The Laplace Vector and the Ice Ages?

The Laplace vector in planetary motion is the vector connecting the Sun to the center of the ellipse forming the orbit of the planet. It's length characterizes the eccentricity of the orbit, and its direction is along the long axis of the ellipse.

If we include the effects of Jupiter on the Earth, the Laplace vector of our orbit will change slowly.

Arnol'd, in Appendix 8 of his book Mathematical Methods of Classical Mechanics, writes:

We note that the motion of the Laplace vector of the earth is, apparently, one of the factors involved in the occurrence of ice ages. The reason is that, when the eccentricity of the earth's orbit increases, the time it spends near the sun decreases, while the time it spends far from the sun increases (by the law of areas): thus the climate becomes more severe as the eccentricity increases. The magnitude of this effect is such that, for example, the amount of solar energy received in a year at the latitude of Leningrad (60 degrees N) may attain that value which now corresponds to the latitudes of Kiev (50 degrees N) (for decreased eccentricity and Taimir (80 degrees N) (for increased eccentricity). The characteristic time of variation of the eccentricity (tens of thousands of years) agrees well with the interval between ice ages.

Questions

  1. Write a program which computes the evolution of the Laplace vector with time. Have the computer draw the Laplace vector as an animation: color the vector according to its length (red for hot years, blue for cold years). The display doesn't need to be updated every year! The challenge will be to find a way to compute Earth's motion fast enough to keep the display fast. (Push comes to shove, we can run it overnight and make an MPEG movie...)
  2. Find out whether this theory is believed by anyone in the ``real world''. For example, I read in a recent popular article in the Smithsonian (page 14, summer 1995) a completely different explanation for the ice ages.
  3. By solving a more realistic problem (three dimensions, real initial conditions, maybe including Saturn and/or the Moon if necessary), or by searching in the literature, find out if the actual ice ages correspond at all to the times of large eccentricity in our orbit!

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).