ASTRONASTROPHYS 1 AST 3018
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Ms. Adrian Buckridge
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This 5 page Class Notes was uploaded by Ms. Adrian Buckridge on Friday September 18, 2015. The Class Notes belongs to AST 3018 at University of Florida taught by Elizabeth Lada in Fall. Since its upload, it has received 24 views. For similar materials see /class/206984/ast-3018-university-of-florida in Astronomy at University of Florida.
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Date Created: 09/18/15
Ptolemy 125 AD Designed a complete geometrical model of the universe that accurately predicted planetary motions with errors within 50 Most ofthe geometric devices and basic foundations of his model did not originate with him but were based on the models ofthe early Greeks such as Aristotle amp Hipparchus Wrote he Almagest Greatest included the original works amp models of Ptolemy included a compilation of past works of Greeks especially Hipparchus 13 volumes Ptolemy s Model Earth was spherical amp 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 amp deferents to explain the observed nonuniform motions of the Sun and planets along the ecliptic amp retrograde motion Introduced eguant to explain the variations in retrograde motions Ptolemy s Equant point inside a circle not at the center 39om which motion along the circumference o the circle would appear to be uniform opposite the circles center 39om the eccentric the Earth that broke Jndamental assumption of uniform circular motion Celestial motions no longerhad to be uniform around the centers of circles W ZDGZEnEyaluprdra Britannicach my a t spam as suns Copernicus 14731543 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 amp 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 to 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 amp rotated on axis once a day His work was published in De revolutionibus in the year of his death De revolutionbus took after the Almagest in outline and basic intention to explain planetary motions Even though it took 20 years to develop this model did predict celestial motions any better than Ptolemy s geocentric model Irru w y com 53 y r 211333 l Heliocentric Model of Copernicus Cosmos nite in size Assumed no forces for heavenly 39 e S Physics of Aristotle Assumed uniform circular motions done for aesthetics followed Aristotle All heavenly spheres revolve around the sun amp the sun is at the center ofthe 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 many however he did not account for the objection that ifthe earth rotated objects should be ung from the su ace 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 Retrograde Motion Explained Copernican Model Copernicus eliminated epicycles to explain retrograde motion Eliminated equant kept uniform circular motion Needed to account for variations in planetary motion so he was forced to add many smaller circles Violated Aristotelian physics amp did not offer new physical ideas to support his model Didn t predict motions any better than Ptolemy s model Retrograde Motion Explained When the earth passes any of the outer planets or when the earth is passed by the inner ones retrograde motion occurs Passing is key to retrograde motion in the heliocentric model Ptolemy Copernicus Tycho s Observations He made a long series of W observations ofthe motions of the planets Very accurate since they were made with a very large quadrant circle lt05 arc minute Made repeated observations and took the average to reduce the errors Made observations over many years 15761591 Realized the motions of planets did not match the predictions of Ptolemy Tycho s Cosmology Refuted Copernican system Placed the earth at the center Due to his inability to measure parallax believed in Aristotlean physics Realized that the Ptolemaic system failed Compromise Stationary earth at center Sun moves around the earth All other celestial bodies move around the sun His worked no better than Ptolemy He needed better mathematics Tycho Brahe 15461601 Danish born member of nobility Stolen by his uncle and adopted as his own son Trained as a lawyer but secretly studied astronomy alter being impressed that mortals could predict astronomical events Very arrogant and hard to get along with and played the role ofa courtly prince with a gold e Supported by the King Frederick H of Denmark he built and observatory on the island of Hven with one ton of gold His adopted father saved Frederick 39om drovming but then died of pneumonia Tycho s Supernova The supernova of 1572 Noticed a brilliant star had appeared in Cassiopeia Observed that it faded slowly over the following 2 years Demonstrated that the universe was changing and imperfect Showed that it had the same position no matter where on earth it was observed thus it was at a great distance Was born a commoner in Germany His father was a mercenary His mother was raised by an aunt who was Went to college at Tubingen were he was While in Graz he felt that the 5 perfect Platonic Attempted to get observations of the planets t Kepler 15711630 burnt as a w tch recognized as a mathematical genius and went toteach math at a Protestant School in Graz solids could explain the motion of the 6 known planets but was incompeten Kepler and Brahe Meet Brahe had to leave Hven for Prague because Fredrick ll drank himself to death Kepler was driven out because the Catholics took over Graz and drove out the Protestants Tycho knew he needed a mathematician to help him model his observations They meet Feb 4 1600 and fought continually Tycho feared that Kepler would eclipse him so he would only sho im data on Mars his most challenging o ject Tycho died October 21 1601 39om over partying Kepler got Tycho s data from the family follow a death bed request by Tycho Let me not seem to have died in vainquot Properties of Ellipses Ellipses belong to the family of conic sections the intersection of a plane and a cone The shape is de ned b the separation between the two foci ofthe ellipse When the foci coincide the shape is a circle As the foci separate from each other the ellipse gets atter The amount byWnich an ellipse i ers 39om a circle is de ned as an ellipse s 39 39 Each point on an ellipse has the property that the sum of its distances to the two foci is the The line through the foci to both sides of the ellipse is called the Semi major m Kepler s 1st Law Kepler Solves The Mystery of Planetary Motions It took Kepler 8 years to solve the motion of Mars He tried various combinations of circular motions He finally abandoned circular motion and tried ovals and other geometric shapes He found that an ellipse could produce the motions of the planets Kepler s 1St Law of Ellipses 1609 Planets move in elliptical orbits with the sun at one focus The other focus is empty amp located in space m u gt Distance between the planet and the sun changes as the planet moves along its elliptical orbit Planet move along orbits which have a special and regular geometrical shape Gets rid of idea of uniform circular motions Kepler s 2nd Law of Equal Areas 1609 Kepler noted that Mars slowed down when it approached the sun He found that a W 39 anytime during its orbit Planetary motions are nonuniform but vary in a regular way Planets move more slowly when they are far from the sun and fastest when they are nearthe sun The increase in speed as a planet moves toward the sun makes it appear that the sun is pulling on the planet Kepler s 2nd Law Kepler s 3nd Harmonic Law 1618 twmmm The Harmonic Law p2 k a3 p is the period ofthe planets orbit a is the planets average distance to the Sun k is a constant which is the same for all planets E mm mm mm The more distant a planet from the Sun The slower it moves in its orbit The longer it takes to complete and orbit Since a single constant works for all planets suggests a single physical cause for their orbits Kepler s Laws Kepler s scheme correctly described planetary motions when compared to the accurate observations of Tycho Together laws 2 and 3 imply that there exists a force between the sun and planets that weakens with increasing distance Invested Sun with physical properties necessary for the uniform description of planetary motions Kepler recognized there must be a force at work but could not gure out what it was He speculated it may be magnetism Astronomy Enters a New Era Astronomical objects are viewed as actual bodies not distant ethereal or mythical entities Realization that the laws of nature are the same for both the earthly and heavenly domains
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