Lecture #4: Plan. Early Ideas of the Heavens (cont d): Geocentric Universe Heliocentric Universe
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1 Lecture #4: Plan Early Ideas of the Heavens (cont d): Shape & size of the Earth Size & distance of Moon & Sun Geocentric Universe Heliocentric Universe
2 Shape of the Earth Aristotle (Greece, B.C.) During a lunar eclipse, the Earth s shadow on the Moon is clearly curved A traveler moving south sees stars that were previously hidden below the southern horizon
3 Distance and Size of the Moon Aristarchus (Greece, B.C.) d EM Lunar eclipse: Aristarchus: D E ~ 3 D M Modern: D E ~ 4 D M Total length of lunar eclipse vs length of Moon s motion through zodiac Measured: 3 vs 660 hours Implies: D E vs 2 π d EM Circumference of Moon s orbit 2 π d EM = (660/3) x D E = 220 D E Radius of Moon s orbit d EM = 220 D E / 2π ~ 35 D E Modern value d EM = 30 D E!
4 Distance and Size of the Sun Aristarchus (Greece, B.C.) d EM d ES At Quarter Moon: cosine(a) d EM / d ES d ES = d EM / cosine(a) ~ 20 d EM (A = 87 o ; Aristarchus) d ES ~ 400 d EM (A = 89.9 o ; modern)
5 Distance and Size of the Sun (cont d) Aristarchus (Greece, B.C.) Solar Eclipse: A M ~ A S D M / d EM ~ D S / d ES D S ~ (d ES / d EM ) D M ~ 20 D M (Aristarchus) ~ 400 D M (modern) Since, according to Aristarchus, D S = 20 D M and D E ~ 3 D M D S ~ 7 D E D S ~ (400 / 4) D E = 100 D E (modern)
6 The First Heliocentric Universe! Aristarchus (Greece, B.C.) Amazingly, he also postulated that the Earth goes around the Sun But his critics claimed that if this were true, they would see the positions of the stars change relative to each other
7 Parallax Shift in an object s apparent position caused by the observer s motion
8 The First Heliocentric Universe! Aristarchus (Greece, B.C.) Amazingly, he also postulated that the Earth goes around the Sun But his critics claimed that if this were true, they would see the positions of the stars change relative to each other But no shift in position observed at the time Model rejected!!!
9 Observed: 1. In Alexandria, the Sun casts a shadow at noon on the day of summer solstice 2. In Syene, the Sun is directly overhead at noon on that same day and casts no shadow Size of the Earth Erathosthenes (Egypt, B.C.)
10 Definitions: A angle between obelisk and the Sun (7 o ) d distance between Alexandria and Syene (5000 stadia ~ 500 miles) C circumference of Earth Proportions: A / 360 o = d / C 7 o / 360 o = d / C C = (360/7) d ~ 50 x 500 ~ 25,000 miles Modern: C = 24,662 miles! Size of the Earth Erathosthenes (Egypt, B.C.)
11 Geocentric Model Earth at the center Natural common sense Don t feel Earth s motion No parallax All objects move around Earth affixed to crystalline spheres
12 Geocentric ( Ptolemaic ) Model Retrograde Motion: Apparent backward (= East-to-West) motion of a planet with respect to stars Ptolemy (~150 A.D.): explained it with epicycles = small spheres attached to larger ones
13 Heliocentric Universe Nicolas Copernicus (Poland, ) Revived Sun-centered model of the Heavens (On the Revolutions of Celestial Orbs) Explained retrograde motion (circular orbits)
14 Copernicus and Planetary Distances He was able to calculate a planet s distance from the Sun by noting the planet s position at various times Opposition: When the Earth lies directly between the Sun and the planet Conjunction: When the planet lies directly on the Earth-Sun line Inferior conjunction: Planet is between the Earth and the Sun Superior conjunction: When the Sun lies directly between the Earth and the planet Quadrature: When the planet s position makes a right angle with the Earth-Sun line
15 Mercury and Venus Mercury and Venus are closer to the Sun than the Earth, since they are never found very far from the Sun in the sky Mercury s greatest elongation, or angular separation from the Sun, is never more than 28 o Venus s greatest elongation is never more than 47 o Mercury is therefore closer to the Sun than Venus
16 Distances to the Other Planets Copernicus measured the time it took a planet to move from opposition to quadrature, and calculated the planet s relative distance from the Sun Remarkably accurate! Planet Copernicus s Calculation (AU) Actual Distance (AU) Mercury Venus Earth Mars Jupiter Saturn
17 Lecture Activity #1: Retrograde Motion Answer the following questions in your own words: A. What is retrograde motion? B. How did Ptolemy explain it? C. How did Copernicus explain it?
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