Atoms and Stars ist 2420



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Atoms and Stars IST 2420

  • Class 5, February 11
  • Winter 2008
  • Instructor: David Bowen
  • Course web site: www.is.wayne.edu/drbowen/aasw08

Handouts & Announcements

  • 2/11/07
  • Atoms and Stars, Class 5
  • Class 5 Notes
  • Initial the sign in sheet
  • Due tonight
  • Essay 1, on a 3½” diskette
  • Report for Lab 3 Part 1A

Lab Tonight

  • 2/11/07
  • Atoms and Stars, Class 5
  • Lab 3, Part 1, parts after A
  • We are no longer following the lab schedule in the Syllabus
  • We will follow that, behind.

Online Grade Reports (repeat)

  • 2/11/07
  • Atoms and Stars, Class 5
  • See your line in my grade book
  • Disabled by default – turn in form if you want this (you should want this)
    • Check to enable and write a password
  • Demo
  • Later
    • Will have averages, projected grade
    • How to make up each assignment
  • www.is.wayne.edu/drbowen/aasw08

EAA Grades (repeat):

  • 2/11/07
  • Atoms and Stars, Class 5
  • -H: deficient in homework
  • -L: deficient in lab work
  • -E: deficient in exams and/or quizzes
  • -T: deficient in attendance
  • Can be doubled up, e.g. –LT
  • ---: three or more problems
  • These are the online grades, but they get spelled out in letter (email?)

Lab Reports:

  • 2/11/07
  • Atoms and Stars, Class 5
  • Data Sheet (original only)
    • At the top: your name and the Experiment / Lab #
    • “Setting” section: date of lab session, full names of lab group members, title of lab
    • Section 1 (repeat for each section):
      • Procedure: what you did
      • Observation or measurement: what you say or measured after the Procedure
      • Hypothesis (if present): why that happened
  • Analysis: typed answers to all other questions not answered on the Data Sheet

In the News…

  • 2/11/07
  • Atoms and Stars, Class 5
  • Science may not have answers when needed
    • Autism Spectrum (inability to form relationships)
    • Rate of diagnosis has increased, but why?
    • Treatment of mild cases is recently successful

Comments on Lab 2

  • 2/11/07
  • Atoms and Stars, Class 5
  • Block and can do not weigh the same. Aristotle said that if the can weighed twice as much, it should fall twice as fast. So, for Aristotle, difference here was important.
  • In a vacuum, a hammer and a feather fall at the same rate, and hit the ground together. This experiment has been done.

(Skipped on 2/4) Reading (Euclid’s Elements)

  • 2/11/07
  • Atoms and Stars, Class 5
  • Propositions: proven
  • Proposition 13: A straight line consists of two right angles (180º): CBE + EBD = 180º
  • Next, Proposition 15.

Reading (Euclid’s Elements)

  • 2/11/07
  • Atoms and Stars, Class 5
  • Proposition 15: If two straight lines cut each other, the vertical angles are equal (i.e. AEC = DEB)
  • Proof on next slide, relies upon earlier Postulate #4, Common Notions #1 & #3, and Proposition #13.

Reading (Euclid’s Elements)

  • 2/11/07
  • Atoms and Stars, Class 5
  • AEC + CEB = 180º Q10 (AEB is a straight line)
  • DEB + CEB = 180º (DEC is a straight line)
  • AEC + CEB = DEB + CEB (Things equal to the same thing are equal)
  • AEC = DEB (subtract CEB from each, equals subtracted from equals are equal)

Reading (Euclid’s Elements)

  • 2/11/07
  • Atoms and Stars, Class 5
  • Proposition 47: Pythagorean Theorem
  • For a right triangle (has one right angle), a2 + b2 = c2
    • Example: 3, 4, 5 triangle, 32 + 42 = 9 + 16 = 25 52 = 25, so 32 + 42 = 52
  • Formula known to Egyptians, maybe earlier, but proven by Pythagoras

Reading (Euclid’s Elements)

  • 2/11/07
  • Atoms and Stars, Class 5
  • Mathematics
    • start with assumptions
    • draw unarguable conclusions from assumptions
    • assumptions can be wrong – spherical geometry
      • on a sphere, angles of a triangle add up to less than 360º
  • Physical science can be put on this basis (axiomatic)
    • Assumptions and results can be overturned with new experiments

(Skipped 2/5) Some Greek Science (cont’d)

  • 2/11/07
  • Atoms and Stars, Class 5
  • Aristotle (cont’d):
    • Celestial physics: heavens are perfect
      • Smooth, spherical, flawless
      • Natural state: moving in a circle with constant speed
      • Earth at center (geocentric)
    • Elements – not made up of other matter
      • Earth, water, air, fire – from center of earth out
      • “Element”: these are not made up of anything else, everything else is made up of these. Elements do not have parts, cannot be subdivided or split
  • Science changed Aristotle’s ideas!

