{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9253539a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:22.697243Z",
     "iopub.status.busy": "2025-07-31T14:29:22.697067Z",
     "iopub.status.idle": "2025-07-31T14:29:23.110488Z",
     "shell.execute_reply": "2025-07-31T14:29:23.109859Z"
    },
    "nbsphinx": "hidden"
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9953acec",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:23.112439Z",
     "iopub.status.busy": "2025-07-31T14:29:23.112205Z",
     "iopub.status.idle": "2025-07-31T14:29:23.277884Z",
     "shell.execute_reply": "2025-07-31T14:29:23.277313Z"
    },
    "nbsphinx": "hidden"
   },
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'ZMQInteractiveShell' object has no attribute 'magic'",
     "output_type": "error",
     "traceback": [
      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
      "\u001b[31mAttributeError\u001b[39m                            Traceback (most recent call last)",
      "\u001b[36mFile \u001b[39m\u001b[32m~/work/gala/gala/docs/tutorials/nb_setup:1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43mmagic\u001b[49m(\u001b[33m'\u001b[39m\u001b[33mconfig InlineBackend.figure_format = \u001b[39m\u001b[33m\"\u001b[39m\u001b[33mretina\u001b[39m\u001b[33m\"\u001b[39m\u001b[33m'\u001b[39m)  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[32m      3\u001b[39m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mmatplotlib\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mpyplot\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mplt\u001b[39;00m\n\u001b[32m      5\u001b[39m plt.style.use(\u001b[33m\"\u001b[39m\u001b[33mdefault\u001b[39m\u001b[33m\"\u001b[39m)\n",
      "\u001b[31mAttributeError\u001b[39m: 'ZMQInteractiveShell' object has no attribute 'magic'"
     ]
    }
   ],
   "source": [
    "%run nb_setup"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8bf5f22a",
   "metadata": {},
   "source": [
    "# Integrate an orbit with uncertainties in Milky Way model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "231c521d",
   "metadata": {},
   "source": [
    "`gala` provides a simple mass model for the Milky Way based on recent\n",
    "measurements of the enclosed mass compiled from the literature. See the\n",
    "[Defining a Milky Way potential\n",
    "model](define-milky-way-model.html) documentation for more\n",
    "information about how this model was defined.\n",
    "\n",
    "In this example, we will use the position and velocity and uncertainties of\n",
    "the Milky Way satellite galaxy \"Draco\" to integrate orbits in a Milky Way mass\n",
    "model starting from samples from the error distribution over initial\n",
    "conditions defined by its observed kinematics. We will then compute\n",
    "distributions of orbital properties like orbital period, pericenter, and\n",
    "eccentricity.\n",
    "\n",
    "Let's start by importing packages we will need:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f19c4f48",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:23.279724Z",
     "iopub.status.busy": "2025-07-31T14:29:23.279545Z",
     "iopub.status.idle": "2025-07-31T14:29:24.180783Z",
     "shell.execute_reply": "2025-07-31T14:29:24.180141Z"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "import astropy.coordinates as coord\n",
    "import astropy.units as u\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# Gala\n",
    "import gala.dynamics as gd\n",
    "import gala.potential as gp\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8609274a",
   "metadata": {},
   "source": [
    "We will also set the default Astropy Galactocentric frame parameters to the\n",
    "values adopted in Astropy v4.0:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1ebb8f8b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:24.182807Z",
     "iopub.status.busy": "2025-07-31T14:29:24.182552Z",
     "iopub.status.idle": "2025-07-31T14:29:24.188529Z",
     "shell.execute_reply": "2025-07-31T14:29:24.188051Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<ScienceState galactocentric_frame_defaults: {'galcen_coord': <ICRS Coordinate: (ra, dec) in deg...>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coord.galactocentric_frame_defaults.set(\"v4.0\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1a48e68",
   "metadata": {},
   "source": [
    "For the Milky Way model, we'll use the built-in potential class in `gala` (see\n",
    "above for definition):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3b7c05e7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:24.190112Z",
     "iopub.status.busy": "2025-07-31T14:29:24.189924Z",
