GST 2420: Atoms and Stars:
An Historical Introduction to Astronomy, Physics, and Scientific Discovery.
Fall 2002, Section 983, Call Number 16050
Agenda 7 for 10/16

  1. Announcements:
    1. Due: Report on Experiment VIII. Midterm is next week, October 23. Report on tonight's Experiment IXa is due in two weeks on 10/30.
    2. Course web site: http://www.cll.wayne.edu/isp/drbowen/aasf02 (also links from Pipeline).
    3. Online Life at WSU updated and with live links at http://www.cll.wayne.edu/isp/drbowen/OnlineLife
  2. Science in the news
    1. According to an article in The New York Times ("Stung by Courts, F.D.A. Rethinks Its Rules," 10/15/02 Pg D1, Science section), the Food and Drug Administration is reconsidering its approach to regulation. The agency has lost several court cases in which it was attacked for violating the free speech rights of manufacturers of drugs, supplements, cosmetics and foods. In the most recent such case, in which druggists sued for the right to mix and advertise their own drugs, without going through the F.D.A approval process, the U.S. Supreme Court said, "We have previously rejected the notion that the government has an interest in preventing the dissemination of truthful commercial information in order to prevent members of the public from making bad decisions with that information." Notice that this does not protect untruthful information. A specific example is that dietary calcium is associated with lower blood pressure, but since the F.D.A. says that the association has not been proven so that the claim cannot be made in advertising. Dr. Rhona Applebaum, an official of the National Food Processors Association is quoted as saying, "You could say, 'While inconclusive, new research seems to indicate...'" The F.D.A. is also being criticized for even considering relaxing its present standards.
  3. Syllogism: two or more premises and conclusion
  4. Experiment 3: Inclined planes and falling objects. Please staple!
    1. Class results
      1. Except for the cork balls, most groups found that the times for different weights were very similar, especially considering the variations in the times for single trials. (Taking the average reduces error, but does not eliminate it.) However, many people ignored this evidence and said that heavier objects fell faster.
      2. In the time for falling objects, most groups found that times were similar for the shorter distances. (For longer distances, often the objects were launched upwards, unavoidably.)
      3. These results (times the same for objects of different weights, falling times independent of horizontal motion) are in line with Galileo's results, and with modern results.
    2. Why this was an important experiment
      1. One of the first deliberate experiments.
      2. Results were that times were independent of mass - gave rise to the idea of a "gravitational field"  or influence that acted on all bodies equally.
      3. Results that distances were proportional to t2 led to constant acceleration, v = at, by the following reasoning:

        The distance moved during the very short time interval dt is ds = v × dt. Adding up the total distance, it would be equal to the area under the v = a × t line, but at time t this is a triangle with base b = t and height h = v = a × t and the area of a triangle is ½bh or ½at2, the result that Galileo had gotten. Constant acceleration gave further credence to the idea of a constant gravitational field that acted on all bodies equally.
      4. Since the marks are placed at square distances (1, 4, 9, 16), the times should increase as 1, 2, 3, 4. To show how well or poorly this works, divide the time to E16 by 4, the time to D9 by 3, the time to C4 by 2 and the time to B1 by 1. If the theory is correct, all of the divided times should be equal. Using the data from the Dekutosk i /Frye / McRoy / Sullivan / Walworth group,
        time to B1 time to C4 / 2 time to D9 / 4 time to E16 / 4
        0.50 0.675 0.67 0.75
        Not exact, but not bad, considering how different the distances were.
  5. Readings: Nicholas Copernicus (1473 - 1543), Tycho Brahe (1546 - 1601) and Johannes Kepler (1571 - 1630)
    1. Science always takes place in a social context. Here, the context was increasing prosperity (so that one could earn a living as a scientist), increasing individuality, and an active publishing industry, with publishers often serving as intellectual hubs.
    2. Copernicus asserted heliocentric model to simplify the standard geocentric model with interlocking spheres. However, it did not turn out to be that much simpler! But many well-known phenomena had simple explanations, for example the 24-hour rotation of the sky, and the fact that Mercury and Venus stayed close to the sun.
    3. Brahe was an observational astronomer. That is, he is best known for his naked-eye (but assisted) measurements, good to between 1 and 8 minutes of arc (60 minutes in a degree, thanks to the Babylonians). He measured the positions of the sun, moon and planets for decades, and also the positions of over 700 fixed stars. In 1571 he observed a Nova, and he also showed that the comet of 1577 would have pierced the spheres supposed to hold the planets in position.
    4. Kepler is known for his models that summarized Brahe's observations - his three laws. Finding these laws, which he apparently did not think were very important, took him years of mathematical and geometrical calculations, with many errors and blind alleys. His relationship with Brahe is also bizarre; Brahe essentially sponsored and hired Kepler, expressly to find a model using Brahe's data, but was very reluctant to actually share the data with Kepler. In working with Brahe's data, Kepler made several departures from accepted astronomy; he adopted a heliocentric model, and abandoned the idea of spheres for ellipses. He also completely trusted Brahe's measurements, abandoning his theories at one point when they disagreed by 8 seconds of arc, where Brahe claimed an accuracy of 4 seconds of arc. Kepler's three laws:
      1. Planets move in ellipses, with the sun at one focus. (An ellipse is a kind of flattened circle, with the single center split into to foci. Light from one focus will be focused at the second focus, and vice versa.)
      2. Planetary orbits sweep out equal areas in equal times, as measured from the sun
      3. For a planet, the period t and orbital radius r are related by t2 ~ r3. Planets  For example, if two planets are in orbits with the second 8 times larger than the first, the period of the one with the larger orbit will be 4 times the period of the one with the smaller orbit (cube root of 8 is 2, then square the 2 to get 4).
    5. Biography of Kepler related to his achievements. Kepler was in poor health for much of his life, had few close friends, and seemingly with reason. He was used to persevering in poor circumstances - "soldiering on." Thus he may have been prepared by this earlier life to persevere throughout his later life in working on Brahe's data for Mars.
  6. Review of midterm questions, continued
  7. Video - The Expanding Universe, Part I
  8. Lab IXa. Lab Manual, Pages 42 - 53 (stop at "The Ellipse").