Atoms and Stars IST 2420 Class 5, February 16 Winter 2009 Instructor: David Bowen Course web site:

Atoms and StarsIST 2420

Class 5, February 16

Winter 2009Instructor: David Bowen

Course web site: www.is.wayne.edu/drbowen/aasw09

Atoms and Stars, Class 5 2

Handouts & Announcements

• Initial the sign in sheet

Due tonight

• Essay 1, via BlackBoard Digital DropBox

• Report for Lab 3 Part 2

2/16/09


Lab Tonight

• Lab 8, Part 1

Midterm• Midterm one hour at start of class in three

weeks, March 9

• Review for Midterm in two weeks, March 2, one hour at end of class

2/16/09


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)o Check to enable and write a password

• Demo• Later

o You will be able to track your average, project grade

• www.is.wayne.edu/drbowen/aasw09

2/16/09

Change in EAA Grades

• Yesterday (Sunday February 15) I turned in the EAA grades for this course

• Now normal academic letter grades, overall, not by area (attendance, homework, etc.).

• A grade of C- or below gets an email

• Some grades higher because I allow you to be behind in lab reports (real grade would be lower)

Atoms and Stars, Class 5 52/16/09

2/9/09 Atoms and Stars, Class 4 6

Reading #3

Euclid (Pp 74 – 79), book Elements Q10

Proof in mathematics and geometry

• Postulate #4: all right angles (90º) are equal

• Common notion #1: things equal to the same thing are equal. If a = c and b = c then a = b

• Common notion #3: if equals are subtracted from equals then the remainders are equal. If a = b then a – c = b – c.


Reading: Euclid’s Elements

• Propositions: proven

• Proposition 13:A straight lineconsists of tworight angles(180º): CBE + EBD = 180º

• Next, Proposition 15.

2/16/09



• Proposition 15: Iftwo straight linescut each other,the vertical anglesare equal (i.e. AEC = DEB)

• Proof on next slide, relies upon earlier Postulate #4, Common Notions #1 & #3, and Proposition #13.

2/16/09



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)

2/16/09



• Proposition 47:PythagoreanTheorem

• For a right triangle (has one right angle),a2 + b2 = c2

o Example: 3, 4, 5 triangle, 32 + 42 = 9 + 16 = 2552 = 25, so 32 + 42 = 52

• Formula known to Egyptians, maybe earlier, but proven by Pythagoras

2/16/09


Reading: Euclid’s Elements• Mathematics

o start with assumptionso draw unarguable conclusions from assumptionso 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)o Assumptions and results can be overturned with

new experiments2/16/09


Readings: “Motions in the Solar System”

• Motions in sky known to all civilizations

• Constellation: groups of stars, pattern invariant over human lifetimeo 88 total constellations, Zodiac is 12 of these

• Angular measuremento Degrees: 360° = circle (horizon), 90º horizon to

pole. Fist at arm’s length ~ 10°, finger ~ 1ºo Minute ('): 60' = 1°o Second ("): 60" = 1'

2/16/09


“Motions in the Solar System”

• Stars circle around pole (Pg 97)o All rotate together (seemingly) as if on a sphereo (Really, earth is turning underneath stars)o 360º in 24 hrs = 15º/hr

• Also move annually relative to sun• Five visible planets Mercury, Venus, Mars,

Jupiter, Saturn move with respect to starso Uranus, Neptune, Pluto require telescope

2/16/09



• Planets move through stars west to east like sun and moon, but periodically reverse or retrograde motiono Mercury, Venus stay close to sun (morning &

evening stars)• Retrograde when close to but farthest east of sun,

reappear west of sun

o Mars, Jupiter, Saturn roam with respect to sun• Retrograde when opposite sun

2/16/09



• Suno Highest in sky at Summer Solstice (~June 21,

most daylight)o Lowest at Winter Solstice (~December 21,

longest night)o In between Spring and Vernal (Fall) Equinoxes

– equal day and nighto Reversed in Southern Hemisphereo Also moves east with respect to stars

2/16/09



• Suno As sun moves through stars, traces plane called

“ecliptic”o Moves through 12 constellations of Zodiac

2/16/09


“Motions in the Solar System”• Moon

o Rises in east, sets in west like suno Also moves to the east with respect to starso New moon – moon between earth and suno Full moon – earth between sun and moon

