equinox.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/erik/miniconda3/envs/astro36/lib/python3.6/site-packages/matplotlib/__init__.py:898: MatplotlibDeprecationWarning: The backend.qt4 rcParam was deprecated in version 2.2.  In order to force the use of a specific Qt binding, either import that binding first, or set the QT_API environment variable.\n",
      "  mplDeprecation)\n",
      "/Users/erik/miniconda3/envs/astro36/lib/python3.6/site-packages/matplotlib/__init__.py:898: MatplotlibDeprecationWarning: The backend.qt4 rcParam was deprecated in version 2.2.  In order to force the use of a specific Qt binding, either import that binding first, or set the QT_API environment variable.\n",
      "  mplDeprecation)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "from astropy import units as u\n",
    "from astropy.coordinates import get_sun, GeocentricTrueEcliptic, UnitSphericalRepresentation\n",
    "from astropy.time import Time\n",
    "\n",
    "from scipy import optimize\n",
    "%matplotlib inline\n",
    "from matplotlib import style, pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "first_guess = Time('2018-3-21')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are several possible definitions for \"equinox\".  We consider two here:\n",
    "\n",
    "1. The \"True\" (meaning including precession, nutation, etc) vernal equinox is defined as the moment when the sun passes by the origin of the ecliptic plane of the `GeocentricTrueEcliptic` frame.\n",
    "2. Or it could be the moment the sun passes through the `GCRS` equatorial plane.\n",
    "\n",
    "These are subtly different in various details but the first is probably what most people mean.  For example, the USNO uses the first definition (as you can see by comparing results below to http://aa.usno.navy.mil/data/docs/EarthSeasons.php)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GeocentricTrueEcliptic-based equinox"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's first map out the evolution of the sun in the ecliptic coordinates over the year:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'$\\\\Delta t$ from March 21 [years]')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ecl = lambda time:get_sun(time).transform_to(GeocentricTrueEcliptic(equinox=time))\n",
    "\n",
    "dt = np.linspace(-1, 1, 100)*u.year\n",
    "coo = ecl(first_guess + dt)\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(8, 10))\n",
    "ax1.plot(dt, coo.lat)\n",
    "ax1.axhline(0, color='k')\n",
    "ax2.plot(dt, coo.lon)\n",
    "\n",
    "ax1.set_ylabel('Ecliptic lat [deg]')\n",
    "ax2.set_ylabel('Ecliptic lon [deg]')\n",
    "ax2.set_xlabel(r'$\\Delta t$ from March 21 [years]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the ecliptic coordinates it's a bit ambiguous if the vernal equinox is when it's at the *origin*, vs at the crossing of the longitude = 0 plane... But it turns out they are extremely close anyway, so we will choose the origin.  Hence, the below finds the time when the sun is closest to the origin, given an initial guess."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Time object: scale='utc' format='iso' value=2018-03-20 16:10:14.628>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import optimize\n",
    "\n",
    "def distance_from_origin_ecl(guesstime, spring=True):\n",
    "    guess_coo = get_sun(guesstime).transform_to(GeocentricTrueEcliptic(equinox=guesstime))\n",
    "    lon0 = 0*u.deg if spring else 180*u.deg\n",
    "    origin = guess_coo.frame.__class__(UnitSphericalRepresentation(lat=0*u.deg, lon=lon0))\n",
    "    return origin.separation(guess_coo).to(u.arcsec)\n",
    "\n",
    "def fopt_ecl(x, guess, spring=True):\n",
    "    dt, = x\n",
    "    dist = distance_from_origin_ecl(dt*u.hour+guess, spring=spring)\n",
    "    return dist.value\n",
    "\n",
    "guess = Time('2018-3-21')\n",
    "optres = optimize.minimize(fopt_ecl, (0,), args=guess)\n",
    "equinox_time = optres.x[0]*u.hour + guess\n",
    "equinox_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.664393\\mathrm{{}^{\\prime\\prime}}$"
      ],
      "text/plain": [
       "<Angle 0.6643928 arcsec>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance_from_origin_ecl(equinox_time, spring=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Time object: scale='utc' format='iso' value=2018-09-23 01:48:05.774>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "guess = Time('2018-9-21')\n",
    "optres = optimize.minimize(fopt_ecl, (0,), args=(guess, False))\n",
    "equinox_time = optres.x[0]*u.hour + guess\n",
    "equinox_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.263295\\mathrm{{}^{\\prime\\prime}}$"
      ],
      "text/plain": [
       "<Angle 0.26329549 arcsec>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance_from_origin_ecl(equinox_time, spring=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the above shows, while in principal the sun should should pass through the origin here, there's some subtle definitional differences/approximations that means it doesn't quite match up.  But they are within an arcsec so still very close."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `GCRS`-based equinox"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This approach asks simply where the sun is in the GCRS frame - in principal the 0-crossing is then the sun passing through the actual Earth equatorial plane."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'$\\\\Delta t$ from March 21 [years]')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dt = np.linspace(-1, 1, 100)*u.year\n",
    "coo = get_sun(guess+dt)\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(8, 10))\n",
    "ax1.plot(dt, coo.dec)\n",
    "ax1.axhline(0, color='k')\n",
    "ax2.plot(dt, coo.ra)\n",
    "\n",
    "ax1.set_ylabel(r'GCRS $\\delta$ [deg]')\n",
    "ax2.set_ylabel(r'GCRS $\\alpha$ [deg]')\n",
    "ax2.set_xlabel(r'$\\Delta t$ from March 21 [years]')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Time object: scale='utc' format='iso' value=2018-03-20 22:18:58.045>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def distance_from_origin_gcrs(guesstime, spring=True):\n",
    "    guess_coo = get_sun(guesstime)\n",
    "    lon0 = 0*u.deg if spring else 180*u.deg\n",
    "    origin = guess_coo.frame.__class__(UnitSphericalRepresentation(lat=0*u.deg, lon=lon0))\n",
    "    return origin.separation(guess_coo).to(u.arcsec)\n",
    "\n",
    "def fopt_gcrs(x, guess, spring=True):\n",
    "    dt, = x\n",
    "    dist = distance_from_origin_gcrs(dt*u.hour+guess, spring=spring)\n",
    "    return dist.value\n",
    "\n",
    "guess = Time('2018-3-21')\n",
    "optres = optimize.minimize(fopt_gcrs, (0,), args=guess)\n",
    "equinox_time = optres.x[0]*u.hour + guess\n",
    "equinox_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.41664\\mathrm{{}^{\\prime\\prime}}$"
      ],
      "text/plain": [
       "<Angle 1.41663781 arcsec>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance_from_origin_gcrs(equinox_time, spring=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Time object: scale='utc' format='iso' value=2018-09-23 08:13:10.483>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "guess = Time('2018-9-21')\n",
    "optres = optimize.minimize(fopt_gcrs, (0,), args=(guess, False))\n",
    "equinox_time = optres.x[0]*u.hour + guess\n",
    "equinox_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.481786\\mathrm{{}^{\\prime\\prime}}$"
      ],
      "text/plain": [
       "<Angle 0.481786 arcsec>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance_from_origin_gcrs(equinox_time, spring=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The next few Equinoxes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we stick with the traditional definition (the first case above), we get these for the next several equinoxes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nearest_equinox(guess_time):\n",
    "    spring = guess_time.datetime.month < 7\n",
    "    optres = optimize.minimize(fopt_ecl, (0,), args=(guess_time, spring))\n",
    "    return optres.x[0]*u.hour + guess_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Time object: scale='utc' format='iso' value=2018-03-21 00:00:00.000>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "thisyear_spring = Time('{}-3-21'.format(Time.now().datetime.year))\n",
    "thisyear_autumn = thisyear_spring + 0.5*u.year\n",
    "nextyear_spring = thisyear_spring + 1*u.year\n",
    "\n",
    "years = np.array([thisyear_spring, thisyear_autumn, nextyear_spring])\n",
    "closest_equinox = years[np.argmin(np.abs([(Time.now() - t).jd for t in years]))]\n",
    "closest_equinox"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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       "  Widgets Documentation</a> for setup instructions.\n",
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     "output_type": "stream",
     "text": [
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"d2dtf\" yielded 1 of \"dubious year (Note 5)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"d2dtf\" yielded 1 of \"dubious year (Note 5)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"d2dtf\" yielded 1 of \"dubious year (Note 5)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"d2dtf\" yielded 1 of \"dubious year (Note 5)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"d2dtf\" yielded 1 of \"dubious year (Note 5)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"d2dtf\" yielded 1 of \"dubious year (Note 5)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"d2dtf\" yielded 1 of \"dubious year (Note 5)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"d2dtf\" yielded 1 of \"dubious year (Note 5)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"d2dtf\" yielded 1 of \"dubious year (Note 5)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"d2dtf\" yielded 1 of \"dubious year (Note 5)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"d2dtf\" yielded 1 of \"dubious year (Note 5)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"d2dtf\" yielded 1 of \"dubious year (Note 5)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"d2dtf\" yielded 1 of \"dubious year (Note 5)\" [astropy._erfa.core]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<Time object: scale='utc' format='iso' value=2018-03-20 16:10:14.628>,\n",
       " <Time object: scale='utc' format='iso' value=2018-09-23 01:48:05.774>,\n",
       " <Time object: scale='utc' format='iso' value=2019-03-20 21:52:06.001>,\n",
       " <Time object: scale='utc' format='iso' value=2019-09-23 07:43:13.859>,\n",
       " <Time object: scale='utc' format='iso' value=2020-03-20 03:42:51.725>,\n",
       " <Time object: scale='utc' format='iso' value=2020-09-22 13:23:32.808>,\n",
       " <Time object: scale='utc' format='iso' value=2021-03-20 09:30:49.319>,\n",
       " <Time object: scale='utc' format='iso' value=2021-09-22 19:14:40.687>,\n",
       " <Time object: scale='utc' format='iso' value=2022-03-20 15:27:45.016>,\n",
       " <Time object: scale='utc' format='iso' value=2022-09-23 00:58:46.709>,\n",
       " <Time object: scale='utc' format='iso' value=2023-03-20 21:20:34.833>,\n",
       " <Time object: scale='utc' format='iso' value=2023-09-23 06:46:52.463>,\n",
       " <Time object: scale='utc' format='iso' value=2024-03-20 03:04:38.527>,\n",
       " <Time object: scale='utc' format='iso' value=2024-09-22 12:42:42.649>,\n",
       " <Time object: scale='utc' format='iso' value=2025-03-20 09:01:45.554>,\n",
       " <Time object: scale='utc' format='iso' value=2025-09-22 18:20:44.614>,\n",
       " <Time object: scale='utc' format='iso' value=2026-03-20 14:48:27.626>,\n",
       " <Time object: scale='utc' format='iso' value=2026-09-23 00:08:52.538>,\n",
       " <Time object: scale='utc' format='iso' value=2027-03-20 20:29:19.814>,\n",
       " <Time object: scale='utc' format='iso' value=2027-09-23 06:07:02.302>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import tqdm\n",
    "\n",
    "eqs = []\n",
    "for dt in tqdm.tqdm_notebook(np.arange(20)*0.5*u.year):\n",
    "    neareq = closest_equinox + dt\n",
    "    eqs.append(nearest_equinox(neareq))\n",
    "eqs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Potential astropy feature freeze dates\n",
    "\n",
    "One suggestion for astropy feature freeze dates has been \"the next Friday after one month after the equinox.\"  What would that be?:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2018-04-20 16:10:14.628\n",
      "2018-10-26 01:48:05.774\n",
      "2019-04-19 21:52:06.001\n",
      "2019-10-25 07:43:13.859\n",
      "2020-04-24 03:42:51.725\n",
      "2020-10-23 13:23:32.808\n",
      "2021-04-23 09:30:49.319\n",
      "2021-10-22 19:14:40.687\n",
      "2022-04-22 15:27:45.016\n",
      "2022-10-28 00:58:46.709\n",
      "2023-04-21 21:20:34.833\n",
      "2023-10-27 06:46:52.463\n",
      "2024-04-19 03:04:38.527\n",
      "2024-10-25 12:42:42.649\n",
      "2025-04-25 09:01:45.554\n",
      "2025-10-24 18:20:44.614\n",
      "2026-04-24 14:48:27.626\n",
      "2026-10-23 00:08:52.538\n",
      "2027-04-23 20:29:19.814\n",
      "2027-10-29 06:07:02.302\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\" [astropy._erfa.core]\n",
      "WARNING: ErfaWarning: ERFA function \"d2dtf\" yielded 1 of \"dubious year (Note 5)\" [astropy._erfa.core]\n"
     ]
    }
   ],
   "source": [
    "for eq in eqs:\n",
    "    t = eq + 30*u.day\n",
    "    print(t + u.day*((4 - t.datetime.weekday()) % 7))"
   ]
  }
 ],
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