1. Lecture L02-03- ASTC25 GRAVITATION Back then …and now

2. M.C. Escher V.Kandinsky J. Marr

3. I, II III ?! J. Kepler (1571-1630) I. Newton (1643-1727) R. Hook (1635-1703) I II

4. How Newton (supposedly) deduced the F= -1/r^2 law of gravity

6. Guinness record of acceler. for humans (1953): 62g for 0.04s

7. We will follow the route traveled by to understand the elliptic orbits (originally that of comet Halley), but using more modern formalism and notation.

18. One vector is so special that it had to be discovered and re-discovered a couple of times: Laplace vector = Laplace-Runge-Lenz vector Pierre-Simon, Marquis de Laplace (1749-1827)

21. ..so

23. 2

24. (Make sure you know how to derive Keplerian speed !) centrif.force grav.force

26. The full set of orbital elements (constants describing a Keplerian orbit) includes the two omegas and the inclination angle I, describing orbit’s orientation (shown below), two parameters describing its size and shape: semi-major axis a and eccentricity e, and finally the time of perihelion passage t 0 Alternatively, the orbit could be described by 3 initial components of position vector, and 3 velocity components (there are 6 variables describing the position and velocity).

27. You can find much interesting information about the history of celestial mechanics, for a few centuries the prime example of the power of the human mind, in this web page titled “Orbits and gravitation” http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Orbits.html In addition, please refer to the annotated chapter 2 from the Ostlie+Carroll textbook, linked to our home page at http://planets.utsc.utoronto.ca/~pawel/ASTC25