Greek Astronomy: Aristarchus vs. Ptolemy's Models, Study notes of Astronomy

Download Greek Astronomy: Aristarchus vs. Ptolemy's Models and more Study notes Astronomy in PDF only on Docsity! Admin. 1. Class website http://www.astro.ufl.edu/~jt/teaching/ast1002/index.html 2. Discussion sections Tuesday (period 4, 10.40-11.30am), Bryant 3 Wednesday (period 8, 3pm-3.50pm), Bryant 7 Thursday (period 5, 11.45am-12.35pm), Bryant 3 office hr: Thursday (period 7, 1.40pm - 2.40pm), Bryant 3 or 302 3. Quiz 1 (not for credit) on class website deadline Friday 11am. 4. Homework 1 is on class website and is due 6pm Thur 11th Sept 5. Exam dates: midterm1 25th Sept. midterm2 30th Oct. final 9th Dec. 6. Read pages 1-34 of Chaisson & McMillan, then continue reading from p34 onwards -> Chapter 2. • Open Friday Nights – If classes in session – Weather permitting (call 392-5294 after 7PM to check) • Hours 8:30 – 10:00 p.m. • Location South of Union & West of Eng. Science • See class website for instructions about observing report. Reitz Union Physics Green Pond Engineering Science N o rt h -S o u th D r Museum Rd C en te r D r Wastewater Treatment Observatory Observing Report: Campus Observatory 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 Lecture #7 - Overview • Ancient Greeks & Aristotelian Physics – How did 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 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 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. 7.20 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 & basic trigonometry, he determined that the angle from the vertical was ~70 – this angle = the angle between Syene & Alexandria as seen from the Earth’s center – Alexandria was 5000 stadia from Syene, and so the circumference of the Earth was ~250,000 stadia. – But what is a stadium length?: Modern estimates: 157.2 - 166.7 m Eratosthenes estimated the Earth’s diameter, and thereby took the relative measurements of Aristarchus and placed them on an absolute scale 3600 Earth’s circumference 7. 0 5000 stadia Aristotle’s Physics – Corruptible Universe: a region of change near the Earth made up of four basic elements: • Earth, Water, Air, Fire • Natural Motions – Earthy material moved toward center of cosmos – Fire moved to highest heights – Air below Fire – Water between Earth & Air • Forced Motions – motion of objects on Earth require the application of a force, e.g. cart must be pushed in order to move Question • In Aristotelian physics, the Earth was stationary and at the center of the universe. • Imagine you lived at the time of Aristotle. What observations or evidence could you offer to support the idea of a stationary Earth? Aristotle’s Physics • Aristotle believed Earth was stationary and at the center of the universe because: – Natural motion of earthy material is toward the center of the cosmos. – We do not feel the Earth moving. – If Earth rotated then objects thrown upward would not drop back to their point of departure as they are observed to do. – If Earth moved about the Sun, then one should observe stellar parallax, yet this was not observed. Parallax is the apparent shift in the position of an object compared to background objects because of the motion of the observer Hipparchus • Added geometrical devices to the basic Geocentric model of Aristotle to explain the motions of the planets – Eccentric, Epicycle, Deferent • Eccentric: – a circle along which the Sun or a planet traveled around the Earth, with the Earth displaced from the center – explained the variable motion of the Sun & Planets through the ecliptic Hipparchus • Epicycle & Deferent – Deferent - a large circle, either centered on Earth or offset from Earth (eccentric) – Epicycle - smaller circle, centered on the circumference of the deferent – Combination of Epicycle & Deferent explained retrograde motion: • Planets fixed to the epicycle • Planets moved around epicycle which in turn moved around the deferent Ptolemy (125 A.D.) • Designed a complete geometrical model of the universe that accurately predicted planetary motions with errors within 50 • Most of the geometric devices and basic foundations of his model did not originate with him but were based on the models of the early Greeks such as Aristotle & Hipparchus • Wrote the Almagest (Greatest) – included the original works & models of Ptolemy – included a compilation of past works of Greeks, especially Hipparchus – 13 volumes “Well do I know that I am mortal, a creature of one day. But if my mind follows the winding paths of the stars Then my feet no longer rest on Earth, but standing by Zeus himself I take my fill of ambrosia, the divine dish.” Ptolemy’s Model • Earth was spherical & at center of cosmos - GEOCENTRIC • Cosmos is finite in size • Earth has no motions • Sun, Moon Planets exhibit uniform, circular motions – natural motions - no forces • Used devices of eccentrics, epicycles & deferents to explain the observed non-uniform motions of the Sun and planets along the ecliptic & retrograde motion. • Introduced equant to explain the variations in retrograde motions Ptolemy’s Model • Equant – point inside a circle, not at the center, from which motion along the circumference of the circle would appear to be uniform – lay opposite the circle’s center from the eccentric (the Earth) – nonphysical, totally geometrical device that broke the fundamental assumption that planetary motion had to be uniform along circles • With the introduction of the equant, celestial motions no longer had to be uniform around the centers of circles • Ptolemy used equant so that his model would fit observations Copernicus (1473-1543) • Developed a Heliocentric (Sun centered) model of the cosmos • Why? Ptolemy’s geocentric model lasted for centuries mainly because it accurately predicted celestial motions so there was little reason to discard it • Copernicus studied the works of Aristotle, Pythagoras & Plato • An offshoot of Plato’s philosophy asserted that Sun was godhead of all knowledge • Copernicus objected to equant based on aesthetics - equant not faithful to ideal of uniform motion - makes models too complex Copernicus’ Model • Copernicus worked on his new Heliocentric model for 20 years – Sun was placed at center of cosmos – Earth no longer static, but revolved around Sun once a year & rotated on axis once a day • His work was published in De revolutionibus in the year of his death • De revolutionibus took after the Almagest in outline and basic intention - to explain planetary motions • Even though it took 20 years to develop this model did not predict celestial motions any better than Ptolemy’s geocentric model! Heliocentric Model of Copernicus • Cosmos finite in size • Assumed no forces for heavenly motions – physics of Aristotle • Assumed uniform, circular motions – done for aesthetics - followed Aristotle • All heavenly spheres revolve around the Sun & the Sun is at the center of the cosmos – chosen based on aesthetics and simplicity • The distance from the Earth to the sphere of stars is much greater than the distance from the Earth to the Sun – accounts for lack of observed stellar parallax Heliocentric Model of Copernicus • The daily motion of the heavens relative to the horizon results from the Earth’s motion on its axis – aesthetic appeal since only 1 sphere is rotating not many – however, he did not account for the objection that if the Earth rotated, objects should be flung from the surface • The apparent motion of the Sun relative to the stars results from the annual revolution of the Earth around the Sun • The planets’ retrograde motion occur from the motion of the Earth relative to the other planets – retrograde explained as a natural result of the planet’s revolutions about Sun - what we observe is an illusion