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
- Announcements:
- 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.
- Course web site: http://www.cll.wayne.edu/isp/drbowen/aasf02
(also links from Pipeline).
- Online Life at WSU updated and with live links at http://www.cll.wayne.edu/isp/drbowen/OnlineLife
- Science in the news
- 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.
- Syllogism: two or more premises and conclusion
- Experiment 3: Inclined planes and falling objects. Please staple!
- Class results
- 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.
- 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.)
- 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.
- Why this was an important experiment
- One of the first deliberate experiments.
- 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.
- 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.
- 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.
- Readings: Nicholas Copernicus (1473 - 1543), Tycho Brahe (1546 - 1601) and
Johannes Kepler (1571 - 1630)
- 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.
- 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.
- 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.
- 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:
- 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.)
- Planetary orbits sweep out equal areas in equal times, as measured
from the sun
- 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).
- 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.
- Review of midterm questions, continued
- Video - The Expanding
Universe, Part I
- Lab IXa. Lab Manual, Pages 42 - 53 (stop at "The Ellipse").