{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bec79c69",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import cartopy.crs as ccrs\n",
    "from cartopy.feature import NaturalEarthFeature\n",
    "from matplotlib.patches import Circle\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from astropy.coordinates import SkyCoord\n",
    "from tqdm import tqdm\n",
    "from astropy import units as u\n",
    "from astropy.coordinates import (SkyCoord, Distance, Galactic, \n",
    "                                 EarthLocation, AltAz)\n",
    "import matplotlib as mpl\n",
    "%matplotlib inline\n",
    "\n",
    "ra_center = 110  \n",
    "dec_center = 30  \n",
    "radius = 2.5  \n",
    "\n",
    "\n",
    "center_coord = SkyCoord(ra_center, dec_center, unit=(u.deg, u.deg), frame='icrs')\n",
    "\n",
    "\n",
    "theta = np.linspace(0, 2 * np.pi, 100)  \n",
    "r = np.full_like(theta, radius)  \n",
    "\n",
    "\n",
    "ra_circle = center_coord.ra.deg + r * np.cos(theta)\n",
    "dec_circle = center_coord.dec.deg + r * np.sin(theta)\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(subplot_kw={'projection': 'mollweide'})  # 使用 mollweide 投影\n",
    "\n",
    "\n",
    "ax.plot(np.radians(ra_circle), np.radians(dec_circle), color='red', lw=2, label='LAMOST Field of View')\n",
    "\n",
    "\n",
    "ax.plot(np.radians(ra_center), np.radians(dec_center), 'bo', label='Center (Ra, Dec)')\n",
    "\n",
    "\n",
    "ra_ticks = np.radians([-120, -60, 0, 60, 120])\n",
    "ra_labels = ['240°', '300°', '0°', '60°', '120°']\n",
    "ax.set_xticks(ra_ticks)\n",
    "ax.set_xticklabels(ra_labels)\n",
    "\n",
    "dec_ticks = np.radians([-60, -30, 0, 30, 60])\n",
    "dec_labels = ['-60°', '-30°', '0°', '30°', '60°']\n",
    "ax.set_yticks(dec_ticks)\n",
    "ax.set_yticklabels(dec_labels)\n",
    "\n",
    "\n",
    "\n",
    "ax.set_xlabel('Ra (degrees)')\n",
    "ax.set_ylabel('Dec (degrees)')\n",
    "ax.legend()\n",
    "ax.grid(True)\n",
    "\n",
    "ax.set_title('LAMOST Field of View')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a2be9eaf",
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid decimal literal (575061056.py, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  Input \u001b[1;32mIn [4]\u001b[1;36m\u001b[0m\n\u001b[1;33m    2、银河系的光度大概是10^11太阳光度，半光度半径Re大约是5Kpc。(太阳的V波段绝对星等是4.8等）。如果银河系距离观测者的距离是100kpc，其视星等和Re的视尺度（apparent size）各是多少？Re内的平均表面亮度是多少？如果距离是1Mpc呢？\u001b[0m\n\u001b[1;37m    ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid decimal literal\n"
     ]
    }
   ],
   "source": [
    "2、银河系的光度大概是10^11太阳光度，半光度半径Re大约是5Kpc。(太阳的V波段绝对星等是4.8等）。如果银河系距离观测者的距离是100kpc，其视星等和Re的视尺度（apparent size）各是多少？Re内的平均表面亮度是多少？如果距离是1Mpc呢？\n",
    "解：距离为100kpc时：\n",
    "\n",
    "视半径𝜃=5𝑘𝑝𝑐100𝑘𝑝𝑐×360。2𝜋=3。\n",
    "，视尺度2𝜃=6。\n",
    "\n",
    "𝐿(𝐿⊙)=10−(𝑀−𝑀⊙)/2.5,𝑀⊙=4.8𝑚𝑎𝑔,𝐿=1011𝐿⊙\n",
    "\n",
    "所以银河系的绝对星等𝑀=−22.7𝑚𝑎𝑔\n",
    "\n",
    "银河系的视星等𝑚=𝑀+5𝑙𝑔𝑑−5=−2.7𝑚𝑎𝑔\n",
    "\n",
    "𝑅𝑒\n",
    "内的平均表面亮度𝑚𝑢=𝑚+2.5𝑙𝑜𝑔(𝑎𝑟𝑒𝑎)=−2.7+2.5×𝑙𝑜𝑔(𝜋𝜃2)=18.7𝑚𝑎𝑔/𝑠𝑒𝑐2\n",
    "\n",
    "距离为1Mpc时：\n",
    "\n",
    "视半径𝜃=5𝑘𝑝𝑐1000𝑘𝑝𝑐×360。2𝜋=0.3。\n",
    "，视尺度2𝜃=0.6。\n",
    "\n",
    "𝐿(𝐿⊙)=10−(𝑀−𝑀⊙)/2.5,𝑀⊙=4.8𝑚𝑎𝑔,𝐿=1011𝐿⊙\n",
    "\n",
    "所以银河系的绝对星等𝑀=−22.7𝑚𝑎𝑔\n",
    "\n",
    "银河系的视星等𝑚=𝑀+5𝑙𝑔𝑑−5=−22.7+5×6−5=2.3𝑚𝑎𝑔\n",
    "\n",
    "𝑅𝑒\n",
    "内的平均表面亮度𝑚𝑢=𝑚+2.5𝑙𝑜𝑔(𝑎𝑟𝑒𝑎)=2.3+2.5×𝑙𝑜𝑔(𝜋𝜃2)=18.7𝑚𝑎𝑔/𝑠𝑒𝑐2"
   ]
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