Atoms and Stars ist 2420 and ist 1990



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Atoms and Stars IST 2420 and IST 1990

  • Class #7: October 19 and 24
  • Fall 2005 sections 001, 005, 010 and 981
  • Instructor: David Bowen
  • www.is.wayne.edu/drbowen/aasf05
  • 10/10: corrections on slide 9, 10 & 37

Tonight

  • Handouts
    • Class 7 Notes
    • Revised Lab 3 Part II
  • Initial the sign-in sheet
  • Review of names
  • Due:
    • Lab 8 Report
  • Review for Midterm, last hour tonight
  • Midterm next week, first hour in class

Disproving “nature abhors…”

  • The definitive experiment disproving Aristotle’s “nature abhors a vacuum” was getting a vacuum in a tube of Mercury taller than 30 inches – now there is a vacuum
    • Pascal reserved this honor for tube on a mountain
  • We did not disprove this here
    • Safety problems with Mercury

Life on Other Planets?

  • Life like us?
    • May be alternate forms, but we haven’t come up with any
  • Deep space empty, cold, dark.
    • Life would need self-contained energy, light, materials
  • Stars have energy, but temperatures are millions of degrees, much too hot

Life on Other Planets?

  • So focus on planets
  • In our solar system, no good candidates except Earth
    • Closer ones too hot

Life on Other Planets?

  • So focus on planets
  • In our solar system, no good candidates except Earth
    • Further ones too cold
    • Mars the best other possibility
      • Current search is for water on Mars
      • We may find microscopic life, or its remains
    • Moons too small to have atmospheres

Life on Other Planets?

  • Planets around other stars?
  • We are finding other stars with planets
    • Present techniques best for planets close to star
    • So far, too close to star, too hot
    • If planets around other stars are common, maybe there will be some planets with the right conditions, and maybe some of them will have life

Life on Other Planets?

  • Our other approach is to look for radio signals
    • SETI: Search for Extraterrestrial Intelligence
    • Distances mean powerful signals, imply a much more advanced civilization than ours
    • Long distances imply radio waves started long ago if they reach us now, would be even more advanced
  • Aliens visiting earth not supported in mainstream science

Solar System Examples

  • Heliocentric example (Sun, other planets and our Moon revolve around central Earth):
    • Example: Ptolemy
    • Earth actually not thought of as a planet
  • Geocentric (Moon revolves around Earth, Earth and other planets revolved around central Sun)
  • Geo
  • Helio

Why does sun rise and set?

  • Heliocentric:
    • Sun carried on a sphere, rotates around earth
  • Geocentric (more modern):
    • Earth rotates under sun
    • Night when we face away from sun
    • Noon when we face towards sun
    • Sunrise and sunset about halfway in between
  • Geo
  • Helio

Robert Boyle #1

  • In “The Development of the Concept of Atmospheric Pressure”:
    • Robert Boyle (1627 – 1691) in 1657 followed 1654 von Guericke, vacuum pump and Magdeburg spheres
    • Put Torricellian baromoter (column of Mercury) in a vacuum pump and pumped
    • Level of mercury column fell

Robert Boyle #2

  • (not in Readings) 1662 Boyle published what is now known as Boyle’s Law:
    • At a constant temperature, the volume of a gas is inversely proportional to its pressure
      • Gas is “springy” – today used in gas struts in cars to hold up hatches
    • Easier version: Pressure × Volume at one time = Pressure × Volume at other times (earlier and later), if temperature does not change

Boyle’s Law Examples #1

  • Mathematically: P1 × V1 = P2 × V2
  • Problem: given any three of P1, V1, P2, V2, find the fourth
  • Method:
    • Substitute given values into Boyle’s Law
    • Do multiplication of two on same side
    • Use division to get unknown by itself
    • Do division to yield answer

Boyle’s Law Examples #2

  • Example 1: A gas with pressure = 30” of Mercury and a volume of 20 cubic inches is expanded to 30 cubic inches at the same temperature. What is its new pressure?
    • P1 × V1 = P2 × V2 (insert numbers)
    • 30 × 20 = P2 × 30 (multiply out)
    • 600 = P2 × 30 (now divide by 30)
    • P2 = 600 / 30 = 20(“ of Mercury)

Boyle’s Law Examples #3

  • Example 2: A gas with pressure = 15” of Mercury and a volume of 200 cubic feet is compressed to a pressure of 30” of Mercury. What is its new volume?
    • P1 × V1 = P2 × V2 (insert numbers)