Readings: “Motions in the Solar System”

  • 2/11/07
  • Atoms and Stars, Class 5
  • Motions in sky known to all civilizations
  • Constellation: groups of stars, pattern invariant over human lifetime
    • 88 total constellations, Zodiac is 12 of these
  • Angular measurement
    • Degrees: 360° = circle (horizon), 90º horizon to pole. Fist at arm’s length ~ 10°, finger ~ 1º
    • Minute ('): 60' = 1°
    • Second ("): 60" = 1'

“Motions in the Solar System”

  • 2/11/07
  • Atoms and Stars, Class 5
  • Stars circle around pole (Pg 97)
    • All rotate together (seemingly) as if on a sphere
    • (Really, earth is turning underneath stars)
    • 360º in 24 hrs = 15º/hr
  • Also move annually relative to sun
  • Five visible planets Mercury, Venus, Mars, Jupiter, Saturn move with respect to stars

“Motions in the Solar System”

  • 2/11/07
  • Atoms and Stars, Class 5
  • Planets move through stars west to east like sun and moon, but periodically reverse or retrograde motion
    • Mercury, Venus stay close to sun (morning & evening stars)
      • Retrograde when close to but farthest east of sun, reappear west of sun
    • Mars, Jupiter, Saturn roam with respect to sun
      • Retrograde when opposite sun

“Motions in the Solar System”

  • 2/11/07
  • Atoms and Stars, Class 5
  • Sun
    • Highest in sky at Summer Solstice (~June 21, most daylight)
    • Lowest at Winter Solstice (~December 21, longest night)
    • In between Spring and Vernal (Fall) Equinoxes – equal day and night
    • Reversed in Southern Hemisphere
    • Also moves east with respect to stars

“Motions in the Solar System”

  • 2/11/07
  • Atoms and Stars, Class 5
  • Sun
    • As sun moves through stars, traces plane called “ecliptic”
    • Moves through 12 constellations of Zodiac

“Motions in the Solar System”

  • 2/11/07
  • Atoms and Stars, Class 5
  • Moon
    • Rises in east, sets in west like sun
    • Also moves to the east with respect to stars
    • New moon – moon between earth and sun
    • Full moon – earth between sun and moon
  • Eclipses
    • Moon eclipses sun, orbit tilted so rare
    • Lunar eclipse when earth’s shadow hides full moon

Retrograde Motion #1

  • 2/11/07
  • Atoms and Stars, Class 5
  • Retrograde: moving or directed backwards
    • Backwards motions of planets – a problem for Aristotelian astronomy.
      • Celestial (heavenly) domain is perfect
      • Perfectly circular motion, but retrograde motion didn’t fit in
      • Normally counter-clockwise from above north pole
      • All planets exhibited this sometimes
      • Plato’s theory had extra spheres and features to handle retrograde motion

Retrograde Motion #2

  • 2/11/07
  • Atoms and Stars, Class 5
  • Retrograde: moving or directed backwards
    • “Fixed” stars – most celestial objects (stars) rotate together, today called fixed
      • Now we see they really do move, just very slowly
    • Planet: Greek for “wanderer” – wandered among fixed stars
    • Motion actually very regular
    • Wander through astrological constellations

Retrograde Motion #3

  • 2/11/07
  • Atoms and Stars, Class 5
  • Objects and orbits in solar system close to the same plane
    • Also close to the plane of our galaxy
    • Milky Way is looking out into the plane of our galaxy – we are in it so we see Milky Way 360º
  • Computer demo: Retrograde Motion
    • Click “Model,” stop at “COPERNICUS”
    • Click on “Months,”
    • See “Notes” at bottom of screen to explain what you see
    • Top strip is view from earth to object (e.g. Sun)
      • Imagine strip wrapped around in back of your head
      • Background is astrological constellations (e.g. Pisces)
    • Right-to-left normal, reverse/pause is retrograde

