PHYS 199 HW 6.ipynb

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    "import numpy as np\n",
    "import matplotlib.pyplot as pt\n",
    "import scipy as ci\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "%matplotlib inline"
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   "source": [
    "<font size=5>Problem 1<font>"
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    "def Start(start):\n",
    "    ###################################################################\n",
    "    # This file is week06_moon_shot.py. It creates a lot of png images \n",
    "    # of the solar system for use by iMovie (Mac) or Movie Maker (Windows).\n",
    "    # George Gollin, University of Illinois, June 10, 2016\n",
    "    # import libraries\n",
    "    import week06_solarsystemObject as SSO\n",
    "    import numpy as np\n",
    "    ############# initialize stuff #############\n",
    "    # Let's launch a space probe from low earth orbit intended to arrive at (or\n",
    "    # at least pass near) the moon.\n",
    "    # Our coordinate system is heliocentric: the sun is at the origin. I pretend\n",
    "    # that all planets orbit in perfect circles in the same plane. The x and y\n",
    "    # axes are defined with respect to the fixed stars. This means that we will need\n",
    "    # to translate positions and velocities with respect to earth into quantities\n",
    "    # with respect to the sun.\n",
    "    # At my reference time t = 0 (April 1, 2016 00:00:00 GMT) the earth was a little\n",
    "    # bit on the negative y side of the negative x axis.\n",
    "    # instantiate the solar system!\n",
    "    MySolarSystem = SSO.SolarSystem()\n",
    "    # Let's launch our probe from orbit at a starting time (in seconds) of 0. This\n",
    "    # will be the \"knob\" we will adjust since t = 0 and the parameters set below \n",
    "    # will put the space probe ahead of the moon as it crosses the lunar orbit.\n",
    "    start_time = start\n",
    "    # here's how you figure out where the planets are at a particular instant of \n",
    "    # time. xplanet_all and yplanet_all are arrays.\n",
    "    xplanet_all, yplanet_all = MySolarSystem.get_planet_xy(start_time)\n",
    "    # the x,y positions for the earth are stored in the 4th elements in the arrays\n",
    "    xearth_now = xplanet_all[MySolarSystem.earth_index]\n",
    "    yearth_now = yplanet_all[MySolarSystem.earth_index]\n",
    "    # you can get the planets' velocities (in our heliocentric frame) the same way.\n",
    "    # note the presence of the current time in the function call. \n",
    "    vxplanet_all, vyplanet_all = MySolarSystem.get_planet_vxvy(start_time)\n",
    "    # x,y velocities for the earth right now are the 4th elements in the arrays. \n",
    "    vxearth_now = vxplanet_all[MySolarSystem.earth_index]\n",
    "    vyearth_now = vyplanet_all[MySolarSystem.earth_index]\n",
    "    # TLI is \"Trans Lunar Injection.\" Apollo 11 left earth orbit with an initial speed \n",
    "    # of 35,570 feet per second (10,841.736 m/s) and an altitude of 177 nautical miles\n",
    "    # (203.688 statute miles, or 327,804.157 meters). \n",
    "    # see http://history.nasa.gov/ap11fj/02earth-orbit-tli.htm.\n",
    "    TLI_v0 = 10841.736\n",
    "    TLI_altitude = 327804.157\n",
    "    # angle for probe initial position relative to the earth and +x direction\n",
    "    # when the TLI burn takes place. I picked this because it does what I want. \n",
    "    TLI_theta = 180. * np.pi / 180.\n",
    "    # We will need to transform the earth-centric position and velocity to a \n",
    "    # heliocentric frame of reference. First convert TLI_altitude to distance from \n",
    "    # the center of the earth. Note how I picked the earth radius out of the array \n",
    "    # of planet radii.\n",
    "    TLI_r0 = TLI_altitude + MySolarSystem.planet_radius[MySolarSystem.earth_index]\n",
    "    # use this to calculate x, y offsets for probe from earth's center, then add\n",
    "    # into it the earth's position relative to the sun.\n",
    "    TLI_x0 = TLI_r0 * np.cos(TLI_theta) + xearth_now\n",
