Mirror satellite brightness.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction\n",
    "\n",
    "On Twitter today Jonathan McDowell made the following comment (https://twitter.com/planet4589/status/879927853332213760):\n",
    "\n",
    ">Russian cubesat 'Mayak' to launch Jul 14 will deploy a reflector that may be as bright as mag minus 10. Astronomers likely to be annoyed.\n",
    "\n",
    "This resulted in comprehensive nerd sniping (https://xkcd.com/356/) of both myself (https://twitter.com/vacant3rdman/status/879937146508812289) and Matthew Kenworthy (https://twitter.com/mattkenworthy/status/879954847809888256), and possibly others. As a result I was compelled to attempt to work out the maximum apparent brightness of mirrored surfaces in Earth orbit. This notebook is the result.\n",
    "\n",
    "# Brightness of an orbital mirror\n",
    "\n",
    "The apparent brightness of a specular reflection of sunlight off a flat surface is simply given by the apparent brightness of the Sun scaled by the ratio of the solid angles subtended by the reflector and the Sun from the observer's position and by the specular reflectance of the surface (which will, in general, be a function of wavlength and angle of incidence). Expressed in astronomical magnitudes (yuck), this becomes\n",
    "\n",
    "\\begin{equation}\n",
    "m_\\mathrm{sat} = m_{\\odot} - 2.5 \\times \\log_{10}\\left(\\frac{\\Omega_\\mathrm{sat}}{\\Omega_\\odot}.R_\\mathrm{sat}\\right),\n",
    "\\end{equation}\n",
    "\n",
    "where $m_\\mathrm{sat}$ and $m_\\odot$ are the apparent magnitudes of the satellite and Sun respectively, $\\Omega_\\mathrm{sat}$ and $\\Omega_\\odot$ are their solid angles and $R_\\mathrm{sat}$ is the reflectance of the flat surface on the satellite.\n",
    "\n",
    "For a flat surface of area $A$ at an angle $\\theta$ to the line of sight and seen from a distance $d$ the solid angle (using small angle approximations) is given by\n",
    "\n",
    "\\begin{equation}\n",
    "\\Omega_\\mathrm{sat} = \\frac{A \\cos{\\theta}}{d^2}.\n",
    "\\end{equation}\n",
    "\n",
    "## Conversative upper limit for the Mayak CubeSat\n",
    "\n",
    "We can put an upper limit on the apparent brightness of the satellite by using the minimum distance between observer and satellite (the altitude of the satellite's orbit, $a$) and normal incidence ($\\theta=0$) so that we obtain\n",
    "\n",
    "\\begin{equation}\n",
    "m_\\textrm{sat} > m_{\\odot} - 2.5 \\times \\log_{10}\\left(\\frac{A.R_\\textrm{sat}}{a^2 \\Omega_\\odot}\\right).\n",
    "\\end{equation}\n",
    "\n",
    "Substituting in values for Mayak (http://space.skyrocket.de/doc_sdat/mayak.htm) of $A = 4\\textrm{m}^2$, $a = 500\\textrm{km}$ and $R_\\textrm{sat} = 0.95$ we obtain the following limit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import astropy.units as u\n",
    "import astropy.constants as c\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$6.7905243 \\times 10^{-5} \\; \\mathrm{sr}$"
      ],
      "text/plain": [
       "<Quantity 6.790524307451637e-05 sr>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "omega_sun = (np.pi * (c.R_sun / c.au)**2).to(u.sr, equivalencies=u.equivalencies.dimensionless_angles())\n",
    "omega_sun"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$-26.74 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity -26.74>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_sun = -26.74 * u.dimensionless_unscaled\n",
    "m_sun"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "area = 4 * u.m**2\n",
    "altitude = 500 * u.km\n",
    "reflectance = 0.95 * u.dimensionless_unscaled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.6 \\times 10^{-11} \\; \\mathrm{sr}$"
      ],
      "text/plain": [
       "<Quantity 1.6e-11 sr>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "omega_sat_max = (area / altitude**2).to(u.sr, equivalencies=u.equivalencies.dimensionless_angles())\n",
    "omega_sat_max"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$-10.114851 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity -10.114850699461797>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_sat_min = m_sun - 2.5 * np.log10(omega_sat_max * reflectance / omega_sun)\n",
    "m_sat_min"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**So we find that the apparent brightness of Mayak should be no brighter than magnitude -10.1, which is consistent with the -10 figure quoted on Gunter's Space page.**  It is also in agreement with the result that Matthew Kenworthy arrived at independently, https://twitter.com/mattkenworthy/status/879954847809888256\n",
    "\n",
    "This is a conservative upper limit, however. For the satellite to be at a distance equal to the altitude of its orbit it must be directly overhead of the observer, and $\\theta=0$ implies that the reflector surface is directly facing the observer. For a specular reflection of sunlight to reach the observer the angle of incidence must equal the angle of reflection, i.e. in this case the Sun must be in line with the satellite and observer, in other words on the opposite side of the Earth. The transmission of the entire planet at visible wavelengths is *extremely* low so in practice very little light would reach the satellite in this geometry.\n",
    "\n",
    "## Slightly more rigourous limit\n",
    "\n",
    "In reality the maximum brighness will occur when the observer, satellite and Sun lie in the same plane with the Sun some distance below the horizon from the observer's point of view but above the horizon from the satellite's point of view. The geometry is illustrated in this lovingly hand crafted diagram:\n",
    "\n",
    "![Hand crafted diagram](https://photos.smugmug.com/Other/Stuff/i-Jk4FrC5/0/fab1dcbd/L/IMG20170628221654-L.jpg \"Hand crafted diagram\")\n",
    "\n",
    "This introduces two new variables, the angular distance of the Sun below the horizon at the observer's position, $\\phi$, and the zenith angle of the satellite from the observer's position. We must solve for the line of sight distance between the observer and satellite, $d$, and the angle of incidence and reflection at the mirror surface, $\\theta$ in terms of these two variables. It was at this point that I realised that I had forgotten almost everything that I ever knew about elementary geometry and trigonometry. Fortunately Wikipedia came to the rescue.\n",
    "\n",
    "### Angle of incidence/reflection\n",
    "\n",
    "From the sum of the interior angles of a triangle,\n",
    "\\begin{equation}\\theta = \\frac{\\pi/2 - z - \\phi}{2}.\n",
    "\\end{equation}\n",
    "\n",
    "### Line of sight distance\n",
    "\n",
    "This an instance of the two side and non-included angle triangle problem (https://en.wikipedia.org/wiki/Solution_of_triangles#Two_sides_and_non-included_angle_given_.28SSA.29). The solution for the length of the third side gives\n",
    "\n",
    "\\begin{equation}\n",
    "d = R_\\oplus \\cos(\\pi - z) \\pm  \\sqrt{(R_\\oplus + a)^2 - R_\\oplus \\sin^2(\\pi - z)}.\n",
    "\\end{equation}\n",
    "\n",
    "After a bit of arguably useful rearrangement this becomes\n",
    "\n",
    "\\begin{equation}\n",
    "d = a \\left[ \\sqrt{1 + \\frac{2 R_\\oplus}{a} + \\frac{R_\\oplus^2}{a^2}\\cos^2 z} - \\frac{R_\\oplus}{a} \\cos{z} \\right],\n",
    "\\end{equation}\n",
    "\n",
    "which reassuringly gives $d = a$ when zenith angle is zero. Now we create a function to calculate $d$ as a function of $a$ and $z$ and plot the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def distance(altitude, zenith_angle):\n",
    "    s = 1 + 2 * c.R_earth / altitude + (c.R_earth * np.cos(zenith_angle) / altitude)**2\n",
    "    return (altitude * (s**0.5 - c.R_earth * np.cos(zenith_angle) / altitude)).to(u.km)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
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/f2jWpWTCAC5JkqRa89K8dUyaW8Tn3z+MTm0a9k/OV8cALkmSpFpRURH50cTZ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\nYHX3T0sAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbbb57a9160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "angles = np.arange(-90, 91, 1) * u.degree\n",
    "plt.plot(angles, distance(altitude, angles))\n",
    "plt.xlim(0, 90)\n",
    "plt.ylim(0, 2600)\n",
    "plt.xlabel('Zenith angle / degree')\n",
    "plt.ylabel('Distance / km')\n",
    "plt.title('Line of sight distance as a function of zenith angle for an altitude of 500 km ')\n",
    "plt.gcf().set_size_inches(12, 8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Eclipse condition\n",
    "\n",
    "In order for sunlight to be reflected from the satellite to the observer it is necessary that the Earth is not in the way, i.e. the spacecraft is not in eclipse. Calculating this condition in terms of satellite altitude, zenith angle and observer's Sun elevation required doing some more geometry. The solution is \n",
    "\n",
    "\\begin{equation}\n",
    "(R_\\oplus + a) .\\cos(\\psi - \\phi) > R_\\oplus,\n",
    "\\end{equation}\n",
    "\n",
    "where \n",
    "\n",
    "\\begin{equation}\n",
    "\\psi = \\arcsin\\left(\\frac{d \\sin z}{R_\\oplus + a}\\right).\n",
    "\\end{equation}\n",
    "\n",
    "We will write a function to determine whether the satellite is eclipsed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def is_eclipsed(altitude, zenith_angle, sun_elevation):\n",
    "    los_distance = distance(altitude, zenith_angle)\n",
    "    psi = np.arcsin(los_distance * np.sin(zenith_angle) / (c.R_earth + altitude))\n",
    "    return (c.R_earth + altitude) * np.cos(psi - sun_elevation) < c.R_earth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xFjNzGyN/RcL5s3X4xcFSAHohQ+9Qkrjfr2mKRSntBh4sVQT07LUYEHPoAfQS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\nbWBqkrWBF9LVUL3NyoK+344HPpvkPrqzzie09q2A+wb6/aS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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbbb5a3a7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(angles, is_eclipsed(altitude, angles, +6* u.degree), label='+6$^\\circ$')\n",
    "plt.plot(angles, is_eclipsed(altitude, angles, 0 * u.degree), label='0$^\\circ$')\n",
    "plt.plot(angles, is_eclipsed(altitude, angles, -6 * u.degree), label='-6$^\\circ$')\n",
    "plt.plot(angles, is_eclipsed(altitude, angles, -12 * u.degree), label='-12$^\\circ$')\n",
    "plt.plot(angles, is_eclipsed(altitude, angles, -18 * u.degree), label='-18$^\\circ$')\n",
    "plt.plot(angles, is_eclipsed(altitude, angles, -24 * u.degree), label='-24$^\\circ$')\n",
    "plt.plot(angles, is_eclipsed(altitude, angles, -30 * u.degree), label='-30$^\\circ$')\n",
    "plt.xlim(-90, 90)\n",
    "plt.ylim(1.1,-0.1)\n",
    "plt.xlabel('Zenith angle / degree')\n",
    "plt.yticks((0, 1), ('Not eclipsed', 'Eclipsed'))\n",
    "plt.title('Eclipsed condition for a satellite at 500 km altitude')\n",
    "plt.legend(title='Sun elevation')\n",
    "plt.gcf().set_size_inches(12, 8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The perhaps surprising 'eclipsed' results for positive Sun elevation angles are indicating the situation when the satellite is in daylight but the Sun is on the opposite side of the mirror surface to the observer.\n",
    "\n",
    "### Maximum brightness as a function of zenith angle and Sun elevation\n",
    "\n",
    "Now we can write a function to calculate the maximum apparent brightness as a function of zenith angle and Sun elevation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "omega_sun = (np.pi * (c.R_sun / c.au)**2).to(u.sr, equivalencies=u.equivalencies.dimensionless_angles())\n",
    "m_sun = -26.74 * u.dimensionless_unscaled\n",
    "\n",
    "def m_sat(area, reflectance, altitude, zenith_angle, sun_elevation):\n",
    "    angle_of_incidence = (np.pi * u.radian / 2 - zenith_angle + sun_elevation) / 2 # Elevation negative in twilight\n",
    "    los_distance = distance(altitude, zenith_angle)\n",
    "    omega_sat = (area * np.cos(angle_of_incidence) / \\\n",
    "                 los_distance**2).to(u.sr, equivalencies=u.equivalencies.dimensionless_angles())\n",
    "\n",
    "    m_sat = np.where(is_eclipsed(altitude, zenith_angle, sun_elevation),\n",
    "                     999 * u.dimensionless_unscaled,\n",
    "                     m_sun - 2.5 * np.log10(omega_sat * reflectance / omega_sun)) * u.dimensionless_unscaled\n",
    "    \n",
    "    return m_sat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ajh/miniconda3/envs/astro/lib/python3.6/site-packages/ipykernel_launcher.py:11: RuntimeWarning: invalid value encountered in log10\n",
      "  # This is added back by InteractiveShellApp.init_path()\n"
     ]
    },
    {
     "data": {
      "image/png": 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nt68yU0pt11pPHWxZqRkXQogLQEdzN+V7Gjm8t5HK4iacDjc+PorY9BDyrk4l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vxjqYXhKCXpjBt1Ue2bwcBXWuspgE/pxhLi+irMy2XVjK+oFFKDDneOtLh2cEMCp4+k02loOD6V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\nNEZkz1HCAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbbb59e1d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(angles, m_sat(area, reflectance, altitude, angles, 6* u.degree), label='+6$^\\circ$')\n",
    "plt.plot(angles, m_sat(area, reflectance, altitude, angles, 0 * u.degree), label='0$^\\circ$')\n",
    "plt.plot(angles, m_sat(area, reflectance, altitude, angles, -6 * u.degree), label='-6$^\\circ$')\n",
    "plt.plot(angles, m_sat(area, reflectance, altitude, angles, -12 * u.degree), label='-12$^\\circ$')\n",
    "plt.plot(angles, m_sat(area, reflectance, altitude, angles, -18 * u.degree), label='-18$^\\circ$')\n",
    "plt.plot(angles, m_sat(area, reflectance, altitude, angles, -24 * u.degree), label='-24$^\\circ$')\n",
    "plt.plot(angles, m_sat(area, reflectance, altitude, angles, -30 * u.degree), label='-30$^\\circ$')\n",
    "plt.xlim(-90, 90)\n",
    "plt.ylim(-6,-10.5)\n",
    "plt.xlabel('Zenith angle / degree')\n",
    "plt.ylabel('Maximum brightness / magnitudes')\n",
    "plt.title('Maximum apparent brightness for a 4m$^2$ 95% mirror at 500 km altitude')\n",
    "plt.legend(title='Sun elevation')\n",
    "plt.gcf().set_size_inches(12, 8)\n",
    "plt.savefig('mayak.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Final result\n",
    "\n",
    "We can maximise brightness (minimise magnitude) over zenith angle and Sun elevation to find the highest possible apparent brightness."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   direc: array([[ 1.,  0.],\n",
