Computing the Motion of the Moon Accurately

Before the development of computers, there was a vast industry of mathematical physicists who worked on methods for calculating the motion of the moon. See

Dieter S. Schmidt, in Hamiltonian Dynamical Systems, H. S. Damas, K. R. Myers, & D. S. Schmidt (eds), The IMA Volumes 63, Springer-Verlag, 1995 p. 341. (It's in the Cornell Math library.)

Questions

  1. Look up some of the methods of calculation. Reproduce them with Mathematica or Maple. Check them numerically. I'm guessing, with modern tools, you'll be able to duplicate years of work by one of the masters in the field.
  2. Look into the small denominator problem enough to understand why the convergence of these perturbative methods is subtle.

Jupiter:

How to Get Jupiter

Jupiter is available for Windows 95, Windows NT, Macintosh, and several Unix platforms (the IBM RS6000, Sun Sparc, Dec Alpha (courtesy Kamal Bhattacharya), Linux, and the PowerPC running AIX4.1). The files are available without charge by anonymous FTP (ftp.lassp.cornell.edu) or via the World Wide Web.
Last modified: May 19, 1996

James P. Sethna, sethna@lassp.cornell.edu.

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).