lecture_tan7 - Key Concepts: Lecture 7 Aristarchus and the...

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Key Concepts: Lecture 7 Aristarchus and the relative distances to Moon and Sun Parallax Eratosthenes and the size of the Earth Precession Aristotle, Hipparchus, Ptolemy - a geocentric model of solar system Copernicus and the Heliocentric Model Lecture 7 - Overview Ancient Greeks & Aristotelian Physics – How did most of the early Greeks model the universe? – What are the key physical ideals of Aristotelian physics? Ptolemy - How did Ptolemy apply Aristotle’s physics to model the cosmos? Copernicus - What were the main differences between his model and those of most earlier Greeks? Tycho Brahe - What were his major contributions to Astronomy? Aristarchus of Samos (310-230 B.C.) Estimated relative sizes of the Moon & Earth – timed duration of lunar eclipses – compared the time it takes the Moon to enter the Earth’s shadow with the time it takes the Moon to cross the Earth’s shadow Estimated distance to Moon (relative to Earth’s diameter) – measured angular size of Moon & compared this to the estimate of the Moon’s size relative to Earth’s diameter Estimated distance to Sun (relative to Earth-Moon distance) – Assumed Moon’s orbit was circular & uniform – Measured angle between Sun-Earth-Moon at 1st quarter: estimated this to be 87 deg., so ! =3 deg. – Then Earth-Moon distance is about ( 3 / 360 ) x 2 " x Earth-Sun distance But it was difficult to measure these angles: Aristarchus thought the Sun was 20 times further away than the Moon, but it is really 400 times further. Aristarchus of Samos (310-230 B.C.) Estimated size of Sun from total Solar Eclipse using relationship between angular size, physical size and distance Aristarchus estimated all these quantities in terms of the Earth s diameter Measurement Aristarchus Modern Moon’s Distance 10 Earth Diameters 30 Earth Diameters Moon’s Diameter 0.333 Earth Diameters 0.272 Earth Diameters Sun’s Distance 200 Earth Diameters 11,700 Earth Diameters Sun’s Diameter 7 Earth Diameters 109 Earth Diameters # Aristarchus found that the Sun was much bigger & much farther away than the Moon # He therefore concluded that the Sun, not the Earth was at the center of the Universe! Angular size (measured in radians) = Physical Size Distance
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Parallax If Earth moves around Sun then we should see parallax, i.e. the displacement of foreground stars with respect to background stars. Parallax could not be seen by early Greek astronomers: one argument against the Sun- centered model, e.g. by Aristotle In fact parallax effects are real, but very small as the stars are very far away. 7.2 0 5000 stadia = Eratosthenes (c. 200 B.C.) On the summer solstice, at noon: the Sun was directly overhead in the city of Syene, Egypt but in Alexandria, Egypt, the Sun was displaced from the vertical Using a gnomon (i.e. a stick casting a shadow) & basic trigonometry, he determined that the angle from the vertical was ~7.2 0 this angle = the angle between Syene & Alexandria as seen from the Earth’s center Alexandria was 5000 stadia from
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This note was uploaded on 09/07/2011 for the course AST 1002 taught by Professor Dr.haywoodsmith,jr during the Spring '07 term at University of Florida.

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lecture_tan7 - Key Concepts: Lecture 7 Aristarchus and the...

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