    "    TLI_y0 = TLI_r0 * np.sin(TLI_theta) + yearth_now\n",
    "    # also get the x, y velocity components in a helio-centric coordinate system.\n",
    "    # (FYI: the earth orbits in a counterclockwise direction when seen from a vantage\n",
    "    # point on the positive z axis.)\n",
    "    TLI_vx0 = -TLI_v0 * np.sin(TLI_theta) + vxearth_now\n",
    "    TLI_vy0 = TLI_v0 * np.cos(TLI_theta) + vyearth_now\n",
    "    # now initialize the probe's position. \n",
    "    xprobe_now = TLI_x0\n",
    "    yprobe_now = TLI_y0\n",
    "    # set the initial velocity (m/s) too.\n",
    "    vxprobe_now = TLI_vx0\n",
    "    vyprobe_now = TLI_vy0\n",
    "    # time interval between steps in our numerical integration, in seconds. \n",
    "    TLI_dt = 60\n",
    "    # dt for use inside our loop:\n",
    "    dt = TLI_dt\n",
    "    # current time\n",
    "    time_now = start_time\n",
    "    # maximum total length in days of our space flight\n",
    "    max_days_in_flight = 15\n",
    "    # also calculate the maximum time in seconds.\n",
    "    max_elapsed_time_in_flight = max_days_in_flight * 24 * 3600\n",
    "    # we might not start at start_time = 0, which is April 1, 2016. Take this into\n",
    "    # account here. Time is in seconds.\n",
    "    flight_must_end_by_this_time = max_elapsed_time_in_flight + start_time\n",
    "    # number of steps to calculate: one more step than a specific number of days of\n",
    "    # simulated flight.\n",
    "    max_steps_float = max_days_in_flight * 24 * 60 * (60 / TLI_dt) + 1 \n",
    "    # now turn this into an integer. round up using the ceil (\"ceiling\") function.\n",
    "    max_steps = int(np.ceil(max_steps_float))\n",
    "    # preallocate storage for arrays we will use; initilize them to \"not a number\" \n",
    "    # (nan). this should save time over doing an append each time we want to add an \n",
    "    # element into the array.\n",
    "    # xprobe, yprobe is probe position with respect to the sun.\n",
    "    xprobe = np.array([np.nan] * max_steps)\n",
    "    yprobe = np.array([np.nan] * max_steps)\n",
    "    # now create arrays of x, y points for the earth, also filled with \"nan.\" \n",
    "    xearth = np.array([np.nan] * max_steps)\n",
    "    yearth = np.array([np.nan] * max_steps)\n",
    "    # let's keep track of the probe's velocity with respect to the sun too.\n",
    "    vxprobe = np.array([np.nan] * max_steps)\n",
    "    vyprobe = np.array([np.nan] * max_steps)\n",
    "    # in a later week we will try using dt's that can vary with circumstances so\n",
    "    # add a couple more arrays to help with this.\n",
    "    tprobe = np.array([np.nan] * max_steps)\n",
    "    dtprobe = np.array([np.nan] * max_steps)\n",
    "    # we don't want to draw an image of where the probe is every pass through the \n",
    "    # loop since that would slow us down too much. Let's limit the number of images \n",
    "    # here.\n",
    "    max_images = 50\n",
    "    steps_per_image = np.ceil(max_steps_float / max_images)\n",
    "    # loop index variable\n",
    "    index = 0\n",
    "    # we don't want to have a zillion figure windows open, so set the following flag\n",
    "    # to  True.\n",
    "    close_previous_figure = True\n",
    "    # do we want to stop the loop when we land (or crash) into a planet? If not,\n",
    "    # the loop will pretend that all planets are point masses.\n",
    "    stop_when_probe_lands = False\n",
    "    ############# here's the loop #############\n",
    "    while (index < max_steps) and (time_now <= flight_must_end_by_this_time):\n",
    "        # insert current position into the existing probe position arrays.\n",
    "        xprobe[index] = xprobe_now\n",
    "        yprobe[index] = yprobe_now\n",
    "        # do the same for the probe's velocity.\n",
    "        vxprobe[index] = vxprobe_now\n",
    "        vyprobe[index] = vyprobe_now\n",
    "        # also store time and dt in arrays.\n",
    "        tprobe[index] = time_now\n",
    "        dtprobe[index] = dt\n",
    "        # do the same for the earth's position.\n",
    "        xearth[index] = xearth_now\n",
    "        yearth[index] = yearth_now \n",