     "iopub.status.idle": "2025-07-31T14:29:24.202480Z",
     "shell.execute_reply": "2025-07-31T14:29:24.201996Z"
    }
   },
   "outputs": [],
   "source": [
    "potential = gp.MilkyWayPotential()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de804f83",
   "metadata": {},
   "source": [
    "For the sky position and distance of Draco, we'll use measurements from\n",
    "[Bonanos et al. 2004](https://arxiv.org/abs/astro-ph/0310477). For proper\n",
    "motion components, we'll use the recent HSTPROMO measurements ([Sohn et al.\n",
    "2017](https://arxiv.org/abs/1707.02593)) and the line-of-sight velocity from\n",
    "[Walker et al. 2007](https://arxiv.org/abs/0708.0010)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2df84e98",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:24.204073Z",
     "iopub.status.busy": "2025-07-31T14:29:24.203881Z",
     "iopub.status.idle": "2025-07-31T14:29:24.219685Z",
     "shell.execute_reply": "2025-07-31T14:29:24.219096Z"
    }
   },
   "outputs": [],
   "source": [
    "icrs = coord.SkyCoord(\n",
    "    ra=coord.Angle(\"17h 20m 12.4s\"),\n",
    "    dec=coord.Angle(\"+57° 54′ 55″\"),\n",
    "    distance=76 * u.kpc,\n",
    "    pm_ra_cosdec=0.0569 * u.mas / u.yr,\n",
    "    pm_dec=-0.1673 * u.mas / u.yr,\n",
    "    radial_velocity=-291 * u.km / u.s,\n",
    ")\n",
    "\n",
    "icrs_err = coord.SkyCoord(\n",
    "    ra=0 * u.deg,\n",
    "    dec=0 * u.deg,\n",
    "    distance=6 * u.kpc,\n",
    "    pm_ra_cosdec=0.009 * u.mas / u.yr,\n",
    "    pm_dec=0.009 * u.mas / u.yr,\n",
    "    radial_velocity=0.1 * u.km / u.s,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ca60304",
   "metadata": {},
   "source": [
    "Let's start by transforming the measured values to a Galactocentric reference\n",
    "frame so we can integrate an orbit in our Milky Way model. We'll do this using\n",
    "the velocity transformation support in\n",
    "[`astropy.coordinates`](http://docs.astropy.org/en/stable/coordinates/velocities.html).\n",
    "We first have to define the position and motion of the sun relative to the\n",
    "Galactocentric frame, and create an\n",
    "[`astropy.coordinates.Galactocentric`](http://docs.astropy.org/en/stable/api/astropy.coordinates.Galactocentric.html#astropy.coordinates.Galactocentric)\n",
    "object with these parameters. We could specify these things explicitly, but\n",
    "instead we will use the default values that were recently updated in Astropy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ecfd9ddb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:24.221417Z",
     "iopub.status.busy": "2025-07-31T14:29:24.221248Z",
     "iopub.status.idle": "2025-07-31T14:29:24.225673Z",
     "shell.execute_reply": "2025-07-31T14:29:24.225230Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Galactocentric Frame (galcen_coord=<ICRS Coordinate: (ra, dec) in deg\n",
       "    (266.4051, -28.936175)>, galcen_distance=8.122 kpc, galcen_v_sun=(12.9, 245.6, 7.78) km / s, z_sun=20.8 pc, roll=0.0 deg)>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "galcen_frame = coord.Galactocentric()\n",
    "galcen_frame"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c53e63df",
   "metadata": {},
   "source": [
    "To transform the mean observed kinematics to this frame, we simply do:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "02b12a02",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:24.227261Z",
     "iopub.status.busy": "2025-07-31T14:29:24.227096Z",
     "iopub.status.idle": "2025-07-31T14:29:24.235291Z",
     "shell.execute_reply": "2025-07-31T14:29:24.234799Z"
    }
   },
   "outputs": [],
   "source": [
    "galcen = icrs.transform_to(galcen_frame)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d41cf236",
   "metadata": {},
   "source": [
    "That's it! Now we have to turn the resulting `Galactocentric` object into\n",
    "orbital initial conditions, and integrate the orbit in our Milky Way model.\n",
    "We'll use a timestep of 0.5 Myr and integrate the orbit backwards for 10000\n",
    "steps (5 Gyr):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d4d63567",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:24.236825Z",
     "iopub.status.busy": "2025-07-31T14:29:24.236660Z",
     "iopub.status.idle": "2025-07-31T14:29:24.265027Z",
     "shell.execute_reply": "2025-07-31T14:29:24.264519Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: AstropyDeprecationWarning: The get_name method is deprecated and may be removed in a future version.\n",
      "        Use name instead. [gala.dynamics.core]\n"
     ]
    }
   ],
   "source": [
    "w0 = gd.PhaseSpacePosition(galcen.data)\n",
    "orbit = potential.integrate_orbit(w0, dt=-0.5 * u.Myr, n_steps=10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c5df1e0",
   "metadata": {},
   "source": [
    "Let's visualize the orbit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e970a0be",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:24.266712Z",
     "iopub.status.busy": "2025-07-31T14:29:24.266539Z",
     "iopub.status.idle": "2025-07-31T14:29:24.783924Z",
     "shell.execute_reply": "2025-07-31T14:29:24.783345Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: AstropyDeprecationWarning: The get_name method is deprecated and may be removed in a future version.\n",
      "        Use name instead. [gala.dynamics.orbit]\n",
      "Ignoring fixed x limits to fulfill fixed data aspect with adjustable data limits.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Ignoring fixed x limits to fulfill fixed data aspect with adjustable data limits.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Ignoring fixed x limits to fulfill fixed data aspect with adjustable data limits.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Ignoring fixed x limits to fulfill fixed data aspect with adjustable data limits.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Ignoring fixed x limits to fulfill fixed data aspect with adjustable data limits.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Ignoring fixed x limits to fulfill fixed data aspect with adjustable data limits.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Ignoring fixed x limits to fulfill fixed data aspect with adjustable data limits.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Ignoring fixed x limits to fulfill fixed data aspect with adjustable data limits.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Ignoring fixed x limits to fulfill fixed data aspect with adjustable data limits.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = orbit.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7482bb2",
   "metadata": {},
   "source": [
    "With the `orbit` object, we can easily compute quantities like the pericenter,\n",
    "apocenter, or eccentricity of the orbit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b72b7d3d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:24.786259Z",
     "iopub.status.busy": "2025-07-31T14:29:24.786079Z",
     "iopub.status.idle": "2025-07-31T14:29:24.812784Z",
     "shell.execute_reply": "2025-07-31T14:29:24.812209Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Quantity 45.47408489 kpc>,\n",
       " <Quantity 105.60902722 kpc>,\n",
       " <Quantity 0.39802557>)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orbit.pericenter(), orbit.apocenter(), orbit.eccentricity()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "775fc380",
   "metadata": {},
   "source": [
    "We can also use these functions to get the time of each pericenter or\n",
    "apocenter - let's plot the time of pericenter, and time of apocenter over the\n",
    "time series of the Galactocentric radius of the orbit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e369708b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:24.814496Z",
     "iopub.status.busy": "2025-07-31T14:29:24.814326Z",
     "iopub.status.idle": "2025-07-31T14:29:24.941929Z",
     "shell.execute_reply": "2025-07-31T14:29:24.941443Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$r$ [$\\\\mathrm{kpc}$]')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(orbit.t, orbit.spherical.distance, marker=\"None\")\n",
    "\n",
    "per, per_times = orbit.pericenter(return_times=True, func=None)\n",
    "apo, apo_times = orbit.apocenter(return_times=True, func=None)\n",
    "\n",
    "for t in per_times:\n",
    "    plt.axvline(t.value, color=\"#67a9cf\")\n",
    "\n",
    "for t in apo_times:\n",
    "    plt.axvline(t.value, color=\"#ef8a62\")\n",
    "\n",
    "plt.xlabel(\"$t$ [{}]\".format(orbit.t.unit.to_string(\"latex\")))\n",
    "plt.ylabel(\"$r$ [{}]\".format(orbit.x.unit.to_string(\"latex\")))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e19171ad",
   "metadata": {},
   "source": [
    "Now we'll sample from the error distribution over the distance, proper\n",
    "motions, and radial velocity, compute orbits, and plot distributions of mean\n",
    "pericenter and apocenter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "4d468c39",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:24.943643Z",
     "iopub.status.busy": "2025-07-31T14:29:24.943473Z",
     "iopub.status.idle": "2025-07-31T14:29:24.948649Z",
     "shell.execute_reply": "2025-07-31T14:29:24.948162Z"
    }
   },
   "outputs": [],
