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Kepler Problem 开 普 勒 问 题

Kepler Problem 开 普 勒 问 题. 行星运动的描述 — — 运动学 地球人的观点 Sun path; analemma; star trails 历史的回顾 : 地心说 ； 日心说 ； 开普勒 开普勒问题的文化方面 开普勒问题的物理. 地球人的观点 Sun path; analemma; star trails. Sun path by Justin Quinnell. 2010 Analemma 地球仪 8 字曲线 by Tamas Ladanyi, TWAN. Star trails by Harold Davis. 星迹.

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Kepler Problem 开 普 勒 问 题

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  1. Kepler Problem 开 普 勒 问 题

  2. 行星运动的描述——运动学 地球人的观点 Sun path; analemma; star trails 历史的回顾: 地心说；日心说；开普勒 开普勒问题的文化方面 开普勒问题的物理

  3. 地球人的观点 Sun path; analemma; star trails

  4. Sun path by Justin Quinnell

  5. 2010 Analemma地球仪8字曲线by Tamas Ladanyi, TWAN

  6. Star trails by Harold Davis 星迹

  7. 历史的回顾: 地心说；日心说；开普勒

  8. The frontispiece to Galileo’s Dialogue Concerning the Two World Systems (1632). According to the labels, Copernicus is to the right, with Aristotle and Ptolemy at the left; Copernicus was drawn with Galileo’s face, however

  9. Claudius Ptolemy (127—152 working in Alexandria, Egypt ) Nicolaus Copernicus (1473—1543)

  10. 本轮 epicycle equant eccentric earth 均轮 deferent Ptolemy system(70 circles)

  11. 均轮 偏心 本轮

  12. Ptolemy system (70 circles) Copernicus system (46 circles) Galileo Galilei (1564—1642) Tycho Brahe (1546—1601) Johannes Kepler (1571—1630) Issac Newton (1642 — 1727)

  13. Kepler’s nested set:

  14. Saturn—Jupiter—Mars—Earth—Venus—Mercury cube dodecahedron octahedron tetrahedron icosahedron “Pythagorean” or “Platonic” solids • Mysterium Cosmographorum (Cosmic Mystery)(1596) • Harmony of the World (1619).

  15. Kepler's laws (1) The orbit of each planet about the Sun is an ellipse with the Sun at one focus. (the law of orbit); (2) The line joining any planet and the Sun sweeps out equal areas in equal times. (the law of areas); (3) The square of the period of revolution of a planet about the Sun is proportional to the cube of the planet's mean distance of the Sun. (the law of period or Harmonic law)

  16. 开普勒问题的文化方面

  17. The task of deducing Kepler’s laws from Newton’s laws is called theKepler Problem. Its solution is one of the crowning achievements on Western thought. It is part of our cultural heritage just as Beethoven’s symphonies orShakespeare’s plays orthe ceiling of the Sistine Chapel are part of our heritage. — The Mechanical Universe p498, CIT

  18. 4.4 Kepler problem and *scattering

  19. Mathematician vs Physicist

  20. areal “velocity” can never change sign. Mathematician Physicist m, r; M, rC separate tendency & relative motion standard procedure of differential equation central force, conservation of L r,pco-planar, 1st integrals, conservation of E effective potential classification of orbits (not r1, r2 )

  21. Thanks dxlu@nju.edu.cn

  22. 1 Define reduced mass Mass? Position vector? force? Which particle’s eq?

  23. 2 • L Conservation of L • randpare co-planar • areal “velocity”

  24. 2 • L Conservation of L • randpare co-planar

  25. 2 • L • can never change sign. Conservation of L • randpare co-planar • areal “velocity”

  26. 3 v2 1st integrals L

  27. 4 Effective potential

  28. parabola ellipse hyperbola Total energy Kinetic energy? circle 11

  29. 5

  30. For ellipse orbit

  31. *Hyperbola orbit Scattering angle

  32. Eq.(4.4.17) 2E

  33. Assignment: 4.7, 4.12, *4.14

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