# Newton's Clock

### Chaos in the Solar System

## Ivars Peterson, 1993, Central 521 P485N

- p021 Antikythera machine, unrecognizable lump recovered 1900, "discovered" 1902, in Archeological museum of Athens
p025 1958 analyzed by Derek Price, 1971 X & Gamma ray imaging, gear train structure, counted gear teeth

- p036 perhaps from school of Posidonios on Rhodes, made in 87 BC, lost in 85 BC on the way to Cicero in Rome
p039 Columbus used

*Ephemerides*of Johannes MÃ¼ller (Regiomontanus)- predicted total lunar eclipse on Feb 29, 1504, impressed reluctant Jamaica natives
- calculated longitude but wildly erroneous

- p045-072 Tycho, Ursus, Kepler
- Tycho's measurement errors less than 3 minutes of arc, 1/10th lunar diameter, and continuous
- Kepler used integer fractions, not decimals
Not in book:

*Heavenly Intrigue*Gilder&Gilder 2005 suggested Kepler poisoned Tycho. In 2010 Tycho exhumed, Aarhus University Jens Vellev November 2012 reported no poisons, most likely died of a burst bladder, confirmed 2012 by University of Rostock pathologists.

- p133 Sidereal month: compared to stars, Synodic month: compared to Sun.
- p134 Line of apsides: perigee to apogee. Line of nodes: crosses ecliptic. 8.85 years per full rotation.
- p140 George William Hill US Naval Almanac Office and Ernest W. Brown: periodic lunar model with rapidly converging algebraic perturbations
- p154 phase space, coordinates of position and velocity (6 dimensional?). Trajectories cannot intersect or branch.
- p183 gaps at 1/3, 2/5, 3/7, 1/2 Jupiter periods, peaks between. About 2.0 to 3.2 AU
- Dynamics of planetary rings / Araki / American Scientist 1991
- Comet Orbits and Chaos / Mark Bailey / Nature 1990
- The Origin of the asteroids / Binzel / Scientific American 1991
- Origins of the Near Earth Asteroids / Binzel / Science 1992
- p203 Hyperion tumbles funny
p264 Poincare -> KAM, Kolmogorov / Arnol'd / Mosher : regular quasiperiodic if perturbations small