{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Working with satellites" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## License\n", "\n", "```\n", "Working with the satellites module of pycraf.\n", "Copyright (C) 2015+ Benjamin Winkel (bwinkel@mpifr.de)\n", "\n", "This program is free software; you can redistribute it and/or\n", "modify it under the terms of the GNU General Public License\n", "as published by the Free Software Foundation; either version 2\n", "of the License, or (at your option) any later version.\n", "\n", "This program is distributed in the hope that it will be useful,\n", "but WITHOUT ANY WARRANTY; without even the implied warranty of\n", "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n", "GNU General Public License for more details.\n", "\n", "You should have received a copy of the GNU General Public License\n", "along with this program; if not, write to the Free Software\n", "Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note: GitHub's integrated notebook viewer won't show the embedded videos. You can use the [nbviewer](http://nbviewer.jupyter.org/) service to open the notebook. Or follow the direct [link](http://nbviewer.jupyter.org/github/bwinkel/pycraf/blob/master/notebooks/04a_satellites_plot.ipynb)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import requests\n", "import datetime\n", "import numpy as np\n", "\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from matplotlib import animation, rc\n", "\n", "from astropy import time\n", "from astropy import units as u\n", "from astropy.coordinates import EarthLocation\n", "from pycraf import satellite\n", "\n", "rc('animation', html='html5')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Two-line elements sets (TLE)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To compute positions of a satellite, two-line element sets (TLE) have to be used. These look like the following\n", "\n", " ISS (ZARYA)\n", " 1 25544U 98067A 13165.59097222 .00004759 00000-0 88814-4 0 47\n", " 2 25544 51.6478 121.2152 0011003 68.5125 263.9959 15.50783143834295\n", "\n", "which is the latest TLE for the international space station. The first line has only the name (or identifier) of a satellite. The following two lines contain all the necessary information about the satellite orbit to calculate its position for a certain time. Note that the TLEs are usually published once a day, because the contained parameters quickly change; drag forces cause rapid changes in the orbits of almost all satellites." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course, the position of a satellite depends on the choosen coordinate system. With the help of the [sgp4 package](https://pypi.python.org/pypi/sgp4/) pycraf calculates the ECI position of the satellite (in Cartesian coordinates). ECI is the [Earth-centered inertial frame](https://en.wikipedia.org/wiki/Earth-centered_inertial). But often we are interested in the apparent sky position (horizontal frame) of a satellite with respect to an observer. The latter is not provided by the `sgp4` library, but `pycraf` adds this functionality." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fetching latest satellites from Celestrak" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an example how to use the `pycraf.satellites` module, we will download the latest TLE data of all satellites launched in the last 30 days." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "celestrak_latest = requests.get('http://celestrak.com/NORAD/elements/tle-new.txt')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "'UCLSAT \\r\\n1 42765U 17036A 17203.81611237 .00001374 00000-0 65519-4 0 9998\\r\\n2 42765 97.4477 263.2377 0013153 143.9973 216.2151 15.20727085 4631\\r\\nNIUSAT \\r\\n1 42766U 17036B 17203.90626685 .00001085 00000-0 54219-4 0 9996\\r\\n2 42766 97.4479 263.2715 0017666 131.3164 228.9594 15.19473712 4517\\r\\nCARTOSAT-2E \\r\\n1 42767U 17036C 17203.86449167 .00000565 00000-0 30010-4 0 9995\\r\\n2 42767 97.4470 263.1716 0010141 131.4679 228.7428 15.19244692 4508\\r\\nLITUANICASAT-2 \\r\\n1 42768U 17036D 