Short History of Cosmology

  (extract of Prof. Martin’s old notes)

Building a Cosmology

  Imagine yourself observing the night sky (600 BC)  You observe:

• The Sun: travels in arc overhead • The Moon: travels in arc; has phases • Stars: constellations rotate together, nightly

and seasonally • Planets: complex arcs with different periods

Cultural Worldview

 Regular geometric shapes are the most perfect

 Circles and spheres are true perfection

 Simple ratios yield perfect harmonies

 Human beings are special

Make Sense of Observations in Worldview Context

 All objects seem to travel across our sky  Simple Model #1:

• The Earth must be at the center • The Sun: circular orbit, once per day • The Moon: circular orbit, once per day • Stars: attached to sphere which rotates • Planets: Venus, Mars, Jupiter, Saturn have circular orbits with periods in simple ratios

Model 1: Test

 Model 1 does explain:

• Nightly motion of Sun and Moon across sky • Nightly rotation of constellations

 Well, so far so good...

Model 1: Test (continued)

 Model 1 does not explain: • The phases of the Moon (28 day period) • The seasonal change in constellations

(365 day period) • The orbits of the planets

(both complicated arcs and periods)   Model 1 fails simplest test: it does not explain all

the basic observations!

Improving Model 1

 What:  Add more to Model 1 to improve it

 How??  Creative guessing!  This is the essence of science

 Guidelines (cultural bias + experience)  Simplicity: “Everything should be made as simple as

possible, but no simpler” - Einstein

 Symmetry: Nature seems to like it, humans certainly do

Improving Model 1: Example

 Consider orbit of Mars • Generally follows arc, but sometimes

moves backward • Epicycle! Circle on a circle:

Improving Model 1: Example (cont.)

 Why is epicycle a good solution?   It can explain the observation of planets “going

backwards”

  It retains the circle as the primary element, and circles are “perfect”

E

Greek Model Improvement

 Pythagoras (600 BC): Musical circles/spheres (like model 1)

 Eudoxas (400 BC): 27 spheres, different periods and axes

 Aristotle (350 BC): 54 spheres; outermost: “seat of

unchangeable order”; inner: “unsettled and changeable”

 Hipparchus (100 BC): offset centers and epicycles

 Ptolemy (100 AD): “wrote the book” on ancient cosmology, a full treatise which would become THE book for a millenium+

Society and Politics I

 Greeks at Athens (600-300 BC) • Learning encouraged (Pythagoras-Aristotle) • Flourishing society could afford schools

 Greeks/Egyptians at Alexandria (300 BC - 400 AD) • Learning encouraged (Hipparchus-Ptolemy)

• Built the “Museum”: school and huge library; like an international research institute

 Romans (200 BC - 400 AD): • Learning tolerated; some scholars move East

Society and Politics II

 Christians in Europe (200 AD - middle ages) • Alexandria Library destroyed in 389 • Learning discouraged: e.g. St. Augustine (400 AD): “It is not necessary to probe into the nature of things as was done by (…)

the Greeks. (…) It is enough for the Christian to believe that the only cause of all created things (…) is the goodness of the Creator.”

 Arabs in Middle East (100 BC - middle ages) • Applied learning encouraged: Haroum al-Rashid’s

“House of Wisdom” in Bagdad • Preserved Greek writings rescued from Alexandria • Deveolped new number system and algebra

The Cosmology Saga: continued

 Review Aristotle/Ptolemy Cosmology:   Earth-centered model   “Perfect” circular orbits, spherical shells   Multiple epicycles; offset centers   Fit data fairly well

 Book “lost” after destruction of Museum, preserved by Islamic scholars

A New Idea?

 Dissenting Greek: Aristarchus (100 BC)   Sun-centered (heliocentric) model   Still assumed perfect circular orbits   Didn’t fit some observations as well as

geocentric epicycle model   Explained some observations more simply   Aristotle’s reputation and insistance that Earth

does not move held sway   Heliocentric model forgotten for more than a

millenium...