• Eclipseso Moon eclipses sun, orbit tilted so rareo Lunar eclipse when earth’s shadow hides full

moon2/16/09


Retrograde Motion #1

• Retrograde: moving or directed backwardso 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

2/16/09


Retrograde Motion #2

• Retrograde: moving or directed backwardso “Fixed” stars – most celestial objects (stars)

rotate together, today called fixed• Now we see they really do move, just very slowly

o Planet: Greek for “wanderer” – wandered among fixed stars

o Motion actually very regularo Wander through astrological constellations

2/16/09


Retrograde Motion #3• Objects and orbits in solar system close to the same

planeo Also close to the plane of our galaxyo 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

o Click “Model,” stop at “COPERNICUS”o Click on “Months,”o See “Notes” at bottom of screen to explain what you seeo 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)

o Right-to-left normal, reverse/pause is retrograde2/16/09

http://jove.geol.niu.edu/faculty/stoddard/JAVA/ptolemy.html


New “planets”• Pluto discovered 1930, orbit radius ~30 AU• Quaoar discovered 2002, ~1/8 size of Pluto

o 42 AU from sun (42 × radius of earth’s orbit)• Radius of earth’s orbit = 93 million miles

• 2003 VB12 (“Sedna”) ~ size of Plutoo Orbit radius ~ 39 AU

• 2004 DW ~½ size of Plutoo Orbit radius ~45 AU

• 2005 “Xena” with moon “Gabrielle”o ~ 20% larger than Pluto, 39 to 97 AU (very flattened)o Plane ~ 43° to ecliptic

2/16/09


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)

2/16/09



• Neptune outermost “real” planet

• “Reals” formed from dust cloud, forced orbits to circular

2/16/09



• “Classification” - what is a planet?o Follows “description” in development of

scienceo What are the real differences?

2/16/09

What are these things?? (Q16)Category Greek Modern

Star “Fixed” – travel together

Shines with own light

Planet “Wanderer” – does not travel with stars, Earth not a planet (& retrograde)

Circles a star, shines by reflected light

Moon Only one, like planet

Circles a planet, reflected light


2007 Change

• New planets are not planets, neither is Pluto (“dwarf planet”)o Now, eight planets

• New characteristic of planet: has cleared its orbit of other bodies (Q16)



“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 & Barbarianso Western Roman Empire fell first

• Then: Islamic empire

2/16/09


Locations

Byzantine Emp.“Barbarians”Persian EmpireIslamic Empire

2/16/09


In between…

• Barbarianso Had their own technology e.g. textileso Brought Chinese technology further west

• Byzantineo Inherited Greek cultureo John Philoponos questioned Aristotle

• Spear-throwing – said thrower imparted power to spear to move itself

2/16/09


In between (cont’d)

• Persiano Cultural center Jundishapur (NE today’s Basra)o Translated most Greek writingo Hospital and medical schoolo Astronomy and astrologyo Also developed Greek science

2/16/09



• Islamic Empireo Mohammad 632 A.D.o After 642, started conquering the area in

Northern Africa to Spain and Portugal, in East towards China

o Medicine, astronomy, astrology• Needed to know where Mecca was for praying

o Agricultural science, irrigationo Largest cities in the world (Baghdad)

2/16/09



• Islamic Empire (cont’d)o Respected other traditions, treated them wello Principal heir to Greek scienceo Medicine, astronomy, math and geometry

• Arabic numerals from India

o Sometime after 1,000 A.D., peak and decline• Became fixated on Koran and past?

• Success led to homogenization?

2/16/09



• Islamic Empire (cont’d)o Enormous libraries, many works only in

original manuscript todayo 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

..

