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Ch 2--Gravitation/Planetary Motion

Ch 2--Gravitation/Planetary Motion. “Finally we shall place the Sun himself at the center of the Universe. All this is suggested by the systematic procession of events and the harmony of the whole Universe, if we only face the facts, as they say, with both eyes open.” Nicolaus Copernicus.

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Ch 2--Gravitation/Planetary Motion

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  1. Ch 2--Gravitation/Planetary Motion ASTR103, Sec 3, GMU, Dr. Correll

  2. “Finally we shall place the Sun himself at the center of the Universe. All this is suggested by the systematic procession of events and the harmony of the whole Universe, if we only face the facts, as they say, with both eyes open.” Nicolaus Copernicus

  3. Greek Cosmology • The Greek tradition of scholarship leaves a written record of their studies • The Greeks developed a cosmology--a theory of the overall structure and evolution of the universe • incorporated mathematics • but was not truly scientific in that it was limited by an absence of observational corroboration • Nevertheless, their tradition became the dominant world view in Europe and the Middle East ASTR103, Sec 3, GMU, Dr. Correll

  4. Aristotle (384-322 BCE) • Terrestrial and celestial realms different • Terrestrial realm is corruptible • Celestial realm begins at Moon’s orbit outward and is incorruptible • Terrestrial matter composed of four elements • Earth • Water • Air • Fire ASTR103, Sec 3, GMU, Dr. Correll

  5. Aristotelian Concepts of Motion • Natural motion - "like seeking like” • Earth and water go down • Air and fire up • Forced or violent motion - “forces moving like away from like” • Example - throwing rock upward Fire Air Water Earth Forced motion Natural motion Earth ASTR103, Sec 3, GMU, Dr. Correll

  6. Celestial Motion Prime Mover Celestial realm Planet Moon Earth Sphere of Stars Terrestrial realm ASTR103, Sec 3, GMU, Dr. Correll

  7. Aristarchus (ca. 310 - ca. 230 B.C.) • On the Sizes and Distances of the Sun and Moon • Estimated Sun 20 times farther from Earth than Moon (closer to 400) • Natural to put largest and only self-luminous body the Sun at center--minority opinion • Explained • Daily movement of heavens by Earth’s rotation on its axis • Earth and planets revolve about Sun ASTR103, Sec 3, GMU, Dr. Correll

  8. Geocentric Becomes Dominant • Geocentric became dominant - Ptolemaic system (2nd cent. CE) • Geocentric cosmology dominates until Copernicus’ publishes his book in 1543 CE ASTR103, Sec 3, GMU, Dr. Correll

  9. Geocentric System Order Saturn Jupiter Mars Sun Venus Mercury Moon Earth ASTR103, Sec 3, GMU, Dr. Correll

  10. Accounting for Retrograde Motion Retrograde motion--change in direction of motion of a planet as seen against the fixed stars ASTR103, Sec 3, GMU, Dr. Correll

  11. Geocentric Cosmology • Ptolemaic System used Cycles, Deferents and Epicycles to account for retrograde motion ASTR103, Sec 3, GMU, Dr. Correll

  12. Heliocentric Cosmology • Copernican model has a more “natural” explanation of retrograde motion--especially in hindsight ASTR103, Sec 3, GMU, Dr. Correll

  13. Which is better? • As observations of retrograde motion became more detailed, epicycles within epicycles were required, making a very complicated system • Occam’s Razor (William of Occam, 14th Century)--Eliminate unnecessary hypothesis, or “keep it simple” • But true test is observation…so here’s how it happened. ASTR103, Sec 3, GMU, Dr. Correll

  14. Nicolaus Copernicus (1473-1543) ASTR103, Sec 3, GMU, Dr. Correll

  15. Nicolaus Copernicus • Studied mathematics, philosophy, astronomy, and astrology at University of Krakow in Poland • Studied law and medicine at Universities of Bologna and Padua in Italy • Elected Canon of Ecclesiastical Law by the Church • 1543, published, On the Revolutions of the Heavenly Orbs ASTR103, Sec 3, GMU, Dr. Correll

  16. Nicolaus Copernicus 1543, publishedOn the Revolutions of the Heavenly Orbs ASTR103, Sec 3, GMU, Dr. Correll

  17. Copernican System Epicycle • Orbits perfect circles (incorrect!) • Earth and Moon move on circles • Earth about Sun • Moon about Earth • Planets move on epicycles, which move on deferents (fewer epicycles than Ptolemaic system) • Predictive accuracy same as Ptolemaic system Moon Planet Earth Sun Sun Deferent ASTR103, Sec 3, GMU, Dr. Correll