Boyle’s Law

  • Boyle’s Law is an example of “the new Physics”
  • Makes specific mathematical predictions
  • Exhibits mathematical regularities in nature
  • (Modern changes:
    • Correct when atoms in gas are far apart
    • Pressures higher than this when atoms close)

Review of Reading

  • “Copernicus Incites a Revolution”
  • Scientific Revolution ~ 1700 not just a change in content
  • 15th & 16th centuries – a broad background in exploration, technology (including Gutenberg and printing), arts, the occult, new religions

“Copernicus Incites a Revolution”

  • Europeans formerly knew Greeks from Arabic translations, translated again
    • Now, new direct translations
    • New sources, e.g. Archimedes
  • Italian Renaissance –art, poetry
    • Medicine – William Harvey and circulation of the blood
  • Also magic, occult or secret knowledge

“Copernicus Incites a Revolution”

  • Protestant Reformation
    • Challenge to Catholic church
    • 1517 Luther’s Ninety-Five Theses nailed to door of cathedral in Wittenberg, to end of Thirty Years’ (religious) War in 1648
  • Calendar reform: problem of Julian calendar (364 days plus leap years) – errors of ten minutes/year accumulated to 10 days

Copernicus

  • Retrograde motion a problem for geocentrism
  • Copernicus 1473 – 1543
  • Current astronomical model of solar system was Ptolemaic (Ptolemy), geocentric (“geo” = earth), Aristotelian
    • Very cumbersome (slide 34 from Class 3 next)

Slide 34 from Class 3

  • Hellenistic Period (after 323 BC)
    • Ptolemy (2nd cent AD) used new tools to simplify geocentric model of heavens
      • Epicycle (small sphere moved on larger sphere, planet on small sphere)
      • Eccentrics (circle displaced from earth)
      • Equant – point from which planet appeared to move at constant speed
      • Almagest – manual of Astronomy

Copernicus

  • 1514 privately circulated idea of heliocentrism (“helio” = sun)
  • 1543 full theory just before death in De revolutionibus orbium coelestium (Concerning the revolutions of the heavenly spheres)
  • His intent was to preserve Greek ideas of perfection and circular motion

Copernicus

  • Retrograde motion was natural in heliocentrism – relative motion of planets
  • Earth rotated on axis once per day, circled sun once per year
  • But earth carried on solid crystalline sphere, axis would move with it, so he introduced a third motion to keep axis pointed towards north star

Copernicus

  • Objects fall to center of earth, not center of universe
  • We do not spin off of earth because we share its motion
  • No equants but epicycles and eccentrics

Copernicus

  • Objections
    • Not a big simplification over Ptolemey
    • Said stars far away, to explain lack of observed parallax of stars: unsatisfactory
    • Falling bodies have no observed falling behind as earth turns under them
    • Religious objections surfaced after Galileo
  • 1582 led to Gregorian calendar – no leap years for centuries unless divisible by 4

Tycho Brahe

  • 1546 – 1601 Tycho Brahe
  • Danish nobleman and astronomer
  • Built great observatories on his island
  • Fights, duels, possibly died from being drunk, but also careful astronomical measurements
  • Convinced astronomy needed good measurements

Tycho Brahe

  • Naked-eye instruments shielded from wind, kept temperature stable, studied and corrected for errors including atmosphere
  • Accurate to 5 – 10 seconds of arc, sometimes, never worse than 4 minutes
  • Also systematic, over years

Tycho Brahe

  • November 11, 1572: saw extremely bright new object, parallax measurements showed it to be outside of solar system. Lasted for three months.
    • Heavens not unchanging
  • Comet of 1577, parallax measurements showed comet cut through crystalline spheres. They were not real.

Tycho Brahe

  • Rejected Copernicus because no observed stellar parallax
  • Also rejected rotation of earth because cannon fired west should travel further
  • Tycho’s system: geocentric but sun revolves around earth, other planets rotate around sun
    • Simpler, accurate, no spheres

Johannes Kepler

  • 1571 – 1630 Johannes Kepler
  • Obsessed with numerology, mysticism, astrology
  • At first convinced planets fell in orbits determined by five regular solids
  • During counter-Reformation, refused Catholicism, became Brahe’s assistant

Johannes Kepler

  • Assigned eccentric orbit of Mars
  • Six-year heroic effort, errors on top of errors, restarting, blind alleys
  • Achieved accuracy within 8 minutes of arc, but Brahe’s observations good to 4
  • Became convinced Mars traveled in ellipse, not circle

Johannes Kepler

  • Three laws of planetary motion
    • First two 1609 Astronomia Nova (New Astronomy), third buried in Harmonice mundi (Harmonies of the world) 1619
      • Planetary orbits are ellipses with sun at one focus
      • Equal areas in equal times
      • t2 r3 (period squared proportional to radius cubed)
    • Unsatisfactory explanations for these laws
    • Not well received, rejected for the most part

Ellipse

  • Eccentricity (e) – how much different than a circle?
    • e = 0, perfect circle
    • Circle more flattened as e larger than 1
  • e = 0.1

Ellipse

  • Focus
    • A + B = same for each point on ellipse
    • Circle: the two focii coincide, distance is radius
  • e = 0.1
  • Each ellipse has two focii (one is a focus)
  • A
  • B

“The Planet Mars and Kepler’s Three Laws of Planetary Motion”

  • “My Very Excellent Mother Just Sent Us Nine Pizzas” – planets and their order out from the sun
  • Mars a special case for Kepler, for mankind too – life on Mars?
  • Illusory “canals” on Mars, “War of the Worlds”
  • Recent indications of water, “Mars Express” (next slide). Life there?
  • A dust-covered frozen sea?

“The Planet Mars and Kepler’s Three Laws of Planetary Motion”

  • Mars (and other planets) get brighter and dimmer
    • In heliocentric theory, hard to explain this
    • Natural in geocentric – closer and further to us
  • Kepler’s three laws:
    • Planetary orbits are ellipses, sun at one focus
    • Planet sweeps out equal areas in equal times
    • T2  R3 ( means “is proportional to”)
      • Period T (length of year), mean radius R
  • helio
  • geo

A Common Sequence

  • Brahe  Kepler  Newton
  • Accurate measurements  “empirical” theory (little explanatory power, descriptive only)  explanatory theory
  • A Common Sequence
  • Reader says Physics has no explanation for gravity
    • Modern Physics does have explanations

“The Watershed”

  • Arthur Koestler, from The Watershed (1959) biography of Johannes Kepler
  • As noted in Introduction, an unvarnished view of how science comes into being, from Kepler’s own writings

The Watershed

  • Chapter 1: “The Young Kepler”
  • K always precise (time of own conception)
  • Born 1571 in Weil, Germany, still a hero
  • Grandfather was the mayor, but family in decline
    • Age 26, K described them as bad or dead
  • Father and mother ran off, father exiled

The Watershed

  • Mother not much better
  • Six siblings, three lived, two normal, brother Heinrich sickly, fired, died at home
  • K himself put out to work, delayed in school, sickly, accidents
  • Saw comet 1577, moon’s eclipse at nine yrs
  • Excellent educational system, clerical track

The Watershed

  • Miserable and lonely in school, quarrels
  • Extreme self-criticism at 26, but productive
  • Often defended Copernicus, “first motion”
  • Became “mathematicus” at Gratz before graduation
  • In teaching, always off in new directions
  • Lucky astrological table made him popular
    • Love-hate relationship with astrology

The Watershed

  • Chapter 2: The “Cosmic Mystery”
  • 1595 in class felt orbits of planets determined by geometrical shapes – five regular solids
    • False, but motivated him throughout life
  • Pp 91& 182: pictures of Brahe’s instruments and observatories

The Watershed

  • Chapter 3: Tycho and Kepler
  • Brahe old, needed Kepler to make sense of observations
  • Kepler’s draft of a contract with Brahe
    • Stormy relationship, leaving and returning, Brahe magnanimous, Kepler mean-spirited
    • Kepler could be forced back to Styria where Protestants were being persecuted

The Watershed

  • Kepler had to drag data out of Brahe
  • Exiled as Protestant from Gratz, returned to Brahe
  • 1601 Brahe died, wanting Kepler to prove Brahe’s model of solar system
  • Emperor appointed Kepler as his successor “imperial mathematicus”

Assignments 2420

  • Next week:
    • Midterm (first hour)
      • No assignment in Reader – prepare for Midterm
    • Lab
      • Experiment 3 Part II (new handout tonight)
      • Experiment 8 Part II

Moodlers (POL & 1990)

  • See “SUCCESS” on course web site
  • 2420 POL
  • Summaries
  • Average two postings per week
    • Try answering the Exam questions!!!
      • Get me on record in writing
      • Rehearsal – the best way to study

IST 1990

  • Essay 1 due on Moodle (see “19 October - 25 October” , “Science and Religion: Essay 1”)
  • Reading – see Syllabus
  • On the course web site:
    • Essay topics for all three essays
    • Notes on IST 1990 books
  • Postings every week
    • Two credits: average one per week
    • Four credits: average two per week
  • Four credit: extra readings online: PW = “apple”

Review for Midterm




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