“Reserve your right to think, for even to think wrongly is better

““Reserve your right to think, for even to think wrongly is better Reserve your right to think, for even to think wrongly is better than not to think at all. To teach superstitions as truth is a most than not to think at all. To teach superstitions as truth is a most terrible thing.”terrible thing.”

- Hypatia- Hypatia

Bit of Administration ….Bit of Administration ….

• ReadingReading– Bless, Chapters 3-6Bless, Chapters 3-6– BDSV pp. 56-73BDSV pp. 56-73

• Portfolio AssignmentPortfolio Assignment

– The goal of your portfolio is for The goal of your portfolio is for youyou to demonstrate your achievement of: to demonstrate your achievement of:

Knowing the sky and the Solar System as a part of your environment to which you are connected – physically, Knowing the sky and the Solar System as a part of your environment to which you are connected – physically, historically, and culturally/personally.historically, and culturally/personally.

– The portfolio should include 5 documents demonstrating your learning in these dimensions:The portfolio should include 5 documents demonstrating your learning in these dimensions:

• 1) A cultural connection to the sky; you are encouraged to explore non-European cultures.1) A cultural connection to the sky; you are encouraged to explore non-European cultures.• 2) A connection of Newton’s laws of motion and/or gravity to experiences in your life.2) A connection of Newton’s laws of motion and/or gravity to experiences in your life.• 3) A connection of the physics of light to experiences in your life.3) A connection of the physics of light to experiences in your life.• 4) A connection of the Sun’s energy to your life, or the impact of the Second Law of Thermodynamics.4) A connection of the Sun’s energy to your life, or the impact of the Second Law of Thermodynamics.• 5) Your connection to the larger evolutionary processes of the Earth and Solar System.5) Your connection to the larger evolutionary processes of the Earth and Solar System.

– Due April 28; you are encouraged to submit your first documents for review and grading Due April 28; you are encouraged to submit your first documents for review and grading before then in order to develop your skills in advance of doing the entire portfolio.before then in order to develop your skills in advance of doing the entire portfolio.

Earliest CivilizationsEarliest Civilizations

• Plato 400 BCPlato 400 BC

– Geometric Ideals Underly RealityGeometric Ideals Underly Reality• Uniform Circular MotionUniform Circular Motion

– Circular Motion at Constant SpeedCircular Motion at Constant Speed– ““No beginning, no end, no change”No beginning, no end, no change”– Construct a geometric representation of celestial motions using only combinations of Construct a geometric representation of celestial motions using only combinations of

uniform circular motions about the central fixed earthuniform circular motions about the central fixed earth

– Senses are Imperfect and UnreliableSenses are Imperfect and Unreliable• Observation is not important - reason reigns supremeObservation is not important - reason reigns supreme

– Qualitative agreement is acceptableQualitative agreement is acceptable

Early Greek AstronomyEarly Greek Astronomy

• Eudoxus and Calippus 400 BCEudoxus and Calippus 400 BC


• Aristotle 350 BCAristotle 350 BC

– Lunar Phases and EclipsesLunar Phases and Eclipses• Argued that Sun was further than the moonArgued that Sun was further than the moon

– EclipsesEclipses– Slower motion in the skySlower motion in the sky

• Argued that Moon shines by reflected light from SunArgued that Moon shines by reflected light from Sun– Intellectual leap toward relationships that are independent of EarthIntellectual leap toward relationships that are independent of Earth

– Spherical EarthSpherical Earth• Shadow is round during lunar eclipsesShadow is round during lunar eclipses• Travel in latitude changes the positions of the starsTravel in latitude changes the positions of the stars• Elephants were found both to the east in India and to the west in MoroccoElephants were found both to the east in India and to the west in Morocco• Only spherical shape would allow motion to the center to be straight downOnly spherical shape would allow motion to the center to be straight down

– Motion of EarthMotion of Earth• Realized that daily motion could be either earth or celestial sphere spinningRealized that daily motion could be either earth or celestial sphere spinning• Considered heliocentric universe, but rejected because no parallax was seenConsidered heliocentric universe, but rejected because no parallax was seen

– Cosmology of the SpheresCosmology of the Spheres


Right Reasoning, Right Conclusion!

Wrong Reasoning, Right Conclusion!

Right Reasoning, Wrong Conclusion!

Wrong Reasoning, Wrong Conclusion!

• Aristotle 350 BCAristotle 350 BC

– ChemistryChemistry• Earth, Air, Fire, Water - the stuff of the human worldEarth, Air, Fire, Water - the stuff of the human world• Quintessence - the stuff of the celestial bodiesQuintessence - the stuff of the celestial bodies

– PhysicsPhysics• The universe as a machineThe universe as a machine• All vertical motion driven by inclination to natural places All vertical motion driven by inclination to natural places • The natural place of Earth was toward the center of the Universe/EarthThe natural place of Earth was toward the center of the Universe/Earth

– First theory of gravity!First theory of gravity!