  18. Arguments For Copernican System • Quantitative material in his book • Predictive accuracy of Ptolemaic/Copernican systems same • Reduction of number of elements of Copernican system compared to Ptolemaic • Problem: Earth not at the center means you have the possibility of seeing parallax in the position of planets as seen at different seasons on Earth • Parallax may not be observable because of immense distances of sphere of stars ASTR103, Sec 3, GMU, Dr. Correll

  19. Arguments Against • Damage to Aristotelian science, which was more than just a physical system of world • Aristotelian science had become Church orthodoxy - an article of faith • Parallax not seen (should it be?) • Copernican system offered no observation which was explainable only by it and not by Ptolemaic system…at the time ASTR103, Sec 3, GMU, Dr. Correll

  20. Most Important, though... Copernicus’ idea was the watershed event that started a revolution in thought. It even gave a new meaning to the word “revolution”! The Copernican revolution forever displaced the earth and its humble inhabitants from the center of the universe! ASTR103, Sec 3, GMU, Dr. Correll

  21. Tycho Brahe (1546-1601) ASTR103, Sec 3, GMU, Dr. Correll

  22. Tycho Brahe • Extensive naked-eye observations which were basis for acceptance of heliocentric cosmology • Observations accurate to 1 minute of arc - best naked-eye • Published his own cosmology • Planets orbit Sun • Sun and Moon orbit Earth ASTR103, Sec 3, GMU, Dr. Correll

  23. Tycho Brahe • Parallax measurements of supernova in 1572 ASTR103, Sec 3, GMU, Dr. Correll

  24. Johannes Kepler (1571-1630) …and his three laws ASTR103, Sec 3, GMU, Dr. Correll

  25. Johannes Kepler • Convinced that mathematical relations existed that could make sense of planetary motion • Acquired and analyzed Brahe's observations of planets • 1609, New Astronomy, contains first two laws of planetary motion • 1619, The Harmonies of the World, contains third law • Extended laws derived from basically Mars to all planets, regarded laws as universal--very imaginative step • His big idea--orbits are ellipses, not circles! ASTR103, Sec 3, GMU, Dr. Correll

  26. Johannes Kepler • First Law--The orbit of a planet about the Sun is an ellipse with the Sun at one focus ASTR103, Sec 3, GMU, Dr. Correll

  27. Johannes Kepler Semi-minor axis "a" Semi-major axis ASTR103, Sec 3, GMU, Dr. Correll

  28. Johannes Kepler • Second Law--A line joining a planet and the Sun sweeps out equal areas in equal intervals of time ASTR103, Sec 3, GMU, Dr. Correll

  29. Johannes Kepler • Third Law--The square of a planet’s sidereal period around the Sun is directly proportional to the cube of the length of its orbit’s semimajor axis • Where P is the period in years • and a is the semimajor axis in AU of elliptical orbit ASTR103, Sec 3, GMU, Dr. Correll

  30. Johannes Kepler ASTR103, Sec 3, GMU, Dr. Correll

  31. Galileo Galilei (1564-1642) ASTR103, Sec 3, GMU, Dr. Correll

  32. Galileo Galilei • 1632, The Dialogues of Galileo Galilei on the Two Principal Systems of the World: The Ptolemaic and Copernican • Powerful enemies convinced Pope that Galileo had cast Ptolemaic system in unfavorable light • 1633, book banned and Galileo publicly humiliated before papal tribunal • Forced to recant Copernican views • Last 9 years of life spent in Arcetri under house arrest ASTR103, Sec 3, GMU, Dr. Correll

  33. Galileo Galilei • Galileo’s dispute with Church often recited as classic example of “war between theology and science” • mostly true, but there were also conflicts of personalities--priests and scientists are human, too! ASTR103, Sec 3, GMU, Dr. Correll

  34. Galileo’s Astronomical Observations • Devised telescope in 1609 having heard of its invention in Holland • Discoveries and observations with telescope • Jupiter's four large satellites • Craters and mountains on Moon • Phases of Venus • Milky Way composed of individual stars • Observes sunspots (not new) • 1609, published discoveries in Starry Messenger ASTR103, Sec 3, GMU, Dr. Correll

