From: crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass)
Subject: Re: TIME HAS INERTIA AND THE PRINCIPLE OF TENDENCY OF MAINTAINING THE
Organization: University of Virginia
Date: Sat, 17 Oct 1992 03:09:38 GMT

In article <1992Oct16.222931.4237@lmpsbbs.comm.mot.com> bhv@areaplg2.corp.mot.com (Bronis Vidugiris) writes:
>In article <1992Oct16.123737.28771@murdoch.acc.Virginia.EDU> crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass) writes:
>
>)     Typical misuse of the language to make a point that is 
>)     tenuous at best.   Numerical integration of the solar system
>)     out to 100 million years 'confirms' little.  One interesting quotation is
>)     'additional numerical experiments indicate that the Jovian planet
>)     subsystem is chaotic, although some small variations in the model
>)     can yield quasiperiodic motion'.  
>
>IMO, the context of 'confirms' was wrt the other mathematical studies that
>were previously mentoned that also indicated the solar system was chaotic. 
>This study agreed with the other ones (cited in the article) - hence, it
>'confirms' them.

     I would distinguish numerical studies from analytic.  I also have
     extreme doubts that all relevant effects were modeled for 100 million
     year timespans.  It could be a very common occurrence in this
     timespan that, say, huge hot plasma streamers are ejected from the
     sun causing shock waves of sufficient magnitude in the interplanetary
     medium and in such a manner that the solar system is completely 
     stabilized.  I can think of several other possibilities.
     I have doubts that we *know* all of the relevant effects.
	     
     Further, the necessity of numerical integration 
     introduced spurious conservation laws into the system and that
     numerical truncation introduced still others.  If the numerical
     system shows sensitive dependence on initial conditions, my guess is
     that it also shows sensitive dependence on truncation schemes as
     well.

     Most such numerical schemes show such effects, so the most one
     can say at this juncture is 'the numerical scheme is chaotic'.
     It is generous to say that connection of any of these studies with 
     the solar system is tenous.
     
>I can't think of any way that the chaotic nature of the actual solar system
>could be confirmed by physical experiment, as we only have one solar system
>and don't have another to test the effects of small disturbances on :-)

     Sure we can, simply wait and see irregular behavior.  There is
     one big datapoint that we seem to be missing here, if the earth's
     orbit has varied wildly over the last, say, 100 million years,
     our understanding of the interactions between our orbital location
     and global biology is deficient.  If, however, our
     understanding of biology is appropriate, the calculations are
     wrong.  I'd bet on fuzzy calculations when they tell you right
     off the bat that they are not getting stable results.

>However, it is an interesting mathematical feature of the models used.  I
>suppose you could call the above a 'mathematical experiment'.  (Come to think
>of it, that's what the authors did do according to your quote above).  One
>does has to have confidence in the models used (as well as the numerical
>methods used to solve them) to believe that the results will apply to the
>physical solar system.  The paper did compare their results with the results
>of other simulations.  There is not all that surprisingly a trade-off
>between rigor of the mathematical simulation and computational speed.

     Absolutely, with completely tenuous connection to solar system
     behavior.  All of these simulations suffer from truncation effects
     of one nature or another, and I'd bet the models are not complete
     either.  All the ones I saw when I was interested in such things
     were inadequate to the conclusions they were drawing.

>The sensitivity of the chaotic vs. quasiperiodic behavior to initial
>conditions mentioned in the paper is definitely a point worth mentioning, as
>is the lack of understanding of a mechanism to explain the simulated
>behavior.

     You did not report simply sensitivity to initial conditions, 
     but sensitivity to the *model*.  There is a big difference.
     For instance, Magnetic effects of Jupiter on some of its moons 
     are substantial, and not well understood.   I doubt that we even
     have enough data for good 'engineering' estimates, much less for
     long term orbital dynamics calculations.   I suspect that the 
     sensitivity to the *model* also extends to the solar system.

     As far as the lack of a mechanism goes, that comment of theirs
     puzzles me.  Presumably the 'mechanism' would be simply the 
     inherent nature of multibody orbital dynamics calculations.

     One question before I let this one go.  Did they include effects
     like GR (from perturbation theory alone, Mercury's perihelion advances
     208 radians in 100 million years, earth's about 30, to say nothing
     of possible cooperative effects), Poynting-Robertson drag on 
     smaller bodies, solar wind, detailed positions of all asteroids, 
     magnetispheric interactions, gravitational perturbations of solar dust? 
     Or did they just do a simple Newtonian integration with a few
     perturbations thrown in (perturbations that are usually invalidated
     by orbital changes)?

     One hundred million years is a long time compared to the amount of 
     time we have been observing and we have a very limited command 
     of analytical multibody dynamics, and we haven't sent many probes out
     yet.  

                               dale bass

-- 
C. R. Bass                                           crb7q@virginia.edu
Department of Mechanical and Aerospace Engineering
University of Virginia
Charlottesville, Virginia                            (804) 924-7926