    "        # let's keep track of whether or not the probe has crashed into the surface\n",
    "        # of something. The value returned by the class function call will be \n",
    "        # negative if we haven't hit anything. If non-negative it is the index \n",
    "        # number of what we hit. 0 is the sun, 1 is Mercury, 2 is Venus, 3 is Earth, \n",
    "        # etc. The moon is 10.      \n",
    "        the_probe_has_landed = MySolarSystem.crash_landing(time_now, xprobe_now, \\\n",
    "        yprobe_now)    \n",
    "        # do I want to draw the solar system? draw it when the modulus of index \n",
    "        # and steps_per_image is zero. \n",
    "        draw_the_solar_system = (index % steps_per_image == 0)\n",
    "        # If we decide to break out of the loop when we land, rather than continuing\n",
    "        # to loop, we might draw the solar system one last time. But only enable\n",
    "        # this code if you are going to exit the loop, otherwise you'll draw a zillion\n",
    "        # plots, one for each pass through the loop after a landing.\n",
    "        draw_the_solar_system = draw_the_solar_system or \\\n",
    "        (the_probe_has_landed >= 0 and stop_when_probe_lands)\n",
    "        # now draw it if we want to.\n",
    "        if draw_the_solar_system:\n",
    "            # figure out the probe's speed so we can put this number on the plot.\n",
    "            # calculate it both with respect to the earth (useful for a moon shot)\n",
    "            # and with respect to the sun (useful for a Mars shot).\n",
    "            # get the earth's with respect to the x,y velocity for the earth right now:\n",
    "            vxplanet_all, vyplanet_all = MySolarSystem.get_planet_vxvy(time_now)\n",
    "            vxearth_now = vxplanet_all[MySolarSystem.earth_index]\n",
    "            vyearth_now = vyplanet_all[MySolarSystem.earth_index]\n",
    "            # now calculate the probe's speed with respect to the sun.\n",
    "            speed_wrt_sun = np.sqrt(vxprobe_now**2 + vyprobe_now**2)   \n",
    "            # now calculate the probe's speed with respect to the earth.\n",
    "            speed_wrt_earth = np.sqrt((vxprobe_now - vxearth_now)**2 + \\\n",
    "            (vyprobe_now - vyearth_now)**2)   \n",
    "            # calculate probe positions arrays referenced to the current earth position.\n",
    "            # note that xprobe and xearth are arrays, but xearth_now is just a number.\n",
    "            xprobe_wrt_moving_earth = xprobe - xearth + xearth_now\n",
    "            yprobe_wrt_moving_earth = yprobe - yearth + yearth_now\n",
    "            # the following uses the earth as the origin in showing the probe.\n",
    "            # use it for a moon shot.\n",
    "            MySolarSystem.draw_earth_centric(time_now, close_previous_figure, \\\n",
    "            xprobe_wrt_moving_earth, yprobe_wrt_moving_earth, speed_wrt_earth)\n",
    "            # this drawing function plots a larger portion of the solar system.\n",
    "            # MySolarSystem.draw_solar_system(time_now, close_previous_figure, xprobe, \\\n",
    "            # yprobe, speed_wrt_sun)\n",
    "        # break out of the loop if the probe just landed and we don't want to \n",
    "        # continue adjusting pisition and velocity.\n",
    "        if the_probe_has_landed >= 0 and stop_when_probe_lands:\n",
    "            print(\"Probe landed: end loop at elapsed time \", time_now - start_time, \\\n",
    "            \" seconds = \", (time_now - start_time)/(24*3600), \" days\" )\n",
    "            break\n",
    "        # now update probe position and velocity using the higher order integration\n",
    "        # technique from last week. use the same variable names as last week to\n",
    "        # avoid errors and confusion.\n",
    "        # position components\n",
    "        xn = xprobe_now\n",
    "        yn = yprobe_now\n",
    "        # velocity components...\n",
    "        vxn = vxprobe_now\n",
    "        vyn = vyprobe_now\n",
    "        # time\n",
    "        tn = time_now\n",
    "        # calculate dxn, etc. Note the call to a class function that gives us\n",
