{ "cells": [ { "cell_type": "markdown", "id": "d91afd13-7ad9-4754-96cb-fdc7cab9cd02", "metadata": {}, "source": [ "# PY3109: Observational Astrophysics\n", "\n", "**Module Objective:** To provide students with an overview of observational astrophysics.\n", "\n", "**Module Content**: Magnitude brightness scale, optical telescopes, introduction to radio, IR, UV, X-ray astronomy, Hertzsprung-Russell diagram, stellar spectra & classification, variable and binary stars.\n", "\n", "**Learning Outcomes**: On successful completion of this module, students should be able to:\n", "\n", "1. Perform simple numerical calculations covering a wide range of astronomical topics, inluding magnitude brightness scale, radio, IR, UV and X-ray astronomy.\n", "2. Explain the theory of star formation, stellar atmospheres and stellar structure.\n", "3. Apply stellar structure theory to white dwarfs and neutron stars.\n", "4. Demonstrate the ability to perform astronomical observations and gather astronomical data.\n", "\n", "**Assessment**: Total Marks 100: Formal Written Examination 80 marks; Continuous Assessment 20 marks (10 assignments, 2 marks each)." ] }, { "cell_type": "code", "execution_count": 2, "id": "fc1f7cfe-d43c-4f0d-818a-92b51e2b9813", "metadata": { "tags": [] }, "outputs": [], "source": [ "#Setup cell importing modules used in this notebook\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from astropy.time import Time\n", "from astropy.coordinates import solar_system_ephemeris, EarthLocation\n", "from astropy.coordinates import get_body_barycentric, get_body, get_moon" ] }, { "cell_type": "markdown", "id": "3cb716cd-0a1f-4bd0-b1df-72e89d732b1e", "metadata": {}, "source": [ "# Section 1: The Coordinate System\n", "**Relevant Literature**: Chapter 1 of Ryden & Peterson" ] }, { "cell_type": "markdown", "id": "6668ef10-013c-4d8c-9f00-5993c0faaf4b", "metadata": {}, "source": [ "
\n", " Key Question \n", "How do we convey the positions of stars in the night sky to people who are observing from a different place on the Earths surface, or who live at different time to us (and make sense of observations taken thousands of years ago)? Defining a coordinate system which accounts for the tilt and precession of the Earths spin axis relative to the Sun-Earth orbital plane is non-trivial, and in order to understand it, we must go back to the ancient Greeks.\n", "
" ] }, { "cell_type": "markdown", "id": "a0aa5148-2ff6-4aae-8f08-522f63b06fb8", "metadata": {}, "source": [ "## The evolution of the solar systems geometry - Geocentrism" ] }, { "cell_type": "markdown", "id": "a14f9d44-71ba-4fac-be67-9478c9442f74", "metadata": {}, "source": [ "Humans have a long history of studying the position of stars in the night sky. One of the oldest models is the geocentric model, proposed by Plato. In this model, the Earth lies at the centre of everything, and the stars and planets are on a celestial sphere which is rotating around us\n", "\n", "![Geocentric Model](Figures/Figure_1.png)\n", "\n", "This model works well at explaning the diurnal motion of stars, but the \"wandering stars\", or planets, could not be. These planets would slowly move West to East with respect to the fixed background stars, but would occassionally reverse direction before reverting back to West to East. An example of this movement is shown below for Venus." ] }, { "cell_type": "code", "execution_count": 3, "id": "d4735a09-8aa4-42b2-a5c8-1b0d4a78f277", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "times = np.arange(57192,57322,2) #This is just arbitrary MJDs I've chosen, sampled at 2 day intervals.\n", "ts = Time(times,format='mjd',scale='utc') #Convering the MJDs to a Time format which Astropy can read.\n", "loc = EarthLocation.of_site('greenwich') #Our observations have to be taken somwhere, let's use Greenwich for ease of use.\n", "with solar_system_ephemeris.set('builtin'):\n", " venus = get_body('venus', ts, loc) # Get the location of venus\n", "plt.figure(figsize=[4,3],dpi=200)\n", "plt.plot(venus.ra,venus.dec,'-') #Plotting the RA and Dec of venus\n", "plt.arrow(venus.ra.value[4],venus.dec.value[4],3,-1.5,width=0.3)\n", "plt.arrow(venus.ra.value[29],venus.dec.value[29],-2.5,0.7,width=0.3)\n", "plt.arrow(venus.ra.value[-4],venus.dec.value[-4],3,-0.9,width=0.3)\n", "plt.title(f\"Location of Venus from {ts[0].isot[:10]} to {ts[-1].isot[:10]}\")\n", "plt.ylabel(\"Dec (deg)\")\n", "plt.xlabel(\"RA (deg)\")\n", "plt.gca().invert_xaxis() #RA normally increases from right to left - we'll explain why this is later on\n", "plt.savefig(\"Figures/Planet_motion.png\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "35c581ed-cf17-46a7-898a-63bc7a9500b1", "metadata": {}, "source": [ "Hipparchus proposed a slight augmentation to Plato's model to explain the retrograde motion of these planets. This model involed a system of circles. For any given planet, it rotated on an **epicycle** which in turn rotated on a larger **deferent** as below. This still didn't agree with the motion of the planets adequately, which led Ptolemy to augment the model by offsetting the Earth from the centre of the deferent and adding an **equant**. The planet still orbits the deferent centre, but it's assumed that $\\frac{d\\theta}{dt}$ is constant, which allows for a circular orbit to give the same observed effects as a body which is following an elliptical orbit. While still not perfect at predicting the motions of the planets, it could easily be adapted to new observations by adding in new circles.\n", "\n", "![Hipparchus Model](Figures/Figure_2.png)" ] }, { "cell_type": "markdown", "id": "c753b7f1-170b-4880-9793-262e5217c1d0", "metadata": {}, "source": [ "
\n", "These models were incredibly precise at predicting the positions of stars, the requirement to constantly add new circles to explain the complex motion of the planets suggested that something was wrong with them.\n", "
" ] }, { "cell_type": "markdown", "id": "0b2f1aed-8966-411a-a97d-a64b4d3b158c", "metadata": {}, "source": [ "## Heliocentrism" ] }, { "cell_type": "markdown", "id": "6cf45783-f68c-4217-8d88-5213fbff96ce", "metadata": {}, "source": [ "It took until the 15th century to move away from this geocentric view of the solar system, when Nicolaus Copernicus proposed a heliocentric model of the planets. One immedate consequence of this was that the maximum angular distance of both Venus (47 degrees) and Mercury (28 degrees) meant that they had to lie within Earth's orbit, and that Mercury had to lie closest to the Sun.\n", "\n", "![Copernicus Model](Figures/Figure_3.png)" ] }, { "cell_type": "markdown", "id": "c77fb23c-9f72-477b-9538-0e743b8a99e3", "metadata": {}, "source": [ "The Copernican model of the Solar system could easily account for the retrograde motion of the planets, which was a major failing of any geocentric models. An example of how the sudden reversals in a planets direction of motion across the night sky is shown in the below Figure. The numbers indicate different observing times, starting from 1 and ending at 6. Between observation 3 and 4, Mars undergoes a \"reversal\" in the night sky.\n", "\n", "![Retrograde motion explained](Figures/Figure_4.png)\n", "\n", "Heliocentrism also allows us to calculate the **true** (sidereal) orbital periods of the planets. Consider a planet which is further from Earth than the Sun. Conjunctions occur when all planets and the Sun lie on a straight line connecting their centres. In the below, when the Earth lies between the Sun and Mars, is called **opposition**. The time between successive oppositions is S, the synodic period. The sidereal period of the planet, P, can then be calculated using\n", "\n", "$$\n", " \\frac{1}{S} = \\frac{1}{P_\\oplus}-\\frac{1}{P} (P>P_\\oplus)\\\\ \n", " \\frac{1}{S} = \\frac{1}{P}-\\frac{1}{P_\\oplus} (P