{ "cells": [ { "cell_type": "markdown", "source": [ "# Defining the orbital plane with $i$ and $\\Omega$\n", "\n", "(Jason Wang, 2021)\n", "\n", "Here we discuss how the orbit plane orientation is defined. We also encourage you to play around with this [interactive orbital elements notebook](https://github.com/sblunt/orbitize/blob/main/docs/tutorials/show-me-the-orbit.ipynb) to get a feel for the orbital elements. Also note that we refer to the values of the angles in degrees when discussing them but all angles are in radians in `orbitize!`. \n", "\n", "Inclination ($i$) and Position angle of the Ascending Node (PAN; $\\Omega$) define the plane of the orbit in the sky. Inclination describes the tilt of the orbital plane relative to the plane in the sky, and PAN describes the rotation of the line of nodes, which is the intersection between the orbital plane and the plane of the sky. \n", "\n", "An intuitive way to think about it is in terms of spherical coordinates. $i$ is equivalent to $\\theta$ (range from 0 to 180 deg), and $\\Omega$ is equivalent to $\\varphi$ (range from 0 to 360 deg) in common spherical notation. The sphere in this case is tilted, with one of the poles pointed towards us. \n", "\n", "## Why do we use a sine prior on inclination?\n", "\n", "You might also hear about using a uniform prior in $\\cos(i)$, which is an equivalent statement. We use a sine prior on inclination because our ultimate goal is to have an isotropic prior on the orbital plane, and due to how we choose coordiantes, this becomes a sine prior on inclination. We can go through some math/visual explaination, but the easiest is perhaps seeing the distribution of orbital plane orientations on a sphere. We use the orbital plane normal (perpendicular vector from the orbit plane) to define the orientation of the plane in 3D space. The normal points to a single point on a unit sphere. Isotropic distributions will uniformly cover the unit sphere. \n", "\n", "In the exercise below, if we randomly draw orbital plane orientations using either an uniform or sine prior for inclination, you'll see that the uniform prior causes more points to cluster near the poles, whereas the sine prior is more uniform. Note that generally the edges of the sphere look darker merely due to a viewing angle effect. \n", "\n" ], "metadata": {} }, { "cell_type": "code", "execution_count": 4, "source": [ "import numpy as np\n", "import matplotlib.pylab as plt\n", "from orbitize.priors import UniformPrior, SinPrior\n", "%matplotlib inline\n", "\n", "def spherical_to_xyz(theta, phi, rho=1):\n", " \"\"\"\n", " Transformation with theta and phi in radians\n", " \"\"\"\n", " z = rho * np.cos(theta)\n", " x = rho * np.sin(theta) * np.cos(phi)\n", " y = rho * np.sin(theta) * np.sin(phi)\n", " return x,y,z\n", "\n", "fig = plt.figure()\n", "\n", "# try a uniform distribution in both\n", "ax1 = fig.add_subplot(121, projection='3d')\n", "\n", "inc_uni_prior = UniformPrior(0, np.pi)\n", "pan_uni_prior = UniformPrior(0, 2*np.pi)\n", "\n", "incs_uni = inc_uni_prior.draw_samples(2000)\n", "pan_uni = pan_uni_prior.draw_samples(2000)\n", "\n", "x_uni, y_uni, z_uni = spherical_to_xyz(incs_uni, pan_uni)\n", "ax1.plot(x_uni, y_uni, z_uni, 'b.', alpha=0.1)\n", "ax1.set_title(\"Uniform in inc\")\n", "\n", "# try a sine distribution for inclination\n", "ax2 = fig.add_subplot(122, projection='3d')\n", "\n", "inc_sine_prior = SinPrior()\n", "\n", "incs_sine = inc_sine_prior.draw_samples(2000)\n", "\n", "x_uni, y_uni, z_uni = spherical_to_xyz(incs_sine, pan_uni)\n", "ax2.plot(x_uni, y_uni, z_uni, 'b.', alpha=0.1)\n", "ax2.set_title(\"Sine in inc\")" ], "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "Text(0.5, 0.92, 'Sine in inc')" ] }, "metadata": {}, "execution_count": 4 }, { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/svg+xml": "\n\n\n\n \n \n \n \n 2021-09-03T15:57:08.877631\n image/svg+xml\n \n \n Matplotlib v3.3.2, https://matplotlib.org/\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n 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}, "metadata": { "needs_background": "light" } } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "## What do the values of $i$ mean?\n", "Inclination in `orbitize!` is defined to go from 0 to 180 degrees. Some other places use -90 to 90 instead, but -90 to 0 is the same as 90 to 180. There are actual a couple of quick things to learn about the orbit from the value of inclination. Here is a summary:\n", "\n", " * $i = 0^\\circ$ : orbit is face-on and body orbits counterclockwise in the sky (North-up, East-left)\n", " * $0^\\circ < i < 90^\\circ$ : orbit is inclined and body orbits counterclockwise in the sky (North-up, East-left)\n", " * $i = 90^\\circ$ : orbit is viewed edge-on\n", " * $90^\\circ < i < 180^\\circ$ : orbit is inclined and body orbits clockwise in the sky (North-up, East-left)\n", " * $i = 180^\\circ$ : orbit is face-on and body orbits clockwise in the sky (North-up, East-left)\n", "\n", "Here are some examples below:" ], "metadata": {} }, { "cell_type": "code", "execution_count": 5, "source": [ "from orbitize.kepler import calc_orbit\n", "\n", "sma = 1\n", "ecc, pan, aop, plx, mtot = 0, 0, 0, 1, 1\n", "tau = 0.3\n", "\n", "incs = np.radians([0, 45, 90, 135, 180])\n", "\n", "all_eps = np.linspace(0, 365.25, 200)\n", "arc_eps = np.linspace(0, 75, 75)\n", "\n", "fig = plt.figure(figsize=(15,4))\n", "for i, inc in enumerate(incs):\n", " ax = fig.add_subplot(1, 5, i+1)\n", "\n", " all_ras, all_decs, _ = calc_orbit(all_eps, sma, ecc, inc, aop, pan, tau, plx, mtot, tau_ref_epoch=0)\n", " ax.plot(all_ras, all_decs, 'k--', alpha=0.5)\n", "\n", " arc_ras, arc_decs, _ = calc_orbit(arc_eps, sma, ecc, inc, aop, pan, tau, plx, mtot, tau_ref_epoch=0)\n", " ax.plot(arc_ras, arc_decs, 'b-', linewidth=2)\n", " ax.plot(arc_ras[-1], arc_decs[-1], 'bo', markersize=7)\n", " \n", " ax.set_title(\"i = {0:d} deg\".format(int(np.degrees(inc))))\n", " ax.set_aspect(\"equal\")\n", " ax.set_xlim([1.1, -1.1])\n", " ax.set_ylim([-1.1, 1.1])\n", " ax.set_xlabel(\"RA\")\n", " ax.set_ylabel(\"Dec\")\n", " \n", "fig.tight_layout()" ], "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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}, "metadata": { "needs_background": "light" } } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "## What do the values of $\\Omega$ mean?\n", "$\\Omega$ or PAN defines the rotation of the orbit in the plane of the sky. Increasing PAN will rotate your orbit counterclockwise in the sky. Here are some examples:" ], "metadata": {} }, { "cell_type": "code", "execution_count": 6, "source": [ "sma = 1\n", "ecc, aop, plx, mtot = 0, 0, 1, 1\n", "inc = np.pi/4 # 45 degrees\n", "tau = 0.3\n", "\n", "pans = np.radians([0, 30, 90, 150, 270])\n", "\n", "all_eps = np.linspace(0, 365.25, 200)\n", "arc_eps = np.linspace(0, 75, 75)\n", "\n", "fig = plt.figure(figsize=(15,4))\n", "for i, pan in enumerate(pans):\n", " ax = fig.add_subplot(1, 5, i+1)\n", "\n", " all_ras, all_decs, _ = calc_orbit(all_eps, sma, ecc, inc, aop, pan, tau, plx, mtot, tau_ref_epoch=0)\n", " ax.plot(all_ras, all_decs, 'k--', alpha=0.5)\n", "\n", " arc_ras, arc_decs, _ = calc_orbit(arc_eps, sma, ecc, inc, aop, pan, tau, plx, mtot, tau_ref_epoch=0)\n", " ax.plot(arc_ras, arc_decs, 'b-', linewidth=2)\n", " ax.plot(arc_ras[-1], arc_decs[-1], 'bo', markersize=7)\n", " \n", " ax.set_title(r\"$\\Omega$ = {0:d} deg\".format(int(np.degrees(pan))))\n", " ax.set_aspect(\"equal\")\n", " ax.set_xlim([1.1, -1.1])\n", " ax.set_ylim([-1.1, 1.1])\n", " ax.set_xlabel(\"RA\")\n", " ax.set_ylabel(\"Dec\")\n", " \n", "fig.tight_layout()" ], "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/svg+xml": "\n\n\n\n \n \n \n \n 2021-09-03T15:57:22.622905\n image/svg+xml\n \n \n Matplotlib v3.3.2, https://matplotlib.org/\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n 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" 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