       "       [ 0.,  1.]])\n",
       "     fun: <Quantity -9.93558237180596>\n",
       " message: 'Optimization terminated successfully.'\n",
       "    nfev: 56\n",
       "     nit: 2\n",
       "  status: 0\n",
       " success: True\n",
       "       x: <Quantity [  8.84357143,-21.33344709]>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = minimize(lambda x: m_sat(area, reflectance, altitude, x[0] * u.degree, x[1] * u.degree),\n",
    "                   (0, -18),\n",
    "                   method='Powell')\n",
    "results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**So the maximum apparent brightness is, apparently, magnitude -9.9, which can occur when the Sun elevation is -21.3° and the satellite is at a zenith angle of 8.8° towards the antisolar direction**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.17926833 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity 0.1792683276558371>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_sat_peak = results['fun']\n",
    "mag_diff = m_sat_peak - m_sat_min\n",
    "mag_diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.84779855 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity 0.8477985489924567>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flux_ratio = 10**(-0.4 * mag_diff)\n",
    "flux_ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.1795255 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity 1.1795254912719808>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inverse_flux_ratio = 10**(0.4 * mag_diff)\n",
    "inverse_flux_ratio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This value is only 0.2 magnitudes fainter than the conservative (and far simpler) upper limit above, which is equivalent to 85% of the flux. I appear to have wasted a *lot* of time for a 18% improvement in accuracy...\n",
    "\n",
    "# Flash duration\n",
    "\n",
    "The entry for Mayak on Gunter's Space Page notes the following\n",
    "\n",
    ">The reflector will provide a -10 optical magnitude at the beginning of the flight to allow for easy tracking. Mayak will be put into a tumbling motion over all axes, with at least 1 revolution per second\n",
    "\n",
    "This suggests that Mayak may initially be in a stable orientation, resulting in flares of comparable duration to those from Iridium satellite (i.e. a few seconds) along a narrow ground track, but will spend most if not all of its mission in a rapid tumble. This will result in bright but very brief flashes of light visible over many different ground tracks as beams of reflected light sweep rapidly over the ground below.\n",
    "\n",
    "## Maximum duration\n",
    "\n",
    "During a flash the observer is effectively looking at a small portion of the Sun reflected in the mirrored surface of the satellite. The direction of the observer's reflected view will move across the sky at twice the angular rotation rate of the mirror, therefore the maximum flash duration will be time it takes for the satellite to rotate by half the angular diameter of the Sun."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$6.2831853 \\; \\mathrm{\\frac{rad}{s}}$"
      ],
      "text/plain": [
       "<Quantity 6.283185307179586 rad / s>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "omega_min = 2 * np.pi * u.radian / u.second\n",
    "omega_min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.73994059 \\; \\mathrm{ms}$"
      ],
      "text/plain": [
       "<Quantity 0.7399405863332114 ms>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "duration_max = (c.R_sun / c.au).to(u.radian, equivalencies=u.equivalencies.dimensionless_angles()) / omega_min\n",
    "duration_max = duration_max.to(u.millisecond)\n",
    "duration_max"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The maximum flash duration is therefore 0.74 milliseconds**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mean flash duration\n",
    "\n",
    "The maximum flash duration will occur when the observer's view of the Sun crosses the centre of the solar disc. In general the track across the disc will be off centre, resulting in a distribution of shorter flash durations. The (angular) length of a chord across the solar disc (angular radius $\\rho_\\odot$) is given by $\\delta = 2 \\rho_\\odot \\sqrt{1 - \\lambda^2 / \\rho_\\odot^2}$, where $\\lambda$ is the offset. The corresponding flash duration is given by \n",
    "\n",
    "\\begin{equation}\n",
    "t = \\frac{\\delta}{2 \\omega_\\mathrm{sat}} = \\frac{\\rho_\\odot}{\\omega_\\mathrm{sat}} \\sqrt{1 - \\frac{\\lambda^2}{\\rho_\\odot^2}} = t_\\mathrm{max} \\sqrt{1 - \\frac{\\lambda^2}{\\rho_\\odot^2}}\n",
    "\\end{equation}\n",
    "\n",
