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The Ptolemaic Model Survives

The Ptolemaic Model Survives. Since the Ptolemaic model matched observations sufficiently and no contrary evidence was produced, it was supported for nearly 1,500 years! After all, if the Earth was moving, shouldn't we feel it?

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The Ptolemaic Model Survives

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  1. The Ptolemaic Model Survives • Since the Ptolemaic model matched observations sufficiently and no contrary evidence was produced, it was supported for nearly 1,500 years! • After all, if the Earth was moving, shouldn't we feel it? • Also, the Greeks were smart enough to realize that if the Earth was orbiting the Sun, it would produce stellar parallax • The Greeks didn't believe it existed because they didn't have telescopes to observe such small variations in a star's position • On top of all this, the Dark Ages provided relatively little advance in any sciences for Europe

  2. Ptolemy’s Geocentric Model

  3. Astronomy in the Dark Ages • While Europe was suffering through the Dark Ages, Islamic nations were undergoing a golden age of astronomy • Much of the knowledge of the Greeks was preserved and expanded upon during this time • Many of the proper names for stars are relics of this era • Rigel, Betelgeuse, Vega ...

  4. Tycho Brahe (1546-1601) • Worked to improve the quality of observations • Still without the use of a telescope • Observed a “new star” • Supernova • Recorded positions of many stars to within less than an arcminute accuracy • Best naked eye observations ever made • Strongly believed in the Sun-centered system, but could not detect parallax • Developed a model with the Sun orbiting the Earth, but all other planets orbiting the Sun

  5. Kepler (1571-1630) • Student of Tycho • Wanted to accurately match the observations of Mars – off by as much as 8 arcminutes • A small angle, but Tycho’s observations were excellent • Developed a new model that did not rely on circles, but instead used ellipses • Kepler’s 3 Laws of Motion

  6. Kepler’s First Law • The orbit of each planet about the Sun is an ellipse with the Sun at one focus

  7. Kepler’s Second Law • As a planet moves around its orbit, it sweeps out equal areas in equal times • To do this, a planet must move slower at aphelion than it does at perihelion

  8. Kepler’s Third Law • More distant planets orbit the Sun at slower average speeds, obeying the mathematical relationship of p2=a3 (p2=ka3) where p is the planet’s orbital period in years and a is the average distance from the Sun in AU’s. • What about comets? Assume a comet has a high eccentricity of 0.95 with a semi-major axis of 40 AU. How long will it take this comet to orbit the Sun? Where at in its orbit will it spend most of its time? Near the Sun at perihelion? Far from the Sun at aphelion? Or maybe somewhere in between?

  9. Galileo (1564-1642) • Answered the 3 main objections to the Copernican Model • Earth could not be moving since birds, falling objects, and clouds would all be left behind • Noncircular orbits contradicted Aristotle’s views that the heavens must be perfect • Stellar parallax should be seen, but isn’t

  10. Galileo’s Answers • All objects will remain in motion until a force acts to stop them • Later revisited by Isaac Newton • Observed sunspots with his telescope, noting that the “heavens” can be imperfect • Did not invent the telescope however • Showed that stellar objects are much further away than previously estimated. Thus, parallax can exist, but is too small to detect

  11. Galileo’s Accomplishments • Sunspots • Jupiter has moons (He observed 4 of them; Ganymede, Callisto, Europa, and Io) • ***Observed phases of Venus *** • Venus must orbit the Sun – this pretty much killed geocentrism • Earth-centered system put to rest • Denounced by Catholic Church and forced recant his claims in 1633 to save his life • Although the Church recognized Galileo was right many years ago, he wasn’t formally vindicated until 1992

  12. Phases of Venus • How did the phases of Venus prove that it must be orbiting the Sun and not the Earth?

  13. Summary • Evidence of astronomical observations present in nearly every culture imaginable • The Greeks were the first to explain motions through the use of models • The Earth-centered model lasted for many years, mainly due the persuasive abilities of Aristotle (who turned out to be wrong) • Sun-centered system gained momentum through the work of Copernicus • Tycho, Kepler, and Galileo picked up where Copernicus left off and the Earth-centered system was finally proved without a trace of doubt • Tycho’s very accurate measurements • Kepler’s 3 laws of planetary motion • Galileo’s telescope and observations

  14. Geocentric vs. HeliocentricReaction of Contemporaries • Martin Luther (1483-1546): [Copernicus] “is a fool who wishes to reverse the entire scheme of astronomy; but sacred scripture tells us that Joshua commanded the Earth to stand still, not the Sun.” • Conservative who wanted to reform Church by returning it to a simpler, less corrupt time. • Agitator for the abolishment of indulgences (payment to lessen time of deceased in purgatory). • A founder of the Protestant branch of Christianity. • Response of Catholic Church to threat posed by the Reformation Movement: • At first, tolerance of dissent and liberal treatment of new ideas. • Later, institution of the Counter-Reformation and the Inquisition. • Giordano Bruno (1548-1600): burned at the stake for advocating that stars are suns in their own right, and that there is a plurality of worlds like the Earth. • Galileo (1564-1642): • Ah! Here is the person to decide the debate.

