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:
- 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? 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)
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
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.
- 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
Ellipse - Focus
- A + B = same for each point on ellipse
- Circle: the two focii coincide, distance is radius
- Each ellipse has two focii (one is a focus)
“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
- Brahe Kepler Newton
- Accurate measurements “empirical” theory (little explanatory power, descriptive only) explanatory theory
- 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
- 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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