999976729035667}\n"
     ]
    }
   ],
   "source": [
    "from astroforge.coordinates import keplerian_to_cartesian, cartesian_to_keplerian\n",
    "\n",
    "# All angles are in radians\n",
    "inclination_rad = 0.1\n",
    "raan_rad = 0.2\n",
    "argp_rad = 0.3\n",
    "ecc = 0.4\n",
    "semi_major_axis_km = 10000.\n",
    "mean_anomaly_rad = 0.5\n",
    "\n",
    "x_teted, v_teted = keplerian_to_cartesian(inclination_rad=inclination_rad,\n",
    "                                 raan_rad=raan_rad,\n",
    "                                 argp_rad=argp_rad,\n",
    "                                 ecc=ecc,\n",
    "                                 semi_major_axis_km=semi_major_axis_km,\n",
    "                                 mean_anomaly_rad=mean_anomaly_rad)\n",
    "\n",
    "# Note: The pos/vel arrays need to be converted from shape (1,3) to (3,) for cartesian_to_keplerian\n",
    "keplerian_elements = cartesian_to_keplerian(pos=x_teted[0], vel=v_teted[0])\n",
    "\n",
    "print(x_teted, v_teted)\n",
    "print(keplerian_elements)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Orbital Element Conversions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the True Anomaly from the Mean Anomaly.\n",
    "\n",
    "Note: You can specify the tolerance and max number of iterations for the underlying numerical solver. By default, they will be set to 1.0e-14 and 100, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True Anomaly: 0.6595163855574937 radians\n",
      "Mean Anomaly: 0.2 radians\n"
     ]
    }
   ],
   "source": [
    "from astroforge.coordinates import true_anomaly_from_mean_anomaly, mean_anomaly_from_true_anomaly\n",
    "\n",
    "eccentricity = 0.5\n",
    "mean_anomaly = 0.2\n",
    "\n",
    "true_anomaly = true_anomaly_from_mean_anomaly(e=eccentricity, M=mean_anomaly)\n",
    "mean_anomaly_2 = mean_anomaly_from_true_anomaly(e=eccentricity, v=true_anomaly)\n",
    "\n",
    "print(f\"True Anomaly: {true_anomaly} radians\")\n",
    "print(f\"Mean Anomaly: {mean_anomaly_2} radians\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the True Anomaly from the Eccentric Anomaly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True Anomaly:      0.3441325691613769 radians\n",
      "Eccentric Anomaly: 0.19999999999999996 radians\n"
     ]
    }
   ],
   "source": [
    "from astroforge.coordinates import true_anomaly_from_eccentric_anomaly, eccentric_anomaly_from_true_anomaly\n",
    "\n",
    "eccentricity = 0.5\n",
    "eccentric_anomaly = 0.2\n",
    "\n",
    "true_anomaly = true_anomaly_from_eccentric_anomaly(e=eccentricity, E=eccentric_anomaly)\n",
    "eccentric_anomaly_2 = eccentric_anomaly_from_true_anomaly(e=eccentricity, v=true_anomaly)\n",
    "\n",
    "print(f\"True Anomaly:      {true_anomaly} radians\")\n",
    "print(f\"Eccentric Anomaly: {eccentric_anomaly_2} radians\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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