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    "import astropy as ay\n",
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "from astropy.io import ascii\n",
    "\n",
    "mpl.rcParams['figure.figsize'] = (10, 6)\n",
    "mpl.rcParams['font.size'] = 14\n",
    "import urllib.request"
   ]
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    "# Astronomy 5830, HW 2\n",
    "\n",
    "## Lyra Cao\n",
    "\n",
    "### Problem 1:\n",
    "\n",
    "Signal-to-noise:  An interesting object has been discovered with $r_{AB} = 22$ mag and you would\n",
    "like to observe it further. Note that the SDSS r-band has $\\lambda _c= 0.626 \\mu m$, $d \\lambda = 0.1064 \\mu m$, and the\n",
    "zeropoint of the AB magnitude system is $3631 Jy$.\n",
    "\n",
    "\n",
    "#### 1a. What is the flux zeropoint per unit wavelength $f _{\\lambda}$? Please use $[erg] [s^{-1}] [cm^{-2}] [A^{-1}]$"
   ]
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   "source": [
    "#### Answer, 1a:\n",
    "\n",
    "\\begin{equation}\n",
    "f _{\\nu} = 3631 [Jy] = 3.631 \\times 10^3 \\times 10^{−23} [erg] [s^{−1}] [Hz^{−1}] [cm^{−2}] = 3.631 \\times 10^{−20} [erg] [s^{−1}] [Hz^{−1}] [cm^{−2}]\n",
    "\\end{equation}\n",
    "\n",
    "By the chain rule,\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\partial F}{\\partial \\lambda} = \\frac{\\partial F}{\\partial \\nu} \\frac{\\partial \\nu}{\\partial \\lambda}\n",
    "\\end{equation}\n",
    "\n",
    "So, since $f _{\\nu} \\equiv \\frac{\\partial F}{\\partial \\nu}$ and $f _{\\lambda} \\equiv \\frac{\\partial F}{\\partial \\lambda}$,\n",
    "\n",
    "\\begin{equation}\n",
    "f_{\\lambda} = f_{\\nu} \\left| \\frac{\\partial \\nu}{\\partial \\lambda} \\right|\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "c = \\lambda \\nu\n",
    "\\end{equation}\n",
    "\n",
    "So,\n",
    "\n",
    "\\begin{equation}\n",
    "\\nu = \\frac{c}{\\lambda}\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\partial \\nu}{\\partial \\lambda} = -\\frac{c}{\\lambda ^2}\n",
    "\\end{equation}\n",
    "\n",
    "So,\n",
    "\n",
    "\\begin{equation}\n",
    "f_{\\lambda} = f_{\\nu} \\frac{c}{\\lambda ^2}\n",
    "\\end{equation}\n",
    "\n",
    "With our existing values for $f _{\\nu}$ in cgs units, we multiply by $c=2.99792458 \\times 10^{10}$, and divide by $\\lambda$ in Angstroms ($6260 A$) and $\\lambda$ in cm ($6.26 \\times 10^{-4} cm$).\n",
    "\n",
    "So,\n",
    "\n",
    "\\begin{equation}\n",
    "f_{\\lambda} = 3.631 \\times 10^{−20} [erg] [s^{−1}] [Hz^{−1}] [cm^{−2}] * 2.99792458 \\times 10^{10} [cm] [s^{-1}] * 1/6260 [A^{-1}] * 1/(6.26 \\times 10^{-4}) [cm^{-1}]\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "f_{\\lambda} \\approx 2.778 \\times 10^{-10} [erg] [s^{−1}] [cm^{−2}] [A^{-1}]\n",
    "\\end{equation}\n",
    "\n",
    "The flux zeropoint is $f_{\\lambda} \\approx 2.778 \\times 10^{-10} [erg] [s^{−1}] [cm^{−2}] [A^{-1}]$."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1b. What is the zeropoint in [$\\gamma$][$s^{-1}$][$cm^{-2}$][$A^{-1}$]?"
   ]
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