Re: [Vo]:Mercury's perihelion precession, a question for Vort
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=booksie=UTF8qid=1285262229sr=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
Re: [Vo]:Mercury's perihelion precession, a question for Vort
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. Now I finally understand you clearly, Vincent. What's going on is that your numerical simulations fall short of the complexity you are trying to simulate. Small errors eventually add up, and orbital elements sooner or later escape their orbits. What that means in the end, is that no numerical method, independently of how perfect and precise that it can be, can perfectly simulate the reality of the situation. And it's a fundamental limitation. Because the involved dynamics of the planetary orbits are non mechanicistic, no mathematical method can perfectly reproduce them (i.e. the n-body problem in Classical Mechanics). That was what I intended to mean when I said that the solar system is alive. To say or think that the solar system is completely mechanicistic, would be the same as saying that it is dead. And if that where the case, long ago everything would have escaped the system, or collapsed, i.e. it would have effectively manifested its death, long time ago. And of course, we would not be here. We're here because there's something in the Cosmos that's inherently equal to us, i.e. it's inherently alive. We are no more (and no less) than the most clear, recent, evident manifestation of the living nature of the Universe. 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. I enjoyed every line of Gödel, Escher, Bach. I remember with particular vividness the chapter on Strange Loops and Tangled Hierarchies. I recommend that monumental and beautiful book to anyone with a serious interest in the limits of mathematics and formal systems, and also on how in the end only with the aid of real art and living thought we are able to capture and explain the reality and prodigiousness of the world around us. http://www.amazon.com/Am-Strange-Loop-Douglas-Hofstadter/dp/0465030793/ref=sr_1_3?s=booksie=UTF8qid=1285262229sr=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
Re: [Vo]:Mercury's perihelion precession, a question for Vort
Mauro, I agree that numerical/finite-based simulations can never model real systems like our solar system in the absolute sense. At present I'm certainly not trying to model such systems, at least not in the strictest sense. The best that models like mine can ever hope to achieve would be to generate reasonably acceptable approximations of the living mystery itself. Actually, at present I'm more interested in exploring the strange behavior of CM chaos, in what might be considered a foolish attempt to map out some of the observed characteristics. Who knows, perhaps there may be practical applications. ... To say or think that the solar system is completely mechanicistic, would be the same as saying that it is dead. And if that where the case, long ago everything would have escaped the system, or collapsed, i.e. it would have effectively manifested its death, long time ago. And of course, we would not be here. We're here because there's something in the Cosmos that's inherently equal to us, i.e. it's inherently alive. We are no more (and no less) than the most clear, recent, evident manifestation of the living nature of the Universe. Ah, an eloquent observation. Nevertheless, we must occasionally guard against the danger of waxing on to such perturbat-ed depths as to induce apoplexy within the souls of our brethren who prefer following the sacred path of rationalism, or what often seems to me to be an extreme form of: Worshiping the Deity of External Measurement. But I do agree with you: Seems to me that We simply are - as is the Universe. Is there really a difference. But, once again, returning to objectively perceived manifestations... (:-)) it's conceivable that the same analogy as it pertains to the death of solar systems might also apply to the predicted death of galaxies. It is predicted that most galaxies will fly apart, eventually losing all of their stars. But then... Perhaps the Mystery of MOND will come to our rescue. http://en.wikipedia.org/wiki/Modified_Newtonian_dynamics Regards Steven Vincent Johnson www.OrionWorks.com www.zazzle.com/orionworks
Re: [Vo]:Mercury's perihelion precession, a question for Vort
On 09/23/2010 05:39 PM, OrionWorks - Steven V Johnson wrote: Mauro, I agree that numerical/finite-based simulations can never model real systems like our solar system in the absolute sense. At present I'm certainly not trying to model such systems, at least not in the strictest sense. The best that models like mine can ever hope to achieve would be to generate reasonably acceptable approximations of the living mystery itself. Actually, at present I'm more interested in exploring the strange behavior of CM chaos, in what might be considered a foolish attempt to map out some of the observed characteristics. Who knows, perhaps there may be practical applications. It certainly looks interesting to produce and introduce additional perturbations. That can maybe be a form of mapping or replacement for the missing dynamical character of the celestial mechanics simulation. ... To say or think that the solar system is completely mechanicistic, would be the same as saying that it is dead. And if that where the case, long ago everything would have escaped the system, or collapsed, i.e. it would have effectively manifested its death, long time ago. And of