The History and Nature of Astronomical Discovery - AST 210 H1

Lectures 9-16: The Advent of Astrophysics: Material for Term Test 2

Einstein and Relativity

(Updated on 9 November, 2013)

This section is based on the discussions of Einstein and his relativity theory in Chapters 3 and 15 of the textbook, "In Quest of the Universe". In the outline below, I indicate the material you should read and which of the terms that are highlighted in bold face or italics you should know.

Chapter 3 - Gravity and the Rise of Modern Astronomy

  • 3-7 Beyond Newton: How Science Progresses
  • 3-8,3-9 (3-10 in 5th ed.) General Theory of Relativity: principle of equivalence, space warp, Albert Einstein, the orbit of Mercury, precession (of an elliptical orbit), the correspondence principle, the special theory of relativity, conclusion

Readings from other chapters

  • General Relativity: special theory of relativity, general theory of relativity, the main predictions of general relativity, principle of equivalence (section 15-7 on pages 435-437[5th ed: 466-468; 4th ed: 494-496 including Figures 3-18, 3-19, 3-20 and 3-21].
  • Gravitational lenses (bottom of page 538 (4th ed:567) to middle of page 540 (4th ed.: 569), including Figures 17-27 and 17-28)
  • Perhaps the most active microlensing survey today is OGLE . Many events are shown on the OGLE website , including those caused by planets getting close to Earth mass. A nice brief history and explanation can be seen at this site , but it quickly gets too mathematical for this course!
    Another very active survey is MOA in New Zealand. There are some excellent pages linked from there, including a general description with superb diagrams .
    Animations of microlensing are at Scott Gaudi's site .
    Note that stars in galaxies can cause microlensing on cosmic distance scales, as in this case of the Einstein Cross , work done by York University astronomers.

    The Structure of the Atom and the Nature of Light

    (Updated on 10 Nov. 2012)

    This section of the course is based mainly on the discussions of light and the electromagnetic spectrum and the Bohr model of the atom in Chapter 4 of the textbook. In the outline below, I indicate the material you should read and which of the terms that are highlighted in bold face or italics you should know.

    Chapter 4 - Light and the Electromagnetic Spectrum

    • Introduction
    • 4-1 Temperature Scales: the Kelvin temperature scale and how it differs from the Celsius scale
    • 4-2 The Wave Nature of Light: spectrum, Newton's experiment with a prism, characteristics of wave motion, wavelength, frequency, hertz, relationship among wave speed, wavelength and frequency, light as a wave, nanometer, measuring the speed of light, how Galileo tried to measure it and how Roemer and Fizeau did measure it (see Lecture 9), evidence for the wave model of light, Young's double-slit experiment, constructive and destructive interference, why Newton rejected the wave theory, Maxwell's contribution, electromagnetic radiation, transverse waves, electric field, magnetic field
      Note: It was because of Maxwell's work that Einstein concluded that the speed of light is the same, regardless of the motion of the measurer and this led him to conclude that Newton's laws become increasingly inaccurate with increasing speed.
    • 4-3 The Electromagnetic Spectrum: different regions of the electromagnetic spectrum (gamma rays, X-rays, ultraviolet, visible, infrared and radio), how these regions are ranked in wavelength and frequency and which ones are blocked by the Earth's atmosphere
    • 4-4 The Colours of Planets and Stars: colour from reflection - the colours of planets, colour as a measure of temperature, thermal spectrum, Wien's law, blackbody radiation, continuous spectrum, Stefan-Boltzmann law
    • 4-5 Types of Spectra: Kirchhoff's laws and the three types of spectra that are produced: continuous spectrum, bright line spectrum, dark line spectrum
    • 4-6 The Bohr model of the atom: nucleus (of an atom), electron, photon, the three postulates of Bohr's model, energy states of an electron, ground state, how the Bohr model accounts for emission and absorption spectra, the Balmer, Lyman and Paschen series of hydrogen spectral lines, why the Lyman lines have shorter wavelengths and the Paschen lines have longer wavelengths than the Balmer lines, the photoelectric effect, the wave-particle duality of light
    • 4-7 The Doppler Effect: redshift, blueshift, radial velocity, tangential velocity, equation for calculating radial velocity from the Doppler shift, how the Doppler shift can provide evidence for the Earth's orbital motion around the Sun, other Doppler effect measurements, e.g. the rotation of the Sun and planets, relative or real speed?
    • 4-8 The Inverse Square Law of Radiation, Conclusion

    Other Relevant Information:

    • The Electromagnetic Force - is an electric or magnetic force. Any particle having an electric charge, such as an electron or proton in an atom, exerts an electromagnetic force on any other charged particle. (In the discussion of Bohr's first postulate, on page 115 of the textbook, it is noted that the negatively charged electrons are being attracted to the positively charged nucleus of an atom. This is the electromagnetic force.)
      Like gravity, the strength of the electromagnetic force decreases with distance according to an inverse-square law. Unlike gravity, electromagnetic forces can repel (between like charges) as well as attract (between opposite charges). Although this force can be effective over an infinite range, positive and negative charges tend to neutralize each other, greatly diminishing their net electromagnetic influence. Above the microscopic level, most objects are close to being electrically neutral.

    • The Strong Nuclear Force - is about 100 times stronger than the electromagnetic force. It binds together the protons and neutrons in the nucleus of an atom. Although it produces an extremely powerful bond, it is effective over only very small distances, i.e. within the nucleus of an atom.

    • In the section on "Einstein and Relativity", we discussed the the source of the Solar energy (section 11-2). Because of the electrical repulsion force between protons (hydrogen nuclei), the hydrogen fusion reaction can take place only at high temperatures. This is illustrated in figure 11-8. In the Sun's centre where the hydrogen fusion takes places, the temperature is about 15.7 million K and the density is 20 times the density of iron (section 11-3).
    • In the cores of more massive stars, the temperatures and densities can be even higher so that nuclear fusion of helium, carbon, and other heavier elements can occur. Table 15-2 on page 421 (5th ed.: 479) lists the nuclear reactions that occur in the core of a 15 solar mass star and one can see that the more protons there are in the nucleus of an atom, the higher the temperature required for the fusion to occur. There are a couple of errors on lines 4 and 5 of Table 15-2. Line 4 should indicate that oxygen can be fused to produce neon and magnesuim and line 5 should list neon as the element that is fused.

    • 11-1 Solar properties
    • 11-2 Solar energy. Fusion.
    • 11-2 Solar energy: luminosity, power, the source of the Sun's energy, solar nuclear reactions, proton, neutron, the "Bohr" atom, nuclear fusion, proton-proton chain, deuterium, positron, neutrino, fission and fusion power on Earth
    • 11-3 Solar interior: pressure, temperature and density. Hydrostatic equilibrium. Energy Transport. The Solar Neutrino problem.
    • 11-4 Helioseismology; solar neutrino experiments.
    • 11-5 The Solar Atmosphere. Limb darkening, sunspots, chromosphere, corona, solar wind. Interaction with Earth. Interaction of solar wind with interstellar medium.
    • 11-6 Sunspots and the solar activity cycle; Maunder minimum.
    • 11-6 Solar flares, mass ejections .

    • Notes about the solar wind, the Sun's activity cycle and interaction with Earth: There is controversy about the effect of cosmic rays on the Earth's climate. See this old news item. A nice explanation of the hypothesis and model is here , but the model may not predict temperatures correctly over a longer period of time (Svensmark and others claim that cosmic rays have been decreasing over recent decades, hence leading to global warming, contrary to the standard model which makes human-caused CO2 the green-house gas culprit). A big problem is that we don't know the strength of the effect of cosmic rays on global temperatures, despite a correlation being claimed.
    • A nice history of the discovery of the Maunder Minimum is here. This article (in 1998) by Beckman and Mahoney makes the point that `` should be aware of the political background to this delicate issue, and not fall into the trap of using possible solar warming as an excuse for delay in reducing man-made emissions of greenhouse gases. Whatever the magnitude of the effects of these in the long term, there is no doubt that their concentration has increased dramatically in the past 30 years, and that for many reasons this is not a desirable path to follow." There is also possible evidence that we may be entering a new Maunder Minimum in twenty years. If the cosmic ray model is correct, that would imply that the effects of human-caused greenhouse gas generation may be masked in coming decades, but when the future "Maunder Minimum" is over, all hell breaks loose ...

      Measuring Stellar Properties

      This section of the course is based on material about determining the distances of stars and galaxies. The material appears in several different chapters of the textbook.
      In the outline below, I indicate the material you should read and which of the terms that are highlighted in bold face or italics you should know.

      Chapter 12 - Measuring the Properties of Stars

    • 12-1 Stellar Luminosity: apparent magnitudes - the system of Hipparchus and the one we use today, [You should understand Table 12-1 and Figure 12-3.]
    • 12-2 Measuring Distances to Stars: parallax angle, parsec, absolute magnitude, luminosity, how the luminosity or absolute magnitude can be derived from the apparent magnitude and distance (no formula memorizing required - you should understand figures 12-6 and 7)
    • 12-3 Motions of stars: how tangential velocity is related to distance and proper motion, how space velocity is related to radial velocity and tangential velocity
    • 12-4 Spectral types: determining the spectral type of a star, how spectral type can be related to temperature (you should understand figure B12-1 on page 349 (5th ed. p. 404) and how it relates to Fig 12-14, lines in spectra), the contributions of Annie Cannon and Cecilia Payne-Gaposchkin; Hertzsprung-Russell (HR) diagram, the main sequence, white dwarfs, giants, supergiants and where they are located in the HR diagram
      spectroscopic parallax; luminosity classes; analyzing the spectroscopic parallax procedure; how the absolute magnitude of a star can be determined from its luminosity class and temperature and how the distance can be determined from apparent magnitude and absolute magnitude (see Fig 12-20 and recall Fig 12-6); luminosity and the sizes of stars, white dwarfs, giants and supergiants.

    • 12-5 Multiple star systems (visuasl binaries, spectroscopic and eclipsing binaries.
    • 12-6 Stellar masses and sizes from binary star observations.
    • 12-7 The mass-luminosity relation: mass-luminosity diagram, (note that the mass-luminosity relation is valid only for the MAIN SEQUENCE stars)

    • 12-8 Cepheid variables as distance indicators: light curve, period-luminosity diagram; Henrietta Leavitt's study of the Cepheids in the Small Magellanic Cloud (see notes here), the difference between Cepheid I and Cepheid II stars and RR Lyrae stars; Cepheid and RR Lyrae variables on the HR diagram (Fig 14-15 on page 402 in 6th ed., p. 459 in 5th)
    • The AAVSO Website has a fine article concerning the history of the discovery of variability in Delta Cephei.
    • Conclusion

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