    "Both the angular offset and orientation of the track (which has no effect on duration) can be assumed to be randomly and uniformly distributed so that the normalised probability of a given offset, $P(\\lambda)\\,d\\lambda = 2 \\lambda/ \\rho_\\odot^2\\,d\\lambda$. The expected value for flash duration is then given by\n",
    "\n",
    "\\begin{equation}\n",
    "\\left<t\\right> = \\int_0^{\\rho_\\odot}{t(\\lambda) P(\\lambda)\\,d\\lambda} = t_\\mathrm{max} \\int_0^{\\rho_\\odot} \\sqrt{1 - \\frac{\\lambda^2}{\\rho_\\odot^2}} . 2 \\lambda/ \\rho_\\odot^2\\,d\\lambda = t_\\mathrm{max} \\left[ -\\frac{2}{3} \\left(1 - \\frac{\\lambda^2}{\\rho_\\odot^2} \\right)^\\frac{3}{2} \\right]_0^{\\rho_\\odot} = \\frac{2}{3} t_\\mathrm{max}.\n",
    "\\end{equation}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.49329372 \\; \\mathrm{ms}$"
      ],
      "text/plain": [
       "<Quantity 0.4932937242221409 ms>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "duration_mean = 2 / 3 * duration_max\n",
    "duration_mean    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The mean flash duration from Mayak will be 0.5 millisecond or less, if the tumbling rate exceeds 1 revolution per second.**\n",
    "\n",
    "The flashes from Mayak are so short that it is likely to significantly reduce the perceived brightness as seen by the human eye.\n",
    "\n",
    "## Perceived brightness of short pulses\n",
    "\n",
    "Bloch's Law states that below a certain threshold perceived brightness scales with total pulse energy rather than flux so that a pulse of half the length needs to be twice as bright in order to be perceived as the same brightness, however the situation is complicated by an apparent peak in sensitivity for pulse durations of ~50-100 milliseconds (Broca-Sulzer effect), see for example http://www.pnas.org/content/109/48/19828. If we assume that the Bloch's Law scaling holds for durations of from 40 milliseconds then the 0.74 millisecond maximum duration of the Mayak flashes could mean that they appear a *lot* fainter than magnitude -9.9."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.018498515 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity 0.018498514658330283>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "perception_factor_max = (duration_max / (40 * u.ms)).to(u.dimensionless_unscaled)\n",
    "perception_factor_max"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$54.058394 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity 54.05839433436231>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 / perception_factor_max"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$4.3321579 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity 4.332157854882795>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "perceived_magnitude_offset_min = - 2.5 * np.log10(perception_factor_max)\n",
    "perceived_magnitude_offset_min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$-5.6034245 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity -5.603424516923165>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_sat_peak + perceived_magnitude_offset_min"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**So Bloch's Law suggests that even the longest Mayak flashes would be perceived as if they were ~50 times fainter, or 4.3 magnitudes. This would make even the brightest possible Mayak flashes appear to be magnitude -5.6 or fainter, depending on duration.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.012332343 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity 0.012332343105553523>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "perception_factor_mean = (duration_mean / (40 * u.ms)).to(u.dimensionless_unscaled)\n",
    "perception_factor_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$81.087592 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity 81.08759150154346>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 / perception_factor_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$4.772386 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity 4.772386002521999>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "perceived_magnitude_offset_mean = - 2.5 * np.log10(perception_factor_mean)\n",
    "perceived_magnitude_offset_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$-5.1631964 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity -5.163196369283962>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_sat_peak + perceived_magnitude_offset_mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**A mean duration Mayak flash would be perceived as if they were ~80 times fainter, or 4.8 magnitudes. This would make even the brightest possible Mayak flashes appear no brighter than magnitude -5.2.**"
   ]
  }
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