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Kepler’s Laws of Planetary Motion

Kepler’s Laws of Planetary Motion. Mr. Finn November, 2008. Background. Greek astronomy Ptolemy Copernicus Tycho Brahe Johannes Kepler. Mars. Greek Astronomy. Planets “little wanderers”  hard to explain Mars red planet = “fiery one” retrograde motion  hardest to explain

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Kepler’s Laws of Planetary Motion

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  1. Kepler’s Laws of Planetary Motion Mr. Finn November, 2008

  2. Background • Greek astronomy • Ptolemy • Copernicus • Tycho Brahe • Johannes Kepler Mars

  3. Greek Astronomy • Planets • “little wanderers”  hard to explain • Mars • red planet = “fiery one” • retrograde motion  hardest to explain • Aristarchus • heliocentric system • explains retrograde motion

  4. Retrograde Motion of Mars Download file: “marsmovie.gif” Save in same directory as PowerPoint. Click on image to open html file - Click on “OK” when prompted.

  5. Ptolemaic System • The Algamest • geocentric system • orbits = system of epicycles • explains retrograde motion • infinitely malleable • adjusts to new data • extremely accurate predictions

  6. Copernican System • Heliocentric system • planet orbits = circles • not centered on Sun, but points nearby • explains retrograde motion • simple but inaccurate • not fully consistent with existing data • retains some epicycles

  7. Tycho Brahe • Observational astronomer • best observatory in Europe at Hven (1576-1596) • naked-eye observation • telescope by Galileo in 1609 • 20 years of data on planets • Compromise system • Earth at center • other planets orbit sun

  8. Johannes Kepler • Mathematician • worked for Brahe 1600-1601 • inherited Brahe’s astronomical data • Copernican system • Kepler strong believer • Trials & Tribulations • repeatedly fled wars, religious persecution • mother on trial for witchcraft

  9. Experimental DataKepler’s “War on Mars” • Brahe data on Mars • position relative to distant stars for 20yrs from Earth • Data relative to moving Earth • find positions 1 Martian year apart • Mars at same point in orbit around Sun • seen from different perspectives on Earth • Earth in different position in its orbit • where lines intersect = position of Mars • Find orbit without any preconceptions • traces out ellipse!

  10. Theory - Kepler’s Laws • Orbits of planets are ellipses with sun at one foci • Planets sweep out equal areas in equal times • Relationship between size of orbit & its period • P  a3/2 • P2/a3 = constant Harmonies in the Heavens

  11. Kepler’s 1st Law a = semi-major axis perihelion aphelion 2a Sun at one foci

  12. Kepler’s 2nd Law Equal Times: 1 2 3  4 Planet Equal Areas: A Sun planets move faster when closer to the sun

  13. Kepler’s 3rd Law Unknown to Kepler P  a3/2

  14. Newtonian Synthesis • Newton’s Universal Law of Gravity • Newton’s Laws of Motion • same laws explain heavenly and earthly motion • Aristotle believed two separate laws d Grand Synthesis #1

  15. Celestial Mechanics • Pierre-Simon Laplace • Treatise on Celestial Mechanics (1799) • Napoleon - Why is God missing? • Laplace: “I have no need of that hypothesis.” • “Je n’ai pas besoin de cette hypothèse.” • Rise of the “Mechanical Universe”

  16. Predictions • Edmund Halley predicts return of comet • Discovery of new planets • Neptune, Pluto • Effect of planets on each other • precession of orbits • Mercury partially unexplained

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