   "source": [
    "n_samples = 128\n",
    "\n",
    "rng = np.random.default_rng(42)\n",
    "dist = (\n",
    "    rng.normal(icrs.distance.value, icrs_err.distance.value, n_samples)\n",
    "    * icrs.distance.unit\n",
    ")\n",
    "\n",
    "pm_ra_cosdec = (\n",
    "    rng.normal(icrs.pm_ra_cosdec.value, icrs_err.pm_ra_cosdec.value, n_samples)\n",
    "    * icrs.pm_ra_cosdec.unit\n",
    ")\n",
    "\n",
    "pm_dec = (\n",
    "    rng.normal(icrs.pm_dec.value, icrs_err.pm_dec.value, n_samples) * icrs.pm_dec.unit\n",
    ")\n",
    "\n",
    "rv = (\n",
    "    rng.normal(icrs.radial_velocity.value, icrs_err.radial_velocity.value, n_samples)\n",
    "    * icrs.radial_velocity.unit\n",
    ")\n",
    "\n",
    "ra = np.full(n_samples, icrs.ra.degree) * u.degree\n",
    "dec = np.full(n_samples, icrs.dec.degree) * u.degree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "2091af4b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:24.950210Z",
     "iopub.status.busy": "2025-07-31T14:29:24.950029Z",
     "iopub.status.idle": "2025-07-31T14:29:24.953611Z",
     "shell.execute_reply": "2025-07-31T14:29:24.953128Z"
    }
   },
   "outputs": [],
   "source": [
    "icrs_samples = coord.SkyCoord(\n",
    "    ra=ra,\n",
    "    dec=dec,\n",
    "    distance=dist,\n",
    "    pm_ra_cosdec=pm_ra_cosdec,\n",
    "    pm_dec=pm_dec,\n",
    "    radial_velocity=rv,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "307c656a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:24.955224Z",
     "iopub.status.busy": "2025-07-31T14:29:24.955041Z",
     "iopub.status.idle": "2025-07-31T14:29:24.958637Z",
     "shell.execute_reply": "2025-07-31T14:29:24.958078Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(128,)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "icrs_samples.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "6f3564ec",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:24.960234Z",
     "iopub.status.busy": "2025-07-31T14:29:24.960057Z",
     "iopub.status.idle": "2025-07-31T14:29:24.968071Z",
     "shell.execute_reply": "2025-07-31T14:29:24.967472Z"
    }
   },
   "outputs": [],
   "source": [
    "galcen_samples = icrs_samples.transform_to(galcen_frame)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1f5b5273",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:24.969721Z",
     "iopub.status.busy": "2025-07-31T14:29:24.969556Z",
     "iopub.status.idle": "2025-07-31T14:29:25.076746Z",
     "shell.execute_reply": "2025-07-31T14:29:25.076241Z"
    }
   },
   "outputs": [],
   "source": [
    "w0_samples = gd.PhaseSpacePosition(galcen_samples.data)\n",
    "orbit_samples = potential.integrate_orbit(w0_samples, dt=-1 * u.Myr, n_steps=4000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e9302f5d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:25.078631Z",
     "iopub.status.busy": "2025-07-31T14:29:25.078454Z",
     "iopub.status.idle": "2025-07-31T14:29:25.082360Z",
     "shell.execute_reply": "2025-07-31T14:29:25.081774Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4001, 128)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orbit_samples.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "18c5672c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:25.083962Z",
     "iopub.status.busy": "2025-07-31T14:29:25.083802Z",
     "iopub.status.idle": "2025-07-31T14:29:26.858629Z",
     "shell.execute_reply": "2025-07-31T14:29:26.858040Z"
    }
   },
   "outputs": [],
   "source": [
    "peris = orbit_samples.pericenter(approximate=True)\n",
    "\n",
    "apos = orbit_samples.apocenter(approximate=True)\n",
    "\n",
    "eccs = orbit_samples.eccentricity(approximate=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "58dbed0a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-07-31T14:29:26.860560Z",
     "iopub.status.busy": "2025-07-31T14:29:26.860354Z",
     "iopub.status.idle": "2025-07-31T14:29:27.160315Z",
     "shell.execute_reply": "2025-07-31T14:29:27.159792Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'eccentricity')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 3, figsize=(12, 4), sharey=True)\n",
    "\n",
    "axes[0].hist(peris.to_value(u.kpc), bins=np.linspace(20, 80, 32))\n",
    "axes[0].set_xlabel(\"pericenter [kpc]\")\n",
    "\n",
    "axes[1].hist(apos.to_value(u.kpc), bins=np.linspace(60, 140, 32))\n",
    "axes[1].set_xlabel(\"apocenter [kpc]\")\n",
    "\n",
    "axes[2].hist(eccs.value, bins=np.linspace(0.3, 0.5, 41))\n",
    "axes[2].set_xlabel(\"eccentricity\")"
   ]
  }
 ],
 "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": "3.12.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}