Lecture #4: Plan Early Ideas of the Heavens (cont d): Shape & size of the Earth Size & distance of Moon & Sun Geocentric Universe Heliocentric Universe
Shape of the Earth Aristotle (Greece, 384 322 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
Distance and Size of the Moon Aristarchus (Greece, 310 230 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!
Distance and Size of the Sun Aristarchus (Greece, 310 230 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)
Distance and Size of the Sun (cont d) Aristarchus (Greece, 310 230 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)
The First Heliocentric Universe! Aristarchus (Greece, 310 230 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
Parallax Shift in an object s apparent position caused by the observer s motion
The First Heliocentric Universe! Aristarchus (Greece, 310 230 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!!!
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, 276 195 B.C.)
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, 276 195 B.C.)
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
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
Heliocentric Universe Nicolas Copernicus (Poland, 1473 1543) Revived Sun-centered model of the Heavens (On the Revolutions of Celestial Orbs) Explained retrograde motion (circular orbits)
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
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
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 0.38 0.39 Venus 0.72 0.72 Earth 1.00 1.00 Mars 1.52 1.52 Jupiter 5.22 5.20 Saturn 9.17 9.54
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?