Reminders

1 No Online Quiz this Week2 Midterm 1: Friday Sept 25 (this Friday)

Bring OU IDPencilEraser

3 Practice Midterm on course web page (alsounder Supplementary Material –> Midterm 1)

4 All lectures are posted on Course Webpage

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Lecture 13 – Kepler and Newton’sLaws

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Aristotle

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Aristotle’s Teaching

Earth is center of the universe. Gravity is due to thefact that things want to move towards the center of theuniverse. Heavy things move faster than light things.Earth is corruptible, things change on it.Heavens are perfect and unchanging.Knew Earth was round.

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End of Classical Greece

Ptolemy’s system and textbook Almagest (thegreatest, renamed by the Arabs) remainedvirtually unchanged until the 13th century.With the end of classical Greece, pursuit ofknowledge passed to the Arab world. (TheRomans did little to further scientificknowledge)Arabs updated the tables several times,remember precession causes them tobecome out of date.

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Ptolemy

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Fly in the ointment:Retrograde Motion of Mars

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Astronomy in the Dark Ages

in 13th Century Arabs were driven out ofSpain by Christians, Ptolemy’s book becamemore widely available in Latin.Last great adjustment of Ptolemy’s systemfinanced by Alfonso X of Castille: AlfonsineTablesThe Renaissance was beginning in Europe

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Critics of Aristotle and Ptolemy

Heraclides: A Pythagorean who explainedthe diurnal motion of the stars by positing aneastward axial rotation of the central earth.Nicole Oresme (14th Century A.D.) memberof the Parisian nominalist school. Formulatedwhat we now call Galilean RelativityCritics rejected due to lack of parallaxHow does this illustrate the workings of thescientific method?

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Copernicus 1473-1543

Wrote De Revoluionibus Orbium Coelestium(De Reb) around 1530, not published untilyear of his death.Established heliocentric systemStill used uniform circular motion andepicyclesPrutenic Tables (1551) based on Copernicansystem, but not particularly more accuratethan Alfonsine TablesTriumph: Could explain retrograde motion ofMars

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Copernicus

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Copernicus’ System from De Reb

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Copernicus’ SystemPlanets nearer the sun move faster

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Triumph of Copernican System

Copernicus’ ideas were disseminatedthroughout Europe even before he published.Even though Copernican system wasn’tnecessarily accepted, it was used byastronomers for pragmatic reasons.Remember how inelegant Ptolemy’s systemwas!

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Copernicus’ Explanation forRetrograde Motion

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Tycho (1546-1601)

Keen observerRecognized that the Alfonsine and Prutenictables were in error by as much as a monthDiscovered a “new star” (Tycho’s supernova)in 1572Published his results in De Stella NovaSince the Heavens changed this challengedAristotle’s systemDid careful measurements, devisingmeasuring instruments for 20 years

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Tycho

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Rejected Copernicus again because hedetected no parallax.Why didn’t he?Developed his own (rather weird) systemPatron (Frederik II) died and he moved toPrague to produce Rudolphine Tables.Died (how?) before he could complete themand the observations passed to Kepler

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Tycho at Hveen

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Tycho’s System

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Kepler (1571-1630)

Dedicated CopernicanPublished ideas in MysteriumCosmographicum in 1596Joined Tycho in Prague in 1600After Tycho’s death got full access to Tycho’sobservationsAbandoned uniform circular motion,published Rudolphine Tables in 1627.

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Kepler

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Kepler’s Laws

Kepler’s Three Laws of Planetary Motion1 The orbits of the planets are ellipses with the sun

at one focus

e = c/a

1 − e2 = (b/a)2

2 A line from the sun to the planet sweeps out equalareas in equal times

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P2year = a3

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Ellipse

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Ellipse Axes

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Kepler’s Second Law

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Galileo (1564-1642)

True Scientist, made observations and thentried to interpret themDid not discover Telescope, but built one andpointed it at the HeavensObserved the moon, Jupiter, Saturn, andVenus

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