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 Müller (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
• p203 Hyperion tumbles funny

• p264 Poincare -> KAM, Kolmogorov / Arnol'd / Mosher : regular quasiperiodic if perturbations small