Politics and Society: middle ages

 Moslems take southern Spain:   Cordoba becomes new center of learning   New library collects Arabic translations of

remaining Greek manuscripts and new Arab works

 Cordoban astronomers (Gabir Ben Aflah & Mur Ed Din al Betugi) question Ptolemaic system   No new model forthcoming

Politics and Society: middle ages

 Christians Ease up   Charlemagne (784): monasteries should have

schools   Thomas Aquinas: Natural laws created by God,

can be learned with rational methods   Christians retook Spain (1100’s), discovered

libraries   Church embraces Aristotelian/Ptolemaic

cosmology (1200’s): Earth centered is now Church doctrine!

Politics and Society: middle ages

 Toward Renaissance   Scholars begin to speak out   Roger Bacon: Reliance on ancients and Church

dogma not good enough   Erasmus: argues against Church practices

 Politics   Fall of Constantinople: scholars flee to Europe   Holy Roman Empire disintegrates; National

monarchies rise.

Ptolemaic System Supreme (?)

 Ptolemaic system used to compute Alfonsine astronomical tables and calendar   Very difficult, complicated calculations   Alphonse X: “If God had asked my advice, I

would have suggested a simpler design for the Universe”

  Inaccuracies develop in computation of celestial events: not even that accurate...

Renaissance (1300’s - 1600’s)

 Across-the-board emergence of new ideas, creativity   Art: explosion of nature and human art   Invention: printing press, e.g.   Exploration: age of transcontinental voyages   Science: Cosmology, motion, medicine...

 Cosmology: Copernicus

Copernicus

 Observation and good idea:   Sun-centered cosmological model   Circular orbits with 34 epicycles   Afraid to publish it: Inquisition   Urged by follower, it was published in 1543

when Copernicus is near death

 Preface:   “These hypotheses need not be true or even probable; if

they provide a calculus consistent with the observations, that alone is sufficient”

Copernicus and the Church

 Catholic Curch banned his book   Bruno, 1590’s, is burned at stake for

“worshipping the sun and other heresies”   However: Pope Gregory used his model to

compute new Gregorain calendar in 1582!

  Protestant countries more open: England, Germany, Denmark

Tycho Brahe

 Protestant country, Denmark, gives him land for an observatory (1560’s)   Remember: no telescopes!   Lifetime of observations, the most detailed ever

of planetary motion

  Designed his own Earth-centered cosmology

Johannes Kepler

 Born in Germany, moves to Prague to escape Cathollic/Protestant fighting (1560’s)   Inherited Tycho’s data upon his death (1601)   Tried to fit it with mystical “perfect solids” and

“perfect harmonies” models

  Pretty good fit, but off by 8 minutes of arc!

Johannes Kepler (continued)

 Kepler:   “Since divine goodness has granted us a most

diligent observer, Tycho Brahe, from whose observations the error in this calculation of 8 minutes is Mars revealed, it is fitting that we recognize and make use of this good gift of God with a graceful mind.”

  He threw out his own mystical beliefs based on the 8 minute error! A true scientist...

Johannes Kepler (1571-1630)

New Model based on Tycho’s data:  Heliocentric cosmology with planets

orbiting Sun in Elliptical orbits  Planet-Sun line sweeps out equal areas in

equal times   (Period)2 (Avg. radius)3 ∝

Kepler’s “Laws”

Elliptical Orbits  Sun at one focus, planet describes ellipse

Kepler’s “Laws”

Equal areas in equal times  Means planet moves faster when near the Sun

Kepler’s “Laws”

Period - Radius relation  Means planets closer to Sun have shorter

period  All planets have same relation

P2

r3 = same number for all planets

Kepler’s “Laws”: Goal Attained?

 Tycho: careful observations

 Kepler: empirical model  Makes sense of observations, but…  No explanation: Why ellipses?  No mathematical foundation

 Not yet a justifiable Theory

 Newton saves the day (see previous class)