New “planets”

  • 2/11/07
  • Atoms and Stars, Class 5
  • Pluto discovered 1930, orbit radius ~30 AU
  • Quaoar discovered 2002, ~1/8 size of Pluto
    • 42 AU from sun (42 × radius of earth’s orbit)
      • Radius of earth’s orbit = 93 million miles
  • 2003 VB12 (“Sedna”) ~ size of Pluto
    • Orbit radius ~ 39 AU
  • 2004 DW ~½ size of Pluto
    • Orbit radius ~45 AU
  • 2005 “Xena” with moon “Gabrielle”
    • ~ 20% larger than Pluto, 39 to 97 AU (very flattened)
    • Plane ~ 43° to ecliptic

New “planets” (cont’d)

  • 2/11/07
  • Atoms and Stars, Class 5
  • Pluto discovered 1930, orbit radius ~30 AU
  • Five new candidate planets since 2002 (see next slide)
  • Definition of a planet is in dispute. Also casts doubt on whether or not Pluto is a planet
  • Newest (Xena) may have the best claim – size, moon
  • These are in or near the “Kuiper Belt” (asteroids)

New “planets” (cont’d)

  • 2/11/07
  • Atoms and Stars, Class 5
  • Neptune outermost “real” planet
  • “Reals” formed from dust cloud, forced orbits to circular
  • Term “planet” may be abandoned

New “planets” (cont’d)

  • 2/11/07
  • Atoms and Stars, Class 5
  • “Classification” - what is a planet?
    • Follows “description” in development of science
    • What are the real differences?
    • Interesting to see it going on here

What are these things? (modern)

  • 2/11/07
  • Atoms and Stars, Class 5
  • Star – source of light (gravity has crushed atoms to start nuclear reactions)
  • Planet – large, opaque, nonluminous, circles a star (Pluto is on the smallish side)
  • Moon – a natural satellite of a planet
  • Asteroid – Small planet, size from 1 km (.6 mi) to 1,000 km (620 mi)
  • Comet – Few km, frozen ice & rock, elongated orbit, vaporizes when near sun, makes tail

“In Between” Greece and Europe…

  • 2/11/07
  • Atoms and Stars, Class 5
  • Why “In Between” in quotes? Earlier view: these civilizations merely caretakers, conduits for Greek civilization, Now viewed more for themselves.
  • First period: Eastern Roman Empire, Persia, Byzantine Empire & Barbarians
    • Western Roman Empire fell first
  • Then: Islamic empire

Locations

  • 2/11/07
  • Atoms and Stars, Class 5
  • Byzantine Emp.
  • “Barbarians”
  • Persian Empire
  • Islamic Empire

In between…

  • 2/11/07
  • Atoms and Stars, Class 5
  • Barbarians
    • Had their own technology e.g. textiles
    • Brought Chinese technology further west
  • Byzantine
    • Inherited Greek culture
    • John Philoponos questioned Aristotle
      • Spear-throwing – said thrower imparted power to spear to move itself

In between (cont’d)

  • 2/11/07
  • Atoms and Stars, Class 5
  • Persian
    • Cultural center Jundishapur (NE today’s Basra)
    • Translated most Greek writing
    • Hospital and medical school
    • Astronomy and astrology
    • Also developed Greek science

In between (cont’d)

  • 2/11/07
  • Atoms and Stars, Class 5
  • Islamic Empire
    • Mohammad 632 A.D.
    • After 642, started conquering the area in Northern Africa to Spain and Portugal, in East towards China
    • Medicine, astronomy, astrology
      • Needed to know where Mecca was for praying
    • Agricultural science, irrigation
    • Largest cities in the world (Baghdad)

In between (cont’d)

  • 2/11/07
  • Atoms and Stars, Class 5
  • Islamic Empire (cont’d)
    • Respected other traditions, treated them well
    • Principal heir to Greek science
    • Medicine, astronomy, math and geometry
      • Arabic numerals from India
    • Sometime after 1,000 A.D., peak and decline
      • Became fixated on Koran and past?
      • Success led to homogenization?

In between (cont’d)

  • 2/11/07
  • Atoms and Stars, Class 5
  • Islamic Empire (cont’d)
    • Enormous libraries, many works only in original manuscript today
    • Well-known scientists, court appointments (here I use their Western names)
      • Averroes (1126-1198) – Physician, “The Commentator” (Aristotle)
      • Avicenna (980 – 1037) – earned living as physician to pursue philosophy and science
      • Moses Maimonides (1135 – 1204) – Physician to King of Egypt
  • ..

“Copernicus Incites a Revolution”

  • 2/11/07
  • Atoms and Stars, Class 5
  • 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

  • 2/11/07
  • Atoms and Stars, Class 5
  • 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 36 from Class 3

  • 2/11/07
  • Atoms and Stars, Class 5
  • 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

  • 2/11/07
  • Atoms and Stars, Class 5
  • 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

  • 2/11/07
  • Atoms and Stars, Class 5
  • 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

  • 2/11/07
  • Atoms and Stars, Class 5
  • 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

  • 2/11/07
  • Atoms and Stars, Class 5
  • 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

  • 2/11/07
  • Atoms and Stars, Class 5
  • 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

  • 2/11/07
  • Atoms and Stars, Class 5
  • 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

  • 2/11/07
  • Atoms and Stars, Class 5
  • 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

Johannes Kepler

  • 2/11/07
  • Atoms and Stars, Class 5
  • 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

  • 2/11/07
  • Atoms and Stars, Class 5
  • 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

  • 2/11/07
  • Atoms and Stars, Class 5
  • 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

  • 2/11/07
  • Atoms and Stars, Class 5
  • Eccentricity (e) – how much different than a circle?
    • e = 0, perfect circle
    • Circle more flattened as e larger than 1
  • e = 0.1

Ellipse

  • 2/11/07
  • Atoms and Stars, Class 5
  • 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

Lab 3 Part 1

  • 2/11/07
  • Atoms and Stars, Class 5
  • Part A done last week, this week finish Part 1
  • Track:
    • Must rest firmly on blocks to keep angle the same
    • Use clay to prop it up side-to-side
    • Time the center of the ball
    • Do not push ball to start, do not stop it before center crosses mark

Lab 3 Part 1 (cont’d)

  • 2/11/07
  • Atoms and Stars, Class 5
  • Do A through F, skip G & H, and Part 2
    • F is Analysis, do at home
    • Point of experiment is Part F. If the divided time are equal, then your results support distance (s) – time (t) relationship for constant acceleration (a): s = ½ a t2
      • First shown by Galileo
      • If you want an explanation of how this works out mathematically, see the (optional) Theory section in Manual

Lab 3 Part 1 Calculations

  • 2/11/07
  • Atoms and Stars, Class 5
  • Calculations on the times to roll down the track (from the Lab Manual):
  • First, average the times and find the error for each distance by itself (e.g. the four times for A0 – B1 by itself) in Part E
    • Do not find the average and error for things you do not think are equal (e.g. we do not expect A0 – B1 and A0 – C4 to be equal – the second distance is longer)
  • After #1, then divide the averaged times according to part F in the lab manual
    • Do not divide the errors

Lab 3 Pt 1 Calculations (cont’d)

  • 2/11/07
  • Atoms and Stars, Class 5
  • Calculations on the times to roll down the track:
  • Then (the core): are the divided times equal, within the errors? (also from Part F)
    • Find the highest and lowest divided averages from #2 and subtract them (= DIFF)
    • Find the two highest averages errors from 1 and add them (= ERROR)
    • Are the divided times equal, within the errors?
      • If ERROR > DIFF then results are compatible and your results support s = ½at2 with constant acceleration a
      • If DIFF > 3 ERROR, not compatible, do not support …
      • In between? “Gray area”

Lab 3 Pt 1 Calculations (cont’d)

  • 2/11/07
  • Atoms and Stars, Class 5
  • This is just like comparing the times for the second hand to move ten seconds, for different people within your lab group, EXCEPT:
    • Compare DIVIDED averages
    • Again, DO NOT divide the errors when you divide the averages

Lab 3 Pt 1 Calculations (cont’d)

  • 2/11/07
  • Atoms and Stars, Class 5
  • Distance
  • Average for each distance
  • Divide average by
  • Divided average
  • Error (do not divide it)
  • A0 – B1
  • 1.9
  • 1
  • 1.9
  • .56
  • A0 – C4
  • 4.2
  • 2
  • 2.1
  • .73
  • A0 – D9
  • 5.8
  • 3
  • 1.93
  • .49
  • A0 – E16
  • 7.6
  • 4
  • 1.9
  • .62
  • Compare these values.


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