17203.90431379 .00002179 00000-0 10518-3 0 9990\\r\\n2 42768 97.4476 263.2723 0017729 134.6028 225.6657 15.19603897 4524\\r\\nCE-SAT-I \\r\\n1 42769U 17036E 17203.90329543 .00000640 00000-0 33162-4 0 9992\\r\\n2 42769 97.4478 263.2750 0017098 132.7041 227.5637 15.19611493 4441\\r\\nINFLATESAIL \\r\\n1 42770U 17036F 17203.89906608 .00169738 00000-0 60241-2 0 9995\\r\\n2 42770 97.4499 263.4304 0016176 177.7365 182.3950 15.28213316'" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "celestrak_latest.text[:1000]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The 'tle-new.txt' file apparently simply contains a list of TLEs. Let's fix the line endings (`\\r\\n` to `\\n`) and split into a list of TLEs:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "all_lines = celestrak_latest.text.split('\\r\\n')\n", "tle_list = []\n", "for idx in range(len(all_lines) // 3):\n", " tle_list.append('\\n'.join(all_lines[3 * idx: 3 * (idx + 1)]))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "UCLSAT \n", "1 42765U 17036A 17203.81611237 .00001374 00000-0 65519-4 0 9998\n", "2 42765 97.4477 263.2377 0013153 143.9973 216.2151 15.20727085 4631\n", "NIUSAT \n", "1 42766U 17036B 17203.90626685 .00001085 00000-0 54219-4 0 9996\n", "2 42766 97.4479 263.2715 0017666 131.3164 228.9594 15.19473712 4517\n" ] } ], "source": [ "print(tle_list[0])\n", "print(tle_list[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plotting satellite position" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before we start plotting, we'll use have `sgp4` parse all the satellite strings and construct `sgp4.io.Satellite` instances. These merely contain the orbital parameters, but it will be faster to work the the already parsed data instead of letting the TLEs being parsed in each time step (yes, we are going to do a nice animation)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "('UCLSAT ', <sgp4.model.Satellite at 0x7f0ffb679710>)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sat_list = [satellite.get_sat(tle_string) for tle_string in tle_list]\n", "# contains a list of tuples: (sat_name, sat_instance)\n", "sat_list[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The second ingredient, we need is an array of \"observing\" times. pycraf wants an `astropy.time.Time` object for this, because it has (accurate!) built-in conversion between UTC and sidereal time." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Start time: 2017-07-23 17:08:11.547873\n" ] } ], "source": [ "start_time = time.Time(datetime.datetime.utcnow(), 'utc')\n", "print('Start time:', start_time)\n", "td = time.TimeDelta(np.arange(0, 3600 * 24, 60 * 1), format='sec')\n", "times = start_time + td # one day in steps of 1 min" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ECI position\n", "For this we make use of `sgp4` built-in `propagate` method. This is easy to use, but it doesn't work with numpy arrays. Let's vectorize it:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def _propagate(sat, dt):\n", " '''\n", " True equator mean equinox (TEME) position from `sgp4` at given time.\n", " Parameters\n", " ----------\n", " sat : `sgp4.io.Satellite` instance\n", " Satellite object filled from TLE\n", " dt : `~datetime.datetime`\n", " Time\n", " Returns\n", " -------\n", " xs, ys, zs : float\n", " TEME (=True equator mean equinox) position of satellite [km]\n", " '''\n", "\n", " # pos [km], vel [km/s]\n", " position, velocity = sat.propagate(\n", " dt.year, dt.month, dt.day,\n", " dt.hour, dt.minute, dt.second + dt.microsecond / 1e6\n", " )\n", "\n", " if position is None:\n", " raise ValueError('Satellite propagation error')\n", "\n", " return position\n", "\n", "\n", "vec_propagate = np.vectorize(\n", " _propagate, excluded=['sat'], otypes=[np.float64] * 3\n", " )" ] }, { "cell_type": "code", "execution_count": 10, 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return points, title\n", "\n", "def animate(i):\n", " points._offsets3d = (pos_eci[:, 0, i], pos_eci[:, 1, i], pos_eci[:, 2, i])\n", " title.set_text('{:%y/%m/%d %H:%M}'.format(times[i].datetime))\n", " return points, title\n", "\n", "# call the animator. blit=True means only re-draw the parts that have changed.