  15. Galileo Galilei (1564 – 1642) "Eppur Si Muove“"(And, yet it moves!") • 1610 “Siderius Nuncius” (The Starry Messenger) • “Spots” on the Sun! • The Moon has mountains, craters, rocky surface with imperfections! • The “planet” Jupiter is not a pinpoint star – but a disc in the sky! WITH MOONS! • Venus has “PHASES” like the MOON

  16. Galileo Galilei (1564 – 1642) “Revealing great, unusual and remarkable spectacles, opening these to the consideration of every man, and especially of philosophers and astronomers….” SUNSPOTS

  17. Galileo Galilei (1564 – 1642) The Moon Has Mountains and Valleys

  18. Galileo Galilei (1564 – 1642) Phases of Venus Galileo observed that Venus showed phases entirely like those of the moon from full to crescent, which it must do if the Copernican theory was correct. According to the Ptolemaic theory Venus would have to be a perpetual crescent.

  19. Galileo Galilei (1564 – 1642) Jupiter Has Moons Galilean Moons – 4 Largest “moons” of JupiterIo, Europa, Callisto, & Ganymede

  20. Galileo Galilei (1564 – 1642) 1632: "Dialogo Dei Massimi Sistemi" (In Italian! Not Latin! For the common people!) He published his masterpiece, Dialogue on the Two Chief World Systems, in which he had two people, one representing the view of Ptolemy and other the view of Copernicus, present their arguments before an intelligent layman. Galileo of course gave the Copernican the brilliant best of the battle. The Pope was persuaded that Simplico, the character who upheld the views of Ptolemy in the book, was a deliberate and insulting caricature of himself. The book was all the more damaging to those who felt themselves insulted, because it was written in vigorous Italian for the general public (and not merely for the Latin-learned scholars) and was quickly translated into other languages -- including Chinese!

  21. Galileo Galilei (1564 – 1642) Scientific Martyr • Teaches Heliocentric Ideas • Claims “proof” for Earth’s motion. • Trial by Church (threatened with instruments of torture), forced to recant views (1633). • Confined to house arrest. Formulates “new science” of mechanics. • Loses his sight (blinded) by Sun observations • Most influential combination of experimentalist and theorist world has ever seen. • Often credited rightly with having started modern science.

  22. Johannes Kepler’s Work Advancing science, more than ethics, Kepler simply stole the observations upon the sudden and ironic death of Tycho Math skills - Kelper's skills were extraordinary. He could not reconcile Tycho's very careful observations with the Models of Ptolemy, Copernicus, nor Tycho!!!

  23. An Idea! Orbits are not Circles! His incredible effort took 29 years!! He waged a "war" on understanding the orbit of Mars. Heliocentric Model fits the observations best from a simple view point (Copernician) But *not* circular orbits. Ellipses

  24. Kepler’s Three Empirical Laws of Planetary Motion 1. The orbital paths of the planets are elliptical, with the Sun at one focus

  25. Kepler’s Three Empirical Laws of Planetary Motion 2. An imaginary line connecting the Sun to any planet sweeps out equal areas in equal time.. Area 1 Area 2

  26. Kepler’s Three Empirical Laws of Planetary Motion 3. The square of a planet’s orbital period is proportional to the cube of its semi-major axis. P2(years) = A3(astronomical units) 1 Astronomical Unit = The Earth-Sun Distance (98 million miles)

  27. Kepler’s Third Law

  28. But!!….. Kepler did not know WHYplanets move as they do.

  29. Isaac Newton (1642-1727) Born in England on Christmas day. Bubonic Plague 1665? While home for 2 years with nothing to do he made his most profound discoveries and proposed his most startling theories.

  30. Time Marches On In 1684 – was in a discussion with Edmund Halley, when Halley remarked “But why do planet’s move the way they do?” Newton astounded everyone with the answers ( from his work 20 years earlier!).

  31. “Philosophiae Naturalis Principia Mathematica” Newton’s Three Laws of Motion The laws explained not only why planets move as they do, but why objects in general move as they do.

  32. Newton’s First Law • Objects at rest stay at rest unless a “net force” is applied. • Objects in uniform straight line motion stay in straight line motion unless a “net force” is applied. • Note: Newton’s First Law Does NOT say… • This law does not say that every moving object has a “force” acting on it! • This law does not say an object at rest has “no force(s)” acting on it!

  33. Newton’s Second Law The acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object. a = Fnet/m OR Fnet = ma

  34. Newton’s Third Law Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. “To every action there is an equal and opposite re-action.”

  35. Law of Universal Gravitation Matter attracts matter

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