course, we would not be here. We're here because there's something in the Cosmos that's inherently equal to us, i.e. it's inherently alive. We are no more (and no less) than the most clear, recent, evident manifestation of the living nature of the Universe. Ah, an eloquent observation. Nevertheless, we must occasionally guard against the danger of waxing on to such perturbat-ed depths as to induce apoplexy within the souls of our brethren who prefer following the sacred path of rationalism, or what often seems to me to be an extreme form of: Worshiping the Deity of External Measurement. But I do agree with you: Seems to me that We simply are - as is the Universe. Is there really a difference. Yes. But please don't forget that these observations are true and pertinent. That is, they are not merely an issue of taste, or personal opinion. It's always rational to adhere to verifiable and comprehensible truth, even or particularly if that truth does not conform to our previously held notions. But, once again, returning to objectively perceived manifestations... (:-)) it's conceivable that the same analogy as it pertains to the death of solar systems might also apply to the predicted death of galaxies. It is predicted that most galaxies will fly apart, eventually losing all of their stars. But then... Perhaps the Mystery of MOND will come to our rescue. http://en.wikipedia.org/wiki/Modified_Newtonian_dynamics I've studied MOND, to a certain extent. The problem with MOND, besides its ad-hoc approach, is that MOND is too simple. It only works for radially symmetrical cases; spiral and elliptical galaxies. The best I've found at the moment in relation to modified gravity approaches, is the work of Zhao and Li. In a groundbreaking paper, Zhao and Li propose that gravity is caused by a dynamical dark fluid. Not only that(I had informally proposed the same on my own), but they are also able to show that the different modified gravity theories can be derived from this unique dark fluid vector field. The dark fluid approach dispenses also with dark energy, dark matter and dark energy being just two sides of the same coin. The math is almost incomprehensible, at least to me, but the approach and the results are wonderful: http://arxiv.org/abs/0804.1588 ”One Field which rules them all and in the darkness bind them” as is beautifully said in the paper.
[Vo]:Mercury's perihelion precession, a question for Vort
I haven't been able to get a clarification to a vexing question concerning Mercury's perihelion precession-al orbit, specifically the angular direction such observations manifests as. For example, hypothetically speaking here, let's pretend we have a space ship and have stationed it approximately 90 million miles distant from the sun. Also, our spaceship is not within the ecliptic plane but positioned at one of the Sun's poles. Mercury is observed to be orbiting around the sun in a clock-wise pattern. Under such a scenario what would the angular direction of Mercury's perihelion precession manifest as? I -suspect- the perihelion PRE-cession of Mercury's orbit implies that the phenomenon would manifest in a counter-clockwise direction, but I haven't been able to get a clear answer to that one. Pardon my ignorance, on this matter. I'm wondering out loud, here: Does the term PREcession mean: in the opposite direction of... as to the orbital direction? Mongo don't know. I actually have some legitimate curiosity in regards to this question. I have been running computer simulations based on the simple rules of celestial mechanics for several years now. My CM simulations pertaining to most of the ELLEPTICAL orbits I've plotted always show a distinct counter-rotational pattern, meaning the pattern of successive elliptical orbits that have been plotted are always in the opposite direction that the satellite body is orbiting around the central mass point. Just to be clear on this point, in no way am I attempting to imply that my simple CM simulations have anything directly to do with Einstein's General Relativity, which famously predicted Mercury's perihelion precession around the sun accurately. Can someone clarify my precession confusion? Regards, Steven Vincent Johnson www.OrionWorks.com www.zazzle.com/orionworks
Re: [Vo]:Mercury's perihelion precession, a question for Vort
I haven't been able to get a clarification to a vexing question concerning Mercury's perihelion precession-al orbit, specifically the angular direction such observations manifests as. For example, hypothetically speaking here, let's pretend we have a space ship and have stationed it approximately 90 million miles distant from the sun. Also, our spaceship is not within the ecliptic plane but positioned at one of the Sun's poles. Mercury is observed to be orbiting around the sun in a clock-wise pattern. Under such a scenario what would the angular direction of Mercury's perihelion precession manifest as? I -suspect- the perihelion PRE-cession of Mercury's orbit implies that the phenomenon would manifest in a counter-clockwise direction, but I haven't been able to get a clear answer to that one. Pardon my ignorance, on this matter. I'm wondering out loud, here: Does the term PREcession mean: in the opposite direction of... as to the orbital direction? Mongo don't know. Neither. Precession can be either prograde or retrograde. Mercury's perihelion precession is prograde, if I'm not mistaken. The relativistic component, due to the field curvature, is also prograde. Btw, google Miles Mathis, for an entertaining read. A surprising finding.
Re: [Vo]:Mercury's perihelion precession, a question for Vort
I haven't been able to get a clarification to a vexing question concerning Mercury's perihelion precession-al orbit, specifically the angular direction such observations manifests as. For example, hypothetically speaking here, let's pretend we have a space ship and have stationed it approximately 90 million miles distant from the sun. Also, our spaceship is not within the ecliptic plane but positioned at one of the Sun's poles. Mercury is observed to be orbiting around the sun in a clock-wise pattern. Under such a scenario what would the angular direction of Mercury's perihelion precession manifest as? I -suspect- the perihelion PRE-cession of Mercury's orbit implies that the phenomenon would manifest in a counter-clockwise direction, but I haven't been able to get a clear answer to that one. Pardon my ignorance, on this matter. I'm wondering out loud, here: Does the term PREcession mean: in the opposite direction of... as to the orbital direction? Mongo don't know. Neither. Precession can be either prograde or retrograde. Mercury's perihelion precession is prograde, if I'm not mistaken. I am. Mercury's perihelion advance is retrograde. It happens in the same direction than Earth's axial precession, which is retrograde. See the table called Sources of the precession of perihelion for Mercury in http://en.wikipedia.org/wiki/Tests_of_general_relativity All effects add up.
Re: [Vo]:Mercury's perihelion precession, a question for Vort
Mauro, Thanks for pointing me to the analysis work of Mathis. At present, I don't know if I can make practical use of his mathematical findings or not. It's probably going to make my brain hurt for quite a spell while attempting to get the gist of it all. To clarify what I have been doing: For several years now I have been researching what I have assumed is probably considered by most an uninteresting aspect of Newtonian based Celestial Mechanics, (CM). More to the point, I have focused primarily on computational feed-back loops where chaos is introduced into the solution. I've been plotting the chaotic results for some time now. No doubt, much of this work is related to emergent behavior, fractals, and what-not. It would not surprise me if some of Wolfram's work may have occasionally touched on what I have been studying. (Mike Carroll brought Worlfram's work to my attention.) Serendipitously, I recently discovered that Wolfram used his Mathematica software to study the characteristics of the empty foci belonging to a classic elliptical shaped satellite/planetary orbit. I was gratified to discover that the results Wolfram's Mathematica produced seemed to mirror some of my own independently researched findings. I have assumed (perhaps incorrectly) that the specific CM branch I'm studying (the chaotic aspect) is probably considered uninteresting and not of much practical value to most scientists researchers. I assume so because of the fact that when it comes to accurately plotting the orbits of celestial bodies like planets, moons, and satellites the last thing one wants to do is introduce the effects of chaos into the algorithm! For obvious reasons the effects of chaos must be kept at a minimum in order to accurately plot a future position of a celestial body. This is accomplished by making sure the computational iterative samples one feeds into the algorithm are sufficiently small, from plotted point to the next plotted point. Things can quickly get squirrely as one's satellite approaches the main attractor body, and the plotted point-to-point positions increase in distance from each other geometrically. But there by the Grace of God go I. I've discovered that within the unpredictable realms of chaos a wealth of strange and weird-like behavior is worth exploring. At the razor's edge, where the boundary between Order and Chaos meet, I find tantalizing behavior. My chaotic research continues. I hope to eventually put some of my findings out on the net. Much more work needs to be done... It's daunting. Regards Steven Vincent Johnson www.OrionWorks.com www.zazzle.com/orionworks
Re: [Vo]:Mercury's perihelion precession, a question for Vort
Hi, I'm in the same situation at the moment regarding the work of Mathis. I've just found out about his, at least at first sight, surprising and impressive body of work, when doing research to answer your question. Regarding your research: We talked here on vortex-l in the past about so called chaotic (stochastic) behavior. It is my understanding that if it were not for stochastic phenomena, the solar system would be dead long ago, i.e. everything would have collapsed into stability. It's due to the fact that always new small impulses are added to or produced in the system, that the planets continue moving in their orbits. If you carry the CM computations far enough, everything eventually stalls, or collapses. So, your addition of small chaotic perturbations could be closer to the truth than what is normally assumed. I've also ran Newtonian simulations of the solar system in the past, to observe the effect of outer bodies on the perihelion of the orbits of the inner planets, with practