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SMAS
Southwest Montana Astronomical Society

Measuring the Universe

A lecture series and work group conducted by our former club president and current Star Wrangler editor Fred Birk is ongoing at this time. The subject is "Measuring the Universe. Part I - The Solar System". Prerequisites are high school mathematics and elementary physics.

Part I. The Solar System. Distances, Sizes, and Masses.

Appendix

Outline

  1. Earth diameter.
    1. Method of Eratosthenes (276-195 B.C.E.)
    2. How we would apply the method today?
  2. Aristarchus (265 B.C.E.). Earth/Moon to Earth/Sun distance ratio.
  3. Distance to the moon
    1. Method of Hipparchus (~150 B.C.E.)
    2. Parallax measurement from two Earth locations
    3. Apparent Moon diameter change with altitude (group exercise: allow for orbit eccentricity)
    4. (Method of parallactic libration, optional)
    5. (Occultation of stars by the moon, optional))
  4. Planetary Distances, sizes, and masses in the solar system
    1. Relative distances in the solar system
      1. Inferior planets (Mercury, Venus)
      2. Relation between synodic and sidereal period
      3. Superior planets (Mars, Jupiter, ...)
    2. Kepler’s third law
    3. Comparing the relative distance method with Kepler’s 3rd Law
    4. Derivation of Newton’s universal law of gravitation (1667)
    5. Newton's general form of Kepler's 3rd Law
    6. Mars parallax and the a.u. (1673 Cassini et. al)
    7. Absolute scale of the solar system
    8. Sizes of the sun and the planets
    9. Relative masses of the planets in the solar system
    10. Universal constant of gravitation measured by Cavendish (1798)
    11. Absolute masses of the Sun and the planets
  5. Refinements
    1. Venus transit and the astronomical unit A.U., (Halley's method applied in 1761/1769)
    2. A.U. from stellar spectral line shift (Doppler) due to earth orbital velocity
    3. A.U. from aberration of starlight due to earth orbital movement
    4. A.U. from method of radar and laser reflection
  6. Miscellaneous selected Fun Applications - Group Work
    1. The Astronomical Unit, key to stellar distances
    2. Moon mass
    3. Luminosity of the sun
    4. Mountains on the moon elevations
    5. Escape velocity and planetary atmospheric retention
    6. More results. Group discussion

Updated 2008-02-03