– Encyclopedic Treatises on Nearly Every FieldEncyclopedic Treatises on Nearly Every Field

For 2000 years the Universe was AristotelianFor 2000 years the Universe was Aristotelian(though primary impact was after 1200 AD)(though primary impact was after 1200 AD)


• Located in Egypt, but center of Greek culture after 330 BCLocated in Egypt, but center of Greek culture after 330 BC• Conquests of Babylonia by Alexander the Great brought rich Conquests of Babylonia by Alexander the Great brought rich

observational dataobservational data

The Alexandrian SchoolThe Alexandrian School


• Aristarchus of SamosAristarchus of Samos 300 BC300 BC

"You King Gelon are aware the 'universe' is the name given by most astronomers to "You King Gelon are aware the 'universe' is the name given by most astronomers to the sphere the center of which is the center of the Earth, while its radius is equal to the sphere the center of which is the center of the Earth, while its radius is equal to the straight line between the center of the Sun and the center of the Earth. This is the straight line between the center of the Sun and the center of the Earth. This is the common account as you have heard from astronomers. But Aristarchus has the common account as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than consequence of the assumptions made, that the universe is many times greater than the 'universe' just mentioned. His hypotheses are that the fixed stars and the Sun the 'universe' just mentioned. His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun on the circumference of a remain unmoved, that the Earth revolves about the Sun on the circumference of a circle, the Sun lying in the middle of the orbit, and that the sphere of fixed stars, circle, the Sun lying in the middle of the orbit, and that the sphere of fixed stars, situated about the same center as the Sun, is so great that the circle in which he situated about the same center as the Sun, is so great that the circle in which he supposes the Earth to revolve bears such a proportion to the distance of the fixed supposes the Earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface." stars as the center of the sphere bears to its surface."

» ArchimedesArchimedes

The Alexandrian SchoolThe Alexandrian School• Aristarchus of SamosAristarchus of Samos 300 BC300 BC

– Relative Distances of Moon and SunRelative Distances of Moon and Sun

Earth Sun

E S

M

= cos MESEMES


– Relative Distances of Moon and SunRelative Distances of Moon and Sun• Requires measuring the angle MESRequires measuring the angle MES• Suggested measuring time from first quarter to third quarter and Suggested measuring time from first quarter to third quarter and

time from third quarter to first quarter, then taking the ratiotime from third quarter to first quarter, then taking the ratio• Used 87Used 87oo with no mention of origin with no mention of origin• Found that the Sun is 20x further than the MoonFound that the Sun is 20x further than the Moon• But in fact ….But in fact ….

E S

M

Earth Sun


– Relative Distances of Moon and SunRelative Distances of Moon and Sun• Requires measuring the angle MESRequires measuring the angle MES• Suggested measuring time from first quarter to third quarter and time from Suggested measuring time from first quarter to third quarter and time from

third quarter to first quarter, then taking the ratiothird quarter to first quarter, then taking the ratio• Used 87Used 87oo with no mention of origin with no mention of origin• Found that the Sun is 20x further than the MoonFound that the Sun is 20x further than the Moon• Measurement of angle MES is impossible; Sun is 400x further than the MoonMeasurement of angle MES is impossible; Sun is 400x further than the Moon

EarthSunSun


– Relative Sizes of Moon and SunRelative Sizes of Moon and Sun


– Relative Sizes of Moon and SunRelative Sizes of Moon and Sun• Sun and Moon are same angle in the sky (0.5Sun and Moon are same angle in the sky (0.5oo))• Sun is 20x further away than the MoonSun is 20x further away than the Moon• Sun must be 20x larger than the MoonSun must be 20x larger than the Moon

1

20

Earth


– Relative Sizes of Earth, Moon and SunRelative Sizes of Earth, Moon and Sun

Time 1Time 10 hr0 hr



Earth

1 32

Earth’s Shadow is 3x Diameter of MoonEarth’s Shadow is 3x Diameter of Moon



Earth

• Found that Sun is 6-7x larger than the Earth, compared to 109xFound that Sun is 6-7x larger than the Earth, compared to 109x• The Sun is larger than the Earth!The Sun is larger than the Earth!• Led him to suggest a Sun-centered (“heliocentric”) universeLed him to suggest a Sun-centered (“heliocentric”) universe



• Found that Sun is 6-7x larger than the Earth, compared to 109xFound that Sun is 6-7x larger than the Earth, compared to 109x• The Sun is larger than the Earth!The Sun is larger than the Earth!• Led him to suggest a Sun-centered (“heliocentric”) universeLed him to suggest a Sun-centered (“heliocentric”) universe

"[Cleanthes, a contemporary of Aristarchus] thought it was the duty of the Greeks to indict "[Cleanthes, a contemporary of Aristarchus] thought it was the duty of the Greeks to indict Aristarchus of Samos on the charge of impiety for putting in motion the Hearth of the Aristarchus of Samos on the charge of impiety for putting in motion the Hearth of the universe [i.e. the earth], . . . supposing the heaven to remain at rest and the earth to universe [i.e. the earth], . . . supposing the heaven to remain at rest and the earth to revolve in an oblique circle, while it rotates, at the same time, about its own axis." revolve in an oblique circle, while it rotates, at the same time, about its own axis."

»PlutarchPlutarch

The Alexandrian SchoolThe Alexandrian School• EratosthenesEratosthenes 200 BC200 BC

– The Size of the EarthThe Size of the Earth• Note that all of Aristarchus’ results are Note that all of Aristarchus’ results are relativerelative sizes sizes

From Sun

From Sun

Light rays from very distant objects arrive at every point on Earth from the same direction!

HK

NY

Earth

From Sun

From Sun

7 o

Alexandria

7 o

Syene

Distance around Earth = 360o/7o x Distance Syene to Alexandria = 50 x 5000 stades !

From SunFrom Sun


• The Size of the Universe, circa 200 BCThe Size of the Universe, circa 200 BC

• Earth’s DiameterEarth’s Diameter 13,00013,000 kmkm 12,75612,756kmkm

• Moon’s DiameterMoon’s Diameter 4,3004,300 34763476• Sun’s DiameterSun’s Diameter 9 x 109 x 1044 1.39 x 101.39 x 1066

• Earth-Moon DistanceEarth-Moon Distance 4 x 104 x 1055 3.84 x 103.84 x 1055

• Earth-Sun DistanceEarth-Sun Distance 101077 1.50 x 101.50 x 1088

“Reserve your right to think, for even to think wrongly is better

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