Hi Mario, At present I don't believe that the way I'm applying the use of Newtonian-like Celestial Mechanics (CM) algorithms can be applied to accurately modeling the retrograde orbital characteristics observed in planets like Mercury. At present all I can say is that I find it interesting that simple CM based algorithms seem to manifest the same retrograde characteristics in the plotting of ALL elliptical orbits. Is there a tie-in? I don't know. At present I'm only studying simple two-body solutions. It is conceivable that at a future date I may get into the quagmire of researching 3-body and larger numbers. God help me. What could go wrong!!!!
Insofar as what my own Celestial Mechanics research seems to indicate: No elliptical orbits are stable. None. Strictly speaking, and in Neutonian terms, using differential equations and feed-back algorithms, my research indicates that eventually all elliptical orbits will decay. By "decay" I mean to imply that all elliptical orbits eventually fly apart. The satellite's orbit eventually begins to manifest weird perturbations. It is precisely this manifested "weirdness" that I've have been researching for several years now. The weirdness, the patterns generated, don't seem to follow logical sequences - thus the term "chaotic." The "breakdown" of stability is certainly not a gradual process either. For example, as instability begins to manifest islands of apparent stability can suddenly reestablish themselves. Eventually, however, all orbits become chaotic again. This back-and-forth behavior, the tug between stability and chaos, can go on for quite a spell. Eventually the satellite is completely thrown out of the system. I've been attempting to develop a slew of computer programs and accompanying graphics to help display some of this weird behavior. I hope to better visualize what seems to be going on in ways that help us all acquire a better grasp of the fundamental principles that seem to manifest. BTW, to clarify something previously mentioned, my hypothesis is that as one plots orbital solutions that approach the circumference of a perfect circle the measured time of stability increase exponentially. At a certain point, and for all practical purposes, near-perfect circular orbits can be considered "stable" - forever. Nevertheless, I suspect they aren't, simply because of the fact that they aren't perfect circles. (Such conjecture is analogous to the on-going debate as to whether fundamental particles like protons and electrons are truly/absolutely stable, or just nearly so.) Mathis's work reminds me of another prominent Pulitzer winning author: Douglas Hofstadter, aka "Godel, Escher, Bach: An Eternal golden Braid". A more recent publication by Douglas is titled, "I'm a Strange Loop". http://www.amazon.com/Am-Strange-Loop-Douglas-Hofstadter/dp/0465030793/ref=sr_1_3?s=books&ie=UTF8&qid=1285262229&sr=1-3 http://tinyurl.com/2etgl57 I suspect there may be tie-ins between what Douglas has been trying to reveal in his impressive body of publications, and the tiny branch of research I've chosen to diddle about in. For example, while my computer algorithms are based on classic Celestial Mechanical formulas I suspect similar formulas and algorithms could possibly be applied (perhaps in clever ways we have yet to conceive) to the study, oh... say...: Maybe artificial intelligence, the nature of consciousness - how consciousness manifests within our reality, aka: "I'm a Strange Loop". -- Regards Steven Vincent Johnson www.OrionWorks.com www.zazzle.com/orionworks