  35. Galileo’s Astronomical Observations ASTR103, Sec 3, GMU, Dr. Correll

  36. Method of Experimental Science • Galileo establishes standard for doing experimental science with Starry Messenger • Design experiment • Build equipment • Take and analyze data • Publish results ASTR103, Sec 3, GMU, Dr. Correll

  37. External Force Modern Concepts of Motion • Body in motion will continue indefinitely at same speed and in same direction (law of inertia) • Force is responsible for change in body’s motion ASTR103, Sec 3, GMU, Dr. Correll

  38. Falling Bodies • Falling body one of most common experience, but also one of most mysterious of experiences • In free fall in vacuum, all objects--of whatever weight, size, or constitution--fall given distance in same interval of time • Free fall is uniformly accelerated motion, i.e., gains equal increments of speed in equal times • Earth exerts influence on body in free fall or rolling down an inclined plane - gravity (not new to scientific discussion) ASTR103, Sec 3, GMU, Dr. Correll

  39. Falling Bodies (cont) Less Massive Body Massive Body Time Distance 0.1 s 0.05 m 0.2 s 0.20 m 0.3 s 0.44 m 1.5 m 0.4 s 0.78 m 0.5 s 1.23 m Strike Together Surface of Earth ASTR103, Sec 3, GMU, Dr. Correll

  40. Galileo’s Contribution • Galileo brings together strands of medieval thought regarding space, time, and motion • 1632, published Dialogues on the Two Great World Systems • 1638, published Discourses and Mathematical Demonstrations Concerning Two New Sciences Pertaining to Mechanics and Local Motion ASTR103, Sec 3, GMU, Dr. Correll

  41. Isaac Newton (1642-1727) ASTR103, Sec 3, GMU, Dr. Correll

  42. Isaac Newton (1642-1727) • Educated at Trinity College, Cambridge University • Entered in 1661 to study mathematics • Years of 1665 and 1666 were Plague years with university closed • Newton spent 1665-66 on family farm • 1687, published Mathematical Principles of Natural Philosophy • Instant success revealing Newton's genius • 1704, published Opticks ASTR103, Sec 3, GMU, Dr. Correll

  43. Newton's Principia ASTR103, Sec 3, GMU, Dr. Correll

  44. Newton's Principia • A most impressive work • Lays out essential physical concepts and laws • Develops a new mathematical formulation of theory • Application to many long-standing problems • Planetary motion • Lunar motion • Tides • Etc. ASTR103, Sec 3, GMU, Dr. Correll

  45. Newton's Principia • Provides a standard for doing scientific investigations (along with Opticks in 1704) • Establishes for all times mathematics not only as language of physics (and all science) but as a means of knowing ASTR103, Sec 3, GMU, Dr. Correll

  46. Newton’s Laws Newton’s Law of Gravity: • Mutual gravitational attraction is proportional to both masses, inversely proportional to distance squared • F is force • G is gravitational constant • m is mass of each body • r12 is separation Newton’s Laws of Motion: • Bodies move in uniform (straight line) motion unless acted on by a force • Acceleration proportional to force, inversely proportional to mass F is force a is acceleration m is mass • To every action there is an equal and opposite reaction ASTR103, Sec 3, GMU, Dr. Correll

  47. Law of Gravity • Always attractive, never repulsive • Based on concept of "action-at-a-distance” • Ability of one body to influence motion of second body without physical contact • For two spheres, r12 is distance between centers, not surfaces • One can think of spherical bodies attracting each other as if they were mathematical points F21 F12 m2 m1 r12 ASTR103, Sec 3, GMU, Dr. Correll

  48. Newtonian Mechanics • Newton's theories of motion and gravitation reigned for over 200 years • accurately described all known phenomenon until late 1800s • precession of perihelion of mercury different than predicted • new theory of light and electomagnetism has some philosophical problems ASTR103, Sec 3, GMU, Dr. Correll

  49. Geometries of Space • Euclidean space - space of our experience • Euclid, Aristotle, Galileo, Newton • Non-Euclidean space - understood from mathematical arguments, not practical experience • Einstein, and others ASTR103, Sec 3, GMU, Dr. Correll

  50. General Relativity • 1916, general relativity devised by Einstein …gravity as curvature! ASTR103, Sec 3, GMU, Dr. Correll

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