\n", "anim = animation.FuncAnimation(\n", " fig, animate, init_func=init, frames=pos_eci.shape[2], interval=20, blit=True\n", " )\n", "\n", "# this takes a while!\n", "plt.close(anim._fig)\n", "anim" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Horizontal position" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the next plot, we need to define an observer position, say the famous Parkes 64-m dish and the Effelsberg 100-m radio telescope." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "obs_loc_parkes = EarthLocation(148.25738, -32.9933, 414.8)\n", "obs_loc_effbg = EarthLocation(6.88375, 50.525, 366.)\n", "\n", "# create a SatelliteObserver instance\n", "sat_obs_parkes = satellite.SatelliteObserver(obs_loc_parkes)\n", "sat_obs_effbg = satellite.SatelliteObserver(obs_loc_effbg)\n", "pos_horiz_parkes = np.array([\n", " sat_obs_parkes.azel_from_sat(sat[1], times)\n", " for sat in sat_list\n", " ])\n", "pos_horiz_effbg = np.array([\n", " sat_obs_effbg.azel_from_sat(sat[1], times)\n", " for sat in sat_list\n", " ])\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "<video width=\"864\" height=\"504\" controls autoplay loop>\n", " <source type=\"video/mp4\" src=\"data:video/mp4;base64,AAAAHGZ0eXBNNFYgAAACAGlzb21pc28yYXZjMQAAAAhmcmVlAAdAI21kYXQAAAKuBgX//6rcRem9\n", "5tlIt5Ys2CDZI+7veDI2NCAtIGNvcmUgMTQ2IHIyNTU1IDBjMjE0ODAgLSBILjI2NC9NUEVHLTQg\n", "QVZDIGNvZGVjIC0gQ29weWxlZnQgMjAwMy0yMDE1IC0gaHR0cDovL3d3dy52aWRlb2xhbi5vcmcv\n", 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"text/plain": [ "<matplotlib.animation.FuncAnimation at 0x7f0fed7e26a0>" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vmin, vmax = np.log10(100), np.log10(100000)\n", "\n", "fig = plt.figure(figsize=(12, 7))\n", "ax1 = fig.add_axes((0.1, 0.5, 0.8, 0.35))\n", "ax2 = fig.add_axes((0.1, 0.1, 0.8, 0.35))\n", "cax = fig.add_axes((0.91, 0.2, 0.02, 0.5))\n", "ax2.set_xlabel('Azimuth [deg]')\n", "ax1.set_ylabel('Elevation [deg]')\n", "for ax in [ax1, ax2]:\n", " ax.set_xlim((-180, 180))\n", " ax.set_ylim((0, 90))\n", " ax.set_xticks(range(-150, 180, 30))\n", " ax.set_yticks(range(0, 91, 30))\n", " ax.set_aspect('equal')\n", " ax.grid()\n", "\n", "points1 = ax1.scatter(\n", " pos_horiz_parkes[:, 0, 0], pos_horiz_parkes[:, 1, 0],\n", " c=np.log10(pos_horiz_parkes[:, 2, 0]),\n", " cmap='viridis', vmin=vmin, vmax=vmax,\n", " )\n", "points2 = ax2.scatter(\n", " pos_horiz_effbg[:, 0, 0], pos_horiz_effbg[:, 1, 0],\n", " c=np.log10(pos_horiz_effbg[:, 2, 0]),\n", " cmap='viridis', vmin=vmin, vmax=vmax,\n", " )\n", "cbar = fig.colorbar(points1, cax=cax)\n", "cbar.set_label('Distance (km)')\n", "cbar.set_ticks([2, 3, 4, 5])\n", "cbar.set_ticklabels([100, 1000, 10000, 100000])\n", "\n", "ax1.text(-170, 75, 'Parkes 64-m', fontsize=16)\n", "ax2.text(-170, 75, 'Effelsberg 100-m', fontsize=16)\n", "title = ax1.text(\n", " 174, 75, '{:%y/%m/%d %H:%M}'.format(times[0].datetime),\n", " fontsize=15, ha='right'\n", " )\n", "\n", "def init():\n", " points1.set_offsets(pos_horiz_parkes[:, 0:2, 0])\n", " points1.set_array(np.log10(pos_horiz_parkes[:, 2, 0]))\n", " points2.set_offsets(pos_horiz_effbg[:, 0:2, 0])\n", " points2.set_array(np.log10(pos_horiz_effbg[:, 2, 0]))\n", " title.set_text('{:%y/%m/%d %H:%M}'.format(times[0].datetime))\n", " return points, title\n", "\n", "def animate(i):\n", " points1.set_offsets(pos_horiz_parkes[:, 0:2, i])\n", " points1.set_array(np.log10(pos_horiz_parkes[:, 2, i]))\n", " points2.set_offsets(pos_horiz_effbg[:, 0:2, i])\n", " points2.set_array(np.log10(pos_horiz_effbg[:, 2, i]))\n", " title.set_text('{:%y/%m/%d %H:%M}'.format(times[i].datetime))\n", " return points, title\n", "\n", "anim = animation.FuncAnimation(\n", " fig, animate, init_func=init, frames=pos_horiz_parkes.shape[2], interval=20, blit=True\n", " )\n", "\n", "# this takes a while!\n", "plt.close(anim._fig)\n", "anim" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [conda root]", "language": "python", "name": "conda-root-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }