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Chapter 21 Homework

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Scholars Online Astronomy - Chapter 21: Black Holes


Reading Preparation

Reading: Astronomy, Chapter 21: Black Holes

Study Guide

  • Section 1: Relativity - Einstein's special theory of relativity predicts length contraction, time dilation, and mass increases for objects in motion, and explains why two observers with different motions experience time and distance differently.
  • Section 2: Equivalence - The general theory of relativity explains why it is impossible to distinguish between force due to gravity and force due to acceleration. the general theory of relativity is supported by observations of light "bending" as it travels through space around massive objects such as galaxies. Because light has a finite velocity, it is possible for massive objects with escape velocities greater than the speed of light to "trap light" so that it cannot escape.
  • Section 3: Binary star systems such as Cygnus X-1 may contain a black hole, when one of the stars which is red giant phase, and contracts, draining mass from its companion until it reaches the limit where v = √(2GM/R) > c. Other possible black hole locations are the cores of galaxies.
  • Section 4: Gamma-ray bursters may be the result of jets from black hole accretion disks that form temporarily as massive stars (collapsars) contract during a supernova explosion.
  • Section 5: Gravitational models based on the revolution of stars around galactic centers indicate the existence of massive cores that exceed the limits required to form black holes.
  • Section 6: Because nothing can escape from a black hole, the only observable characteristics are its mass, radius, and location or center. Distinctions between types of atoms are obliterated by destruction of all atomic structures under the pressure of the hole. The point at which light "falls back" to the material surface of the black hole is its event horizon, and the distance to this point from the center of mass is the Schwarzschild radius.
  • Section 7: Black holes have mass, rotation, and (sometimes) electrical charge. Rotating black holes may interact with the magnetic fields of their accretion disks, even transferring energy from the black hole's rotational momentum to objects outside the hole. Masses drag spacetime as they rotate, so near the surface of a black hole in the ergoregion, an object cannot be at rest.
  • Section 8: An object falling into a black hole experiences time contraction and length dilation, as seen by an outside observer.
  • Section 9: The Heisenberg uncertainty principle requires that we cannot determine both position and speed of a subatomic particle. This is a fundamental principle, not a limitation of observation technology that could at some point be overcome. A collateral effect of this principle is the spontaneous creation and annihilation of virtual particles and their antiparticles. When this happens near the surface of a black hole and one member of the pair falls into the black hole, the other gains energy, converts to real mass, and becomes a real particle. This event is Hawking radiation, which drains energy over time. Evaporation of matter from already low-mass black holes may cause the black hole to vanish.

    Key Formulae to Know

    Escape Velocity v   =   2 GM R G: Gravitational Constant
    M: Mass of primary body
    R: Starting point distance to center of mass M

    Web Lecture

    Read the following weblecture before chat: Black Holes

    Study Activity

    Study the visualization of a black hole at the ESA site. What features do you notice? Would a black hole be invisible in space? How would you detect its presence and be able to identify it?

    Website of the Week: Explore the Black Hole: Gravity's Relentless Pull -- the introductory animation is only the beginning. The site contains both an interactive animation and an in-depth presentation of topics in encyclopaedia form.

    Chapter Quiz

    • Required: Complete the Mastery exercise with a passing score of 85% or better.
    • Go to the Moodle and take the quiz for this chat session to see how much you already know about astronomy!

    Lab Work

    Read through the lab for this week; bring questions to chat on any aspect of the lab, whether you intend not perform it or not. If you decide to perform the lab, be sure to submit your report by the posted due date.