    "        # gravitational acceleration as a function of position with resect to the sun.\n",
    "        dxn = vxn * dt\n",
    "        dyn = vyn * dt\n",
    "        dvxn, dvyn = MySolarSystem.accel(xn, yn, tn) * dt\n",
    "        # update intermediate position, velocity, and time\n",
    "        xn_half = xn + dxn / 2\n",
    "        yn_half = yn + dyn / 2\n",
    "        vxn_half = vxn + dvxn / 2\n",
    "        vyn_half = vyn + dvyn / 2\n",
    "        tn_half = tn + dt / 2\n",
    "        # calculate improved dxn, etc. see the in-class material writeup.\n",
    "        dxn_improved = vxn_half * dt\n",
    "        dyn_improved = vyn_half * dt\n",
    "        dvxn_improved, dvyn_improved = MySolarSystem.accel(xn_half, yn_half, tn_half) * dt\n",
    "        # now update position and velocity.\n",
    "        xn = xn + dxn_improved\n",
    "        yn = yn + dyn_improved\n",
    "        vxn = vxn + dvxn_improved\n",
    "        vyn = vyn + dvyn_improved\n",
    "        # time too...\n",
    "        tn = tn + dt\n",
    "        # now put this back into the variables I am using elsewhere...\n",
    "        xprobe_now = xn\n",
    "        yprobe_now = yn\n",
    "        vxprobe_now = vxn\n",
    "        vyprobe_now = vyn\n",
    "        time_now = tn\n",
    "        # update the x,y position for the earth right now:\n",
    "        xplanet_all, yplanet_all = MySolarSystem.get_planet_xy(time_now)\n",
    "        xearth_now = xplanet_all[MySolarSystem.earth_index]\n",
    "        yearth_now = yplanet_all[MySolarSystem.earth_index]\n",
    "        # update index \n",
    "        index = index + 1\n",
    "        # end of loop. \n",
    "    # we have filled various arrays with indices running from 0 to index - 1.\n",
    "    # now truncate them to have full lengths of index. This might be necessary\n",
    "    # if we hit the maximum elapsed time in flight (due to changes in dt) before\n",
    "    # we run out of array space.\n",
    "    xprobe = np.resize(xprobe, index)\n",
    "    yprobe = np.resize(yprobe, index)\n",
    "    vxprobe = np.resize(vxprobe, index)\n",
    "    vyprobe = np.resize(vyprobe, index)\n",
    "    tprobe = np.resize(tprobe, index)\n",
    "    dtprobe = np.resize(dtprobe, index)\n",
    "    xearth = np.resize(xearth, index)\n",
    "    yearth = np.resize(yearth, index)\n",
    "    ############# all done! #############\n"
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      "\n",
      "Now instantiating the solar system.\n",
      "planetary configuration for U.S. Central Time  Sun Apr  3 19:00:00 2016\n"
     ]
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4PyjXvBGdPhnNgQVLsmQb6EIFbTRqEA1fl6H/M8YX0plzHuwI8WX/IW/i47PH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\ny8DAoMHx/zIf/iYgxC5YAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11eba2f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Start(86400*3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Explaination: It's probably due to the fact that the attraction force is proportional to r^(-2). If the spaceship and Earth are too close in absolute distance (the initial program assumes Earth to be point mass), the force goes to infinity and a slingshot effect is generated, accelerating the spaceship enormously and diverting its direction. It looks like a bug in this plot but the following plot with a later launching time proves that Earth is indeed functioning as an accelerator and shooting the spaceship away as it gets too close.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Now instantiating the solar system.\n",
      "planetary configuration for U.S. Central Time  Sun Apr  3 23:48:00 2016\n"
     ]
    },
    {
     "data": {
      "image/png": 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3tMfL15fdc353t5Q0Sb4EZtULQxjw1As4EvNCLBg4tWkbV06fo8a9nXF4eJCY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\nL22glFLzlFIJSqmOLp8ba8mfrJRqAWwGJgOISEMMq75DKfW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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b7b6e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Start(86400*3.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<font size=5>Problem 2<font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "########## Storing velocities in list and then manipulate later\n",
