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Renaissance Astronomy

Renaissance Astronomy. Nicholas Copernicus 1473 - 1543. (Niklas Koppernigk). Developed a mathematical model for a Heliocentric solar system. Nicholas Copernicus. Synodic Period The orbital period of a planet as measured by a moving observer Sidereal Period

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Renaissance Astronomy

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  1. Renaissance Astronomy

  2. Nicholas Copernicus1473 - 1543 (Niklas Koppernigk) Developed a mathematical model for a Heliocentric solar system

  3. Nicholas Copernicus • Synodic Period • The orbital period of a planet as measured by a moving observer • Sidereal Period • The orbital period of a planet as measured by a stationary observer

  4. Nicholas Copernicus Planet Approximate Sidereal Period Mercury 88 days Venus 7.5 months Earth 1 year Mars 687 day Jupiter 12 years Saturn 30 years

  5. Nicholas Copernicus Planetary Configurations - Inferior Planets

  6. Nicholas Copernicus Planetary Configurations - Superior Planets

  7. Planetary Distances

  8. Tycho Brahe1546-1601 • Danish Aristocrat • Superb naked eye positions of planets • Observations (experiment) can decide between physical models

  9. Planet Sun Kepler’s Laws • First Law • Planets orbit the Sun in ellipses with the Sun at one focus of the ellipse

  10. Ellipses d1 d2 Focus Focus d1 + d2 = constant for any point on ellipse

  11. b a Ellipses a = Semi-major axis b = Semi-minor axis

  12. Eccentricity c a e = c/a

  13. Kepler’s Laws • Second Law • A line drawn from the planet to the Sun sweeps out equal areas in equal intervals of time

  14. The Search for Order • Perfect solids

  15. The Search for Order • Music of the Spheres

  16. Kepler’s Laws • Third Law • The orbital period of a planet squared is proportional to the length of the semi-major axis cubed. P2µ a3

  17. Using the Third Law P2µ a3 P2= (constant)a3 P2= a3 P measured in years, a in AU, object orbits Sun

  18. Kepler’s Laws • Empirical • Kepler could not explain why the planets orbited the Sun (he thought it had something to do with magnetism) • Universal

  19. Galileo Galilei1564-1642 • Among the first to turn a telescope to the sky • Developed the Scientific Method • Believed in the popularization of science • Developed the Law of Inertia

  20. Telescope Discoveries • Milky Way • Objects exist that Aristotle knew nothing about - the combined light of many faint stars can produce an observable result.

  21. Telescope Discoveries • The Moon • Mountains, valleys (Earthlike) features were observed. • But the Moon was in the Celestial Realm

  22. Telescope DiscoveriesThe Moons of Jupiter • Clear example of four objects that do not orbit the Earth. • If Aristotle was wrong here, could he not also be wrong in other areas?

  23. Telescope DiscoveriesPhases of Venus • The full range of phases cannot happen in the Geocentric Model.

  24. The Phases of VenusGeocentric Model

  25. The Phases of VenusHeliocentric Model

  26. Telescope DiscoveriesSunspots • Showed they were really on the Sun • The Sun was the physical mani-festation of God • Board of Inquisition

  27. The Trial of Galileo

  28. Isaac Newton1642 - 1727

  29. Newton’s Laws The 1st Law A body continues to move as it has been moving unless acted upon by an external force.

  30. Newton’s First Law • No mention of chemical composition • No mention of terrestrial or celestial realms • Force required when object changes motion • Acceleration is the observable consequence of forces acting

  31. Newton’s Laws The 2nd Law The Sum of the Forces acting on a body is proportional to the acceleration that the body experiences S F  a S F = (mass) a

  32. Newton’s Laws The 3rd Law For every action force there is an equal and opposite reaction force (You cannot touch without being touched)

  33. m M d Newton’s Universal Gravitation Two masses separated by a distance

  34. Newton’s Universal Gravitation

  35. Newton’s Universal Gravitation • Inverse Square Law Separation Force R F 2R ¼F 3R 1/9F ½R 4F ¼R 16F

  36. Newton’s Universal Gravitation The force of gravity cannot be made zero. • G is small • 6.67 X 10-11 N m2/kg2 • Mass causes gravity • Only one kind of mass • Contrast with the electric force

  37. m M The Apple

  38. Gravity at Work • All objects fall at the same rate in a gravitational field. • Leaning Tower of Pisa - Galileo • Galileo’s Experiment on the Moon • Apparent weightlessness • Lack supporting force

  39. Orbiting • Falling without getting closer to the ground. • Newton’s estimate of orbital velocity • Examples: • Space Shuttle • Elevator • Amusement Park Rides

  40. Moon F R Earth The Earth and Moon

  41. Orbiting - the Complete Story

  42. Velocity Shape < vorb Ellipse vorb Circle vorb<v<vesc Ellipse Hyperbola vesc Parabola > Vesc Hyperbola Circle Ellipse Parabola Link

  43. Where was Newton Wrong? • Moving too fast • Close to the speed of light • Solution was Special Relativity (1905) • Too close to a large gravitational field • Solution was General Relativity (1917) • On very small scales • Inside the atom • Solution was Quantum Mechanics (1927)

  44. The Principle of Elegance • Physicists look for symmetry • Occam’s Razor

  45. End of Renaissance Astronomy

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