PART A CHAPTER 3

• How do we know

  The methods and principles used to determine various astronomical measurements and properties
• Introductory Astronomy, Chapter 3
• What we can know

  • The distance of the Sun
  • The distances of planets
  • The distances of stars and galaxies
  • That the Earth spins
  • That the Earth orbits around the Sun
  • The mass of the Sun
  • The mass of our Galaxy
  • The size and structure of the Galaxy

  
• Measuring distances in astronomy


  The methods and principles used to determine astronomical distances and sizes

  
• Measurements/Principles used


  • Pythagoras (Earth is a sphere)
  • Eratosthenes (Earth diameter)
  • Aristarchus (Lunar parallax, lunar month)
  • Copernicus (Mapping of the Solar System)
  • Cassini & Richer (Parallax of Mars)
  • Halley, Cook (Transit of Venus)
  • Bessel, Struve, Henderson (Stellar parallaxes)
  • Hertzsprung & Russell (H-R Diagram)
  • Leavitt (Cepheids)
  • Hubble (Hubble's Law, Supernovae as standard candles)
• Pythagoras


  570 - 495 BC
• Eratosthenes


  276 - 194 BC
• Aristarchus of Samos


  310 - 230 BC
• Nicolas Copernicus


  1543
• G. Cassini & J. Richer


  1672
• E. Halley, James Cook


  1716, then 1769
• Friedrich Bessel, Struve, Thomas Henderson


  1832-36
• Hertzsprung & Russell


  1910
• Henrietta Leavitt


  1908
• Edwin Hubble


  1929
• Supernovae as standard candles

  1990s
• Aristarchus of Samos


  • Considered the Moon at 1st and Last Quarter phases, noticed it is not at right angles to the Sun in the sky
  • Tried to measure the Sun-Earth-Moon angle at 1st Quarter but found it impossible with available instruments
  • Detected an average time difference of about an hour in the two halves of the lunar month

  
• Lunar eclipse


  The black strip is the Earth's shadow on the Moon

  
• It was probably known before Aristarchus's measurements that the Earth is bigger than the Moon by the factor 4-5

  
• The Earth's shadow on the Moon observed during lunar eclipses had diameter 4-5 times bigger than the Moon

  
• Aristarchus's measurements (in diameters of the Earth)

  • Moon's Distance: 10
  • Moon's Diameter: 0.33
  • Sun's Distance: 200
  • Sun's Diameter: 7

  
• Modern measurements (in diameters of the Earth)

  • Moon's Distance: 30
  • Moon's Diameter: 0.272
  • Sun's Distance: 11,700
  • Sun's Diameter: 109

  
• tan(0.5 deg) ≈ 1/100, where 0.5° is the angular size of the Moon and the Sun on the sky

  
• Angular measurement


  The ratio of the distance to the radius of an object can be determined from the angle measured
• The angular diameter of the Moon is 0.5 degrees, same as the Sun. Just a coincidence?

  
• Aristarchus's reasoning


  • The Moon is 4-5 times smaller than the Earth and orbits it
  • The Earth is 4-5 times smaller than the Sun, so it should orbit the Sun, not vice versa
  • The Sun is the biggest, therefore it occupies the central position in the Universe

  
• Eratosthenes


  • Noticed the Sun shone directly down a well in Syene on the first day of summer, while in Alexandria it was 7.2° south of the zenith
  • Believed the Earth was spherical and the Sun's rays were parallel
  • Calculated the Earth's circumference and diameter based on the 7.2° difference and the distance between Syene and Alexandria

  
• Parallax


  The phenomenon by which a nearby object appears to shift its position against remote background objects when the observer changes position
• Ptolemy's method for finding the distance to the Moon

  • Two observers simultaneously observe the Moon against the starry background from positions 10,000 km apart, and measure the Moon's position shift of 1.4°
  • The Earth-Moon distance can then be calculated using trigonometry

  
• Copernicus's work


  • Calculated and tabulated the distances of the planets from the Sun in terms of the Earth-Sun distance (AU)
  • Proposed the heliocentric system, in contrast to the geocentric system

  
• Aristotle was a Greek philosopher, a student of Plato and teacher of Alexander the Great
• sin (0.7°)


  5000 km / X
• 0.0125


  5000 km / X
• X


  5000 km / 0.0125 = 400,000 km
• Distances


  • 5000 km
  • X
  • Earth
  • Moon

  
• In actual practice, two simultaneous observations are not necessary. The rotation of the Earth during the night will carry a single observer from one point to the other. During this time, however, the Moon will have moved a short distance in its orbit. This motion must be subtracted before the true parallax can be determined.

  
• Helio-centric system


  Copernicus calculated and tabulated the distances of the planets from the Sun in terms of the Earth-Sun distance (AU)

  
• Geo-centric system


  Ptolemaic model of the universe
• Claudius Ptolemy was a Greek astronomer who formulated a geocentric model of the universe
• Nicolaus Copernicus formulated a heliocentric model of the universe, which placed the Sun, rather than the Earth, at the center