    "T=[]\n",
    "Vx=[]\n",
    "Vy=[]\n",
    "def Start1(start):\n",
    "    ###################################################################\n",
    "    # This file is week06_moon_shot.py. It creates a lot of png images \n",
    "    # of the solar system for use by iMovie (Mac) or Movie Maker (Windows).\n",
    "    # George Gollin, University of Illinois, June 10, 2016\n",
    "    # import libraries\n",
    "    import week06_solarsystemObject as SSO\n",
    "    import numpy as np\n",
    "    ############# initialize stuff #############\n",
    "    # Let's launch a space probe from low earth orbit intended to arrive at (or\n",
    "    # at least pass near) the moon.\n",
    "    # Our coordinate system is heliocentric: the sun is at the origin. I pretend\n",
    "    # that all planets orbit in perfect circles in the same plane. The x and y\n",
    "    # axes are defined with respect to the fixed stars. This means that we will need\n",
    "    # to translate positions and velocities with respect to earth into quantities\n",
    "    # with respect to the sun.\n",
    "    # At my reference time t = 0 (April 1, 2016 00:00:00 GMT) the earth was a little\n",
    "    # bit on the negative y side of the negative x axis.\n",
    "    # instantiate the solar system!\n",
    "    MySolarSystem = SSO.SolarSystem()\n",
    "    # Let's launch our probe from orbit at a starting time (in seconds) of 0. This\n",
    "    # will be the \"knob\" we will adjust since t = 0 and the parameters set below \n",
    "    # will put the space probe ahead of the moon as it crosses the lunar orbit.\n",
    "    start_time = start\n",
    "    # here's how you figure out where the planets are at a particular instant of \n",
    "    # time. xplanet_all and yplanet_all are arrays.\n",
    "    xplanet_all, yplanet_all = MySolarSystem.get_planet_xy(start_time)\n",
    "    # the x,y positions for the earth are stored in the 4th elements in the arrays\n",
    "    xearth_now = xplanet_all[MySolarSystem.earth_index]\n",
    "    yearth_now = yplanet_all[MySolarSystem.earth_index]\n",
    "    # you can get the planets' velocities (in our heliocentric frame) the same way.\n",
    "    # note the presence of the current time in the function call. \n",
    "    vxplanet_all, vyplanet_all = MySolarSystem.get_planet_vxvy(start_time)\n",
    "    # x,y velocities for the earth right now are the 4th elements in the arrays. \n",
    "    vxearth_now = vxplanet_all[MySolarSystem.earth_index]\n",
    "    vyearth_now = vyplanet_all[MySolarSystem.earth_index]\n",
    "    # TLI is \"Trans Lunar Injection.\" Apollo 11 left earth orbit with an initial speed \n",
    "    # of 35,570 feet per second (10,841.736 m/s) and an altitude of 177 nautical miles\n",
    "    # (203.688 statute miles, or 327,804.157 meters). \n",
    "    # see http://history.nasa.gov/ap11fj/02earth-orbit-tli.htm.\n",
    "    TLI_v0 = 10841.736\n",
    "    TLI_altitude = 327804.157\n",
    "    # angle for probe initial position relative to the earth and +x direction\n",
    "    # when the TLI burn takes place. I picked this because it does what I want. \n",
    "    TLI_theta = 180. * np.pi / 180.\n",
    "    # We will need to transform the earth-centric position and velocity to a \n",
    "    # heliocentric frame of reference. First convert TLI_altitude to distance from \n",
    "    # the center of the earth. Note how I picked the earth radius out of the array \n",
    "    # of planet radii.\n",
    "    TLI_r0 = TLI_altitude + MySolarSystem.planet_radius[MySolarSystem.earth_index]\n",
    "    # use this to calculate x, y offsets for probe from earth's center, then add\n",
    "    # into it the earth's position relative to the sun.\n",
    "    TLI_x0 = TLI_r0 * np.cos(TLI_theta) + xearth_now\n",
    "    TLI_y0 = TLI_r0 * np.sin(TLI_theta) + yearth_now\n",
    "    # also get the x, y velocity components in a helio-centric coordinate system.\n",
    "    # (FYI: the earth orbits in a counterclockwise direction when seen from a vantage\n",
    "    # point on the positive z axis.)\n",
    "    TLI_vx0 = -TLI_v0 * np.sin(TLI_theta) + vxearth_now\n",
    "    TLI_vy0 = TLI_v0 * np.cos(TLI_theta) + vyearth_now\n",
    "    # now initialize the probe's position. \n",
    "    xprobe_now = TLI_x0\n",
    "    yprobe_now = TLI_y0\n",
    "    # set the initial velocity (m/s) too.\n",
    "    vxprobe_now = TLI_vx0\n",
    "    vyprobe_now = TLI_vy0\n",
    "    # time interval between steps in our numerical integration, in seconds. \n",
    "    TLI_dt = 60\n",
    "    # dt for use inside our loop:\n",
    "    dt = TLI_dt\n",
    "    # current time\n",
    "    time_now = start_time\n",
    "    # maximum total length in days of our space flight\n",
    "    max_days_in_flight = 15\n",
    "    # also calculate the maximum time in seconds.\n",
    "    max_elapsed_time_in_flight = max_days_in_flight * 24 * 3600\n",
    "    # we might not start at start_time = 0, which is April 1, 2016. Take this into\n",
    "    # account here. Time is in seconds.\n",
    "    flight_must_end_by_this_time = max_elapsed_time_in_flight + start_time\n",
    "    # number of steps to calculate: one more step than a specific number of days of\n",
    "    # simulated flight.\n",
    "    max_steps_float = max_days_in_flight * 24 * 60 * (60 / TLI_dt) + 1 \n",
    "    # now turn this into an integer. round up using the ceil (\"ceiling\") function.\n",
    "    max_steps = int(np.ceil(max_steps_float))\n",
    "    # preallocate storage for arrays we will use; initilize them to \"not a number\" \n",
    "    # (nan). this should save time over doing an append each time we want to add an \n",
    "    # element into the array.\n",
    "    # xprobe, yprobe is probe position with respect to the sun.\n",
    "    xprobe = np.array([np.nan] * max_steps)\n",
    "    yprobe = np.array([np.nan] * max_steps)\n",
    "    # now create arrays of x, y points for the earth, also filled with \"nan.\" \n",
    "    xearth = np.array([np.nan] * max_steps)\n",
    "    yearth = np.array([np.nan] * max_steps)\n",
    "    # let's keep track of the probe's velocity with respect to the sun too.\n",
    "    vxprobe = np.array([np.nan] * max_steps)\n",
    "    vyprobe = np.array([np.nan] * max_steps)\n",
    "    # in a later week we will try using dt's that can vary with circumstances so\n",
    "    # add a couple more arrays to help with this.\n",
    "    tprobe = np.array([np.nan] * max_steps)\n",
    "    dtprobe = np.array([np.nan] * max_steps)\n",
    "    # we don't want to draw an image of where the probe is every pass through the \n",
    "    # loop since that would slow us down too much. Let's limit the number of images \n",
    "    # here.\n",
    "    max_images = 50\n",
    "    steps_per_image = np.ceil(max_steps_float / max_images)\n",
    "    # loop index variable\n",
    "    index = 0\n",
    "    # we don't want to have a zillion figure windows open, so set the following flag\n",
    "    # to  True.\n",
    "    close_previous_figure = True\n",
    "    # do we want to stop the loop when we land (or crash) into a planet? If not,\n",
    "    # the loop will pretend that all planets are point masses.\n",
    "    stop_when_probe_lands = False\n",
    "    ############# here's the loop #############\n",
    "    while (index < max_steps) and (time_now <= flight_must_end_by_this_time):\n",
    "        # insert current position into the existing probe position arrays.\n",
    "        xprobe[index] = xprobe_now\n",
    "        yprobe[index] = yprobe_now\n",
    "        # do the same for the probe's velocity.\n",
    "        vxprobe[index] = vxprobe_now\n",
    "        vyprobe[index] = vyprobe_now\n",
    "        # also store time and dt in arrays.\n",
    "        tprobe[index] = time_now\n",
    "        dtprobe[index] = dt\n",
    "        # do the same for the earth's position.\n",
    "        xearth[index] = xearth_now\n",
    "        yearth[index] = yearth_now \n",
    "        \n",
    "        ################################### Appending velocity to list\n",
    "        Vx.append(vxprobe_now)\n",
    "        Vy.append(vyprobe_now)\n",
    "        T.append(time_now)\n",
    "        ################################### Edited above\n",
    "        \n",
    "        # let's keep track of whether or not the probe has crashed into the surface\n",
    "        # of something. The value returned by the class function call will be \n",
    "        # negative if we haven't hit anything. If non-negative it is the index \n",
    "        # number of what we hit. 0 is the sun, 1 is Mercury, 2 is Venus, 3 is Earth, \n",
    "        # etc. The moon is 10.      \n",
    "        the_probe_has_landed = MySolarSystem.crash_landing(time_now, xprobe_now, \\\n",
    "        yprobe_now)    \n",
    "        # do I want to draw the solar system? draw it when the modulus of index \n",
    "        # and steps_per_image is zero. \n",
    "        draw_the_solar_system = (index % steps_per_image == 0)\n",
    "        # If we decide to break out of the loop when we land, rather than continuing\n",
    "        # to loop, we might draw the solar system one last time. But only enable\n",
    "        # this code if you are going to exit the loop, otherwise you'll draw a zillion\n",
    "        # plots, one for each pass through the loop after a landing.\n",
    "        draw_the_solar_system = draw_the_solar_system or \\\n",
    "        (the_probe_has_landed >= 0 and stop_when_probe_lands)\n",
    "        # now draw it if we want to.\n",
    "        if draw_the_solar_system:\n",
    "            # figure out the probe's speed so we can put this number on the plot.\n",
    "            # calculate it both with respect to the earth (useful for a moon shot)\n",
    "            # and with respect to the sun (useful for a Mars shot).\n",
    "            # get the earth's with respect to the x,y velocity for the earth right now:\n",
    "            vxplanet_all, vyplanet_all = MySolarSystem.get_planet_vxvy(time_now)\n",
    "            vxearth_now = vxplanet_all[MySolarSystem.earth_index]\n",
    "            vyearth_now = vyplanet_all[MySolarSystem.earth_index]\n",
    "            # now calculate the probe's speed with respect to the sun.\n",
    "            speed_wrt_sun = np.sqrt(vxprobe_now**2 + vyprobe_now**2)   \n",
    "            # now calculate the probe's speed with respect to the earth.\n",
    "            speed_wrt_earth = np.sqrt((vxprobe_now - vxearth_now)**2 + \\\n",
    "            (vyprobe_now - vyearth_now)**2)   \n",
    "            # calculate probe positions arrays referenced to the current earth position.\n",
    "            # note that xprobe and xearth are arrays, but xearth_now is just a number.\n",
    "            xprobe_wrt_moving_earth = xprobe - xearth + xearth_now\n",
    "            yprobe_wrt_moving_earth = yprobe - yearth + yearth_now\n",
    "            # the following uses the earth as the origin in showing the probe.\n",
    "            # use it for a moon shot.\n",
    "            MySolarSystem.draw_earth_centric(time_now, close_previous_figure, \\\n",
    "            xprobe_wrt_moving_earth, yprobe_wrt_moving_earth, speed_wrt_earth)\n",
    "            # this drawing function plots a larger portion of the solar system.\n",
    "            # MySolarSystem.draw_solar_system(time_now, close_previous_figure, xprobe, \\\n",
    "            # yprobe, speed_wrt_sun)\n",
    "        # break out of the loop if the probe just landed and we don't want to \n",
    "        # continue adjusting pisition and velocity.\n",
    "        if the_probe_has_landed >= 0 and stop_when_probe_lands:\n",
    "            print(\"Probe landed: end loop at elapsed time \", time_now - start_time, \\\n",
    "            \" seconds = \", (time_now - start_time)/(24*3600), \" days\" )\n",
    "            break\n",
    "        # now update probe position and velocity using the higher order integration\n",
    "        # technique from last week. use the same variable names as last week to\n",
    "        # avoid errors and confusion.\n",
    "        # position components\n",
    "        xn = xprobe_now\n",
    "        yn = yprobe_now\n",
    "        # velocity components...\n",
    "        vxn = vxprobe_now\n",
    "        vyn = vyprobe_now\n",
    "        # time\n",
    "        tn = time_now\n",
    "        # calculate dxn, etc. Note the call to a class function that gives us\n",
    "        # gravitational acceleration as a function of position with resect to the sun.\n",
    "        dxn = vxn * dt\n",
    "        dyn = vyn * dt\n",
    "        dvxn, dvyn = MySolarSystem.accel(xn, yn, tn) * dt\n",
    "        # update intermediate position, velocity, and time\n",
    "        xn_half = xn + dxn / 2\n",
    "        yn_half = yn + dyn / 2\n",
    "        vxn_half = vxn + dvxn / 2\n",
    "        vyn_half = vyn + dvyn / 2\n",
    "        tn_half = tn + dt / 2\n",
    "        # calculate improved dxn, etc. see the in-class material writeup.\n",
    "        dxn_improved = vxn_half * dt\n",
    "        dyn_improved = vyn_half * dt\n",
    "        dvxn_improved, dvyn_improved = MySolarSystem.accel(xn_half, yn_half, tn_half) * dt\n",
    "        # now update position and velocity.\n",
    "        xn = xn + dxn_improved\n",
    "        yn = yn + dyn_improved\n",
    "        vxn = vxn + dvxn_improved\n",
    "        vyn = vyn + dvyn_improved\n",
    "        # time too...\n",
    "        tn = tn + dt\n",
    "        # now put this back into the variables I am using elsewhere...\n",
    "        xprobe_now = xn\n",
    "        yprobe_now = yn\n",
    "        vxprobe_now = vxn\n",
    "        vyprobe_now = vyn\n",
    "        time_now = tn\n",
    "        # update the x,y position for the earth right now:\n",
    "        xplanet_all, yplanet_all = MySolarSystem.get_planet_xy(time_now)\n",
    "        xearth_now = xplanet_all[MySolarSystem.earth_index]\n",
    "        yearth_now = yplanet_all[MySolarSystem.earth_index]\n",
    "        # update index \n",
    "        index = index + 1\n",
    "        # end of loop. \n",
    "    # we have filled various arrays with indices running from 0 to index - 1.\n",
    "    # now truncate them to have full lengths of index. This might be necessary\n",
    "    # if we hit the maximum elapsed time in flight (due to changes in dt) before\n",
    "    # we run out of array space.\n",
    "    xprobe = np.resize(xprobe, index)\n",
    "    yprobe = np.resize(yprobe, index)\n",
    "    vxprobe = np.resize(vxprobe, index)\n",
    "    vyprobe = np.resize(vyprobe, index)\n",
    "    tprobe = np.resize(tprobe, index)\n",
    "    dtprobe = np.resize(dtprobe, index)\n",
    "    xearth = np.resize(xearth, index)\n",
    "    yearth = np.resize(yearth, index)\n",
    "    ############# all done! #############"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Now instantiating the solar system.\n",
      "planetary configuration for U.S. Central Time  Sun Apr  3 19:00:00 2016\n"
     ]
    },
    {
     "data": {
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M0SurrJQqAERjDBM/T0vEhHrtMyR2rC2M0e4lM/bKHIRVbV6r3BS/36fxWfQdrtZ7hHxX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\ny8DAoMHx/zIf/iYgxC5YAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1207b4630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Start1(86400*3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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j3PGRzfGsIZHmVBbw93et5aV99Ty86Qi/23aCTbtOceuGKq5aVkFJYfZFHa+j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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1234be128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "########## Calculating absolute differences and make plot\n",
    "dt=60\n",
    "deltax=[]\n",
    "deltay=[]\n",
    "\n",
    "for i in range(1,len(T)-1):\n",
    "    deltax=np.append(deltax,(Vx[i-1]-2*Vx[i]+Vx[i+1])*dt)\n",
    "    deltay=np.append(deltay,(Vy[i-1]-2*Vy[i]+Vy[i+1])*dt)\n",
    "delta=np.sqrt(deltax**2+deltay**2)\n",
    "pt.plot(T[1:len(T)-1],np.log10(delta))\n",
    "pt.xlabel('time')\n",
    "pt.ylabel('error per step')\n",
    "pt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font size=4>Time took: Problem 1: 30 minutes. Problem 2: 1 hour. Collaborator: Completed on my own. Reference: None. <font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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