2/16/09


“Copernicus Incites a Revolution”

• Protestant Reformationo Challenge to Catholic churcho 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

2/16/09


Copernicus• Retrograde motion a problem for

geocentrism

• Copernicus 1473 – 1543

• Current astronomical model of solar system was Ptolemaic (Ptolemy), geocentric (“geo” = earth), Aristoteliano Very cumbersome (slide 34 from Class 3 next)

2/16/09


Slide 27 from Class 3• Hellenistic Period (after 323 BC)

o 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

2/16/09


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

2/16/09


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

2/16/09


Copernicus• Objections

o Not a big simplification over Ptolemeyo Said stars far away, to explain lack of observed

parallax of stars: unsatisfactoryo Falling bodies have no observed falling behind

as earth turns under themo Religious objections surfaced after Galileo

• 1582 led to Gregorian calendar – no leap years for centuries unless divisible by 4

2/16/09


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

2/16/09


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

2/16/09


Tycho Brahe

• November 11, 1572: saw extremely bright new object, parallax measurements showed it to be outside of solar system. Lasted for three months.o Heavens not unchanging

• Comet of 1577, parallax measurements showed comet cut through crystalline spheres. They were not real.

2/16/09


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 suno Simpler, accurate, no spheres

2/16/09


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

2/16/09


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

2/16/09


Johannes Kepler

• Three laws of planetary motiono First two 1609 Astronomia Nova (New

Astronomy), third buried in Harmonice mundi (Harmonies of the world) 16191. Planetary orbits are ellipses with sun at one focus2. Equal areas in equal times3. t2 r3 (period squared proportional to radius cubed)

o Unsatisfactory explanations for these lawso Not well received, rejected for the most part

2/16/09


Ellipse• Eccentricity (e)

– how much different than a circle?o e = 0, perfect

circleo Circle more

flattened as e larger than 1

e = 0.1

2/16/09


Ellipse• Focus

o A + B = same for each point on ellipse

o Circle: the two focii coincide, distance is radius

e = 0.1

Each ellipse has two focii (one is a focus)

AB

2/16/09


Lab 3 Part 1 Calculations (Q2)

Calculations on the times to roll down the track(from the Lab Manual):

1. 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 Eo 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)

2. After #1, then divide the averaged times according to part F in the lab manualo Do not divide the errors

2/16/09


Lab 3 Pt 1 Calculations (cont’d)Calculations on the times to roll down the track:3. Then (the core): are the divided times equal,

within the errors? (also from Part F)A. Find the highest and lowest divided averages from #2

and subtract them (= DIFF)B. Find the two highest errors from 1 and add them (=

ERROR)C. Are the divided times equal, within the errors?

i. If ERROR > DIFF then results are compatible and your results support s = ½at2 with constant acceleration a

ii. If DIFF > 3 ERROR, not compatible, do not support …iii. In between? “Gray area”

2/16/09


Lab 3 Pt 1 Calculations (cont’d)

• Remember:o Compare DIVIDED averageso DO NOT divide the errors when you divide the

averages• Why is this important?

o Errors can make things that are equal appear to be different

• Many reports said that since divided averages are not exactly equal, then the divided times are really different (FALSE)

o Errors can make things that are not equal appear to be equal

2/16/09



Distance Average for each distance

Divide average

by

Divided average

Error (do not

divide it)

A0 – B1 1.8 1 1.8 .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.

2/16/09



• From preceding slide:o DIFF = highest divided average – lowest

= 2.1 – 1.8 = 0.3o ERROR = sum of two highest errors

= 0.73 + 0.62 = 1.35o If ERROR > DIFF then results are equal within

errors, cannot say they are different (Null Hyp/ Q2)

o If DIFF > 3 × ERROR, results not equalo In between, gray area

2/16/09

Lab 8 Part 1

• Rolling carts with good bearingso Case 1: wheels free to turno Case 2: wheels taped so they can’t turn

• Manual says to tape wheels yourself, but instead swap carts – some will do taped first

• Then wheels free, block on top of cart, crash into book

• NOT IN MANUAL: Then tape paper air barrier in back of block, crash again (test of Aristotle’s explanation for coasting motion)


For Lab 8 Part 1

• Motion – Aristotle (terrestrial) and Newtono In many ways, Aristotle and Newton are opposites here

o Aristotle: without a continuing force (a push), nothing moves

• Motion stops as soon as push stops

• Coasting is a problem (see next slide)

o 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 force, then no change in speed or direction


Review: Some Greek Science

• Aristotle:o Terrestrial physics: force necessary for motion

• If something coasts, air must move out of way, then move in behind to push

• Plausible, but later disproven


Documents

Atoms and Stars IST 2420 Class 5, February 16 Winter 2009 Instructor: David Bowen Course web site: