Ptolemy to Galileo Lecture 3 Astronomy of the ancients Many ancient cultures took note of celestial objects and celestial phenomena They noted certain patterns in the heavens and were able to construct calendars The Chinese Egyptians Britons Mayans and others have left us evidence of their interest in astronomy Stonehenge can be used as an astronomical calculator Greek scientist Aristotle showed that the Earth is spherical Aristotle supported his statement that the Earth is round with observations The Earth s shadow on the Moon during a lunar eclipse is always circular The only object that always throws a circular shadow is a sphere The only object whose shadow is always circular is a sphere Aristotle 384 BC 322 BC Eratosthenes ca 200 BC Alexandria Egypt measured the Earth s circumference Eratosthenes 42 000 km Actual 40 000 km Greek astronomers developed a geocentric Earth centered model for the universe Basic assumptions of Greek astronomers Spherical Earth is stationary at the center of the universe Earth is corrupt heavens are perfect Heavenly bodies move with uniform circular motion Bad assumptions bad conclusions Hipparchus of Rhodes 190 120 BC Important early astronomer catalogue of 1000 stars classified stars by brightness discovered precession of the equinoxes determined obliquity of the ecliptic synodic periods of planets inclination of Moon s orbit place of Sun s apogee eccentricity of the Sun s orbit estimate of the Moon s distance using the diameter of the Earth as a baseline He put astronomy on a geometrical basis Ptolemy used epicycles to explain the retrograde motions of planets Ptolemy worked in Alexandria was active around AD 140 Used results of Hipparchus research and measurements to create a model of how the solar system worked Wrote an astronomy text later called the Almagest the best Predicted positions of planets far into the future that were adequately accurate Basic structure of geocentric model Belief in Ptolemy s geocentric model lasted until the 16th century Cosmographia first published 1524 Geocentric models have problems explaining retrograde motion of planets Planets usually move west to east relative to stars during retrograde motion they move east to west Ptolemy s explanation of retrograde motion The planet P moves in a small circle called the epicycle The center of the epicycle A moves in a large circle called the deferent The combination of small and large circles produces loopthe loop motion Ptolemy s model did not fit data During the Middle Ages Ptolemy s model had to be fiddled with more epicycles were added The model was needlessly complicated because it was based on erroneous assumptions OCCAM S RAZOR entia non sunt multiplicanda praeter necessitatem entities should not be multiplied beyond necessity William of Occam c 1285 1347 Copernicus proposed a heliocentric model for the universe Mikolaj Kopernik 1473 1543 Poland Stated that Sun not Earth was at the center of the universe Basic structure of heliocentric model Sun is at center Earth revolves around Sun Earth rotates around axis In the heliocentric model of Copernicus retrograde motion of planets is naturally explained Retrograde motions occur naturally if planets further from the Sun move more slowly Example Earth and Mars Earth s orbital radius 1 A U Earth s orbital speed 30 km sec Mars orbital radius 1 5 A U Mars orbital speed 24 km sec As Earth laps Mars Mars appears to go backward as seen by observer on Earth Earth catches up with Mars a b Passes it b f Apparent westward motion Sees it move to east again g Heliocentric model of Copernicus met with considerable scientific resistance Why It implies that distance from Sun to stars is much greater than distance from Sun to Earth Stars do not vary much in brightness over the course of a year Stars do not show a large parallax over the course of a year r The parallax to the nearest stars is about 1 arcsec Radical aspects of Copernican model Earth is not at center Earth is moving Earth is just another planet Space is big REALLY big Conservative aspects of Copernican model Uniform Circular Motion assumed Epicycles still required Few questions 1 Do the inner planets show retrograde motions 2 See picture on the right Is it real 3 In that picture could you have Venus instead of Saturn tricky Few questions continued 4 See picture on the right Is it real 5 In that picture could you have Saturn instead of Venus 6 Could you have Mercury instead of Venus Tycho Kepler Galileo E pur si muove It still moves Galileo Astronomical movies The Phases of Venus http antwrp gsfc nasa gov apod ap060110 html When Moons and Shadows Dance Jupiter http antwrp gsfc nasa gov apod ap030227 html Large Sunspot Group Sun http antwrp gsfc nasa gov apod ap010411 html Tycho Kepler Galileo Key Concepts 1 Tycho Brahe made accurate measurements of planetary motion 2 Planetary orbits are ellipses with the Sun at one focus 3 A line between planet Sun sweeps out equal areas in equal times 4 The square of a planet s orbital period is proportional to the cube of its average distance from the Sun 5 Galileo made telescopic observations supporting the heliocentric model Tycho Brahe made accurate measurements of planetary motion Tycho Brahe 1546 1601 Danish astronomer Uraniborg Island given to Tycho by the Danish king Built an observatory supported by tenant farmers and government subsidy Cost the equivalent of 5 billion Hven Tycho s island Tycho was an excellent observer Built many instruments Quadrants that measured to 1 arcminute precision Measured as often as possible Attempted to evaluate errors Among the first to do such things sextant armillary sphere Tycho s contributions to astronomy Tycho discovered new star or nova upsetting ancient notion of perfect unchanging heavens Made very accurate measurements of planetary positions Copernican system Tycho s system Johannes Kepler 1571 1630 German Was Tycho s assistant Used Tycho s data to discover Three Laws of Planetary Motion Kepler s First Law of planetary motion The orbits of planets around the Sun are ellipses with the Sun at one focus Ellipse an oval built around two points called focuses or foci SIZE of ellipse Major axis longest diameter of ellipse Semimajor axis half the major axis SHAPE of ellipse Eccentricity distance between foci divided by major axis Foci close together ellipse nearly circular eccentricity close to zero Foci far apart ellipse very flattened eccentricity close to one Example Mars Semimajor axis 1 524
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