Atoms and Stars ist 2420

Atoms and Stars IST 2420

• Class 5, February 12
• Winter 2007
• Instructor: David Bowen
• Course web site: www.is.wayne.edu/drbowen/aasw07

Handouts & Announcements

• Class 5 Notes
• Initial the sign in sheet

• Due tonight

• Essay 1, on a 3½” diskette
• Report for Lab 3 Part 2

Online Grade Reports (repeat)

• 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/aasw06

EAA Grades (repeat):

• -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:

• 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…

• Consider evidence for & against theory
• Before Iraq War, Pentagon office set up to find evidence for Iraq-al-Qaeda link
• CIA, however, considered pro and con, got it right (no connection)
• 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

(Skipped on 2/5) Reading (Euclid’s Elements)

• Propositions: proven
• Proposition 13: A straight line consists of two right angles (180º): CBE + EBD = 180º
• Next, Proposition 15.

Reading (Euclid’s Elements)

• 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)

• 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)

• 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)

• 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)

• 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
• Natural state of terrestrial matter
• “Element”: these are not made up of anything else, everything else is made up of these
• Science changed these ideas!

(Skipped 2/5) Science and Industry

• Scientific method not followed in recent drug-company controversies (e.g. Vioxx)
• Conditions in industry are indeed different
• Data and internal theories are proprietary (trade secrets)
• Executives have authority
• Decisions are made, and are to be followed
• Executives often do not get bad news
• So yes, scientific method often not strictly followed in business and industry

(Skipped 2/5) Aristotle & Archimedes Q11

Science and Industry

• Scientific method not followed in recent drug-company controversies (e.g. Vioxx)
• Conditions in industry are indeed different
• Data and internal theories are proprietary (trade secrets)
• Executives have authority
• Decisions are made, and are to be followed
• Executives often do not get bad news
• So yes, scientific method often not strictly followed in business and industry

Readings: “Motions in the Solar System”

• 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”

• 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
• Uranus, Neptune, Pluto require telescope

“Motions in the Solar System”

• 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”

• 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”

• Sun
• As sun moves through stars, traces plane called “ecliptic”
• Moves through 12 constellations of Zodiac

“Motions in the Solar System”

• 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

• 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

• 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

• 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”

• 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)

• 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)

• Neptune outermost “real” planet
• “Reals” formed from dust cloud, forced orbits to circular
• Term “planet” may be abandoned

New “planets” (cont’d)

• “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)

• 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…

• 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

• Byzantine Emp.
• “Barbarians”
• Persian Empire
• Islamic Empire

In between…

• 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)

• 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)

• 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)

• 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)

• 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”

• 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 36 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

• 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

For Lab 8 Part 1

• Motion – Aristotle (terrestrial) and Newton
• In many ways, Aristotle and Newton are opposites here
• Aristotle: without a continuing force (a push), nothing moves
• Motion stops as soon as push stops
• Coasting is a problem (see next slide)
• Newton: a force causes a change in motion
• Force necessary to start and to stop
• No force, no change – if at rest (not moving), stay at rest, but if moving with no change in speed, direction