{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Light travel time delay\n",
    "\n",
    "A simple example showing the effects of light travel time delay on an edge-on planet in an orbit similar to that of Earth."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "hide_input"
    ]
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "hide_input"
    ]
   },
   "outputs": [],
   "source": [
    "%run notebook_setup.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import starry\n",
    "from astropy import units as u\n",
    "\n",
    "starry.config.lazy = True\n",
    "starry.config.quiet = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "star = starry.Primary(starry.Map(udeg=2, amp=1.0), m=1.0, r=1.0)\n",
    "star.map[1:] = [0.5, 0.25]\n",
    "planet = starry.Secondary(\n",
    "    starry.Map(1, amp=0.0025), porb=365.25, r=0.1, prot=365.25, m=0.0, t0=0.0\n",
    ")\n",
    "planet.map[1, 0] = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sys1 = starry.System(star, planet, light_delay=False)\n",
    "sys2 = starry.System(star, planet, light_delay=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute the delay in the zero-crossing\n",
    "t = np.linspace(-0.01, 0.01, 999)\n",
    "t1 = t[np.argmin(np.abs(sys1.position(t)[0][1].eval()))]\n",
    "t2 = t[np.argmin(np.abs(sys2.position(t)[0][1].eval()))]\n",
    "diff = (t1 - t2) * u.day.to(u.minute)\n",
    "\n",
    "# Plot the transits\n",
    "t = np.linspace(-0.5, 0.5, 20000)\n",
    "fig = plt.figure(figsize=(8, 3))\n",
    "plt.plot(t, sys1.flux(t).eval() - 1, label=\"no delay\")\n",
    "plt.plot(t, sys2.flux(t).eval() - 1, label=\"with delay\")\n",
    "plt.xlabel(\"time [days]\")\n",
    "plt.ylabel(\"relative flux\")\n",
    "plt.legend(fontsize=10, loc=\"lower right\")\n",
    "plt.title(\"Light delay causes transits to occur %.2f minutes early\" % diff, fontsize=14);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute the delay in the zero-crossing\n",
    "t = np.linspace(planet.porb.eval() / 2 - 0.01, planet.porb.eval() / 2 + 0.01, 999)\n",
    "t1 = t[np.argmin(np.abs(sys1.position(t)[0][1].eval()))]\n",
    "t2 = t[np.argmin(np.abs(sys2.position(t)[0][1].eval()))]\n",
    "diff = (t2 - t1) * u.day.to(u.minute)\n",
    "\n",
    "t = np.linspace(planet.porb.eval() / 2 - 0.5, planet.porb.eval() / 2 + 0.5, 20000)\n",
    "fig = plt.figure(figsize=(8, 3))\n",
    "plt.plot(t, sys1.flux(t).eval() - 1, label=\"no delay\")\n",
    "plt.plot(t, sys2.flux(t).eval() - 1, label=\"with delay\")\n",
    "plt.xlabel(\"time [days]\")\n",
    "plt.ylabel(\"relative flux\")\n",
    "plt.legend(fontsize=10, loc=\"lower right\")\n",
    "plt.title(\"Light delay causes eclipses to occur %.2f minutes late\" % diff, fontsize=14);"
   ]
  }
 ],
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