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The Heliocentric Model

The Heliocentric Model. Justin Walega. In The Beginning…. Geocentric Model Symmetry Ptolemy. Imagery. Why?. Appeared all planets orbited regularly Earth is stable. Issues. Dancing planets Epicycles – Apollonius. Early Names. Philolaus Aristarchus Archimedes – a larger universe.

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The Heliocentric Model

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  1. The Heliocentric Model Justin Walega

  2. In The Beginning… • Geocentric Model • Symmetry • Ptolemy

  3. Imagery

  4. Why? • Appeared all planets orbited regularly • Earth is stable

  5. Issues • Dancing planets • Epicycles – Apollonius

  6. Early Names • Philolaus • Aristarchus • Archimedes – a larger universe

  7. Change? • Regiomontanus • Christianity • Calendar issues - Easter

  8. Copernicus • De revolutionibus orbium celestium - 1543 • (On the Revolutions of the Heavenly Spheres) • Gave mathematical description with moving Earth • Spheres • What’s gravity? • Simplest solution

  9. Copernicus • Ptolemy’s methods • 100,000 instead of 60 • Chords • Methods of solving • Plane and spherical triangles

  10. Spherical Triangles • “If in the same sphere two triangles have right angles and another angle equal to another angle and one side equal to one side – whether the sides be adjacent to the equal angles or lie opposite one of the equal sides – they will have the remaining sides and the remaining angle equal to the remaining angle.”

  11. New Issues • Copernicus – Sun not quite center • Protestant vs. Roman Catholic • Chronicles 16:30: "the world also shall be stable, that it be not moved." • Used for calculations rather than accurate • 17th Century

  12. Ancient India • Aryabhata – Aryabhatiya • Spinning axis • Relation to Sun • Nilakantha Somayaji • Aryabhatiyabhasa - commentary • Planets around Sun around Earth • Same as Tycho Brahe’s model

  13. Islamic Views • Alhazen’s Doubts on Ptolemy • Questioned his details • Proposed axis rotation • Heliocentric concept abandoned multiple times • Tusi & Qushji – moving Earth • Never reached heliocentric model

  14. Advancing Through Time • Galileo – Starry Messenger (1610) • Telescope • Galileo’ dialogue • Kepler – elliptical orbit • Eccentricity

  15. Earth’s Eccentricity • (π/4) x ( (186-179)/(186+179) ) ≈ 0.015 • 186 days: March equinox -> Sept. equinox • 179 days: Sept. equinox -> March equinox

  16. The planetary orbit is an ellipse • The Sun is a focal point, not the center

  17. Neither the linear speed nor the angular speed of the planet in the orbit is constant, but the area speed is constant.

  18. The square of the sidereal period is proportionate to the cube of the mean between the maximum and minimum distances from the Sun. • P is the orbital period of planet and a is the semimajor axis of the orbit

  19. Recent Times • Not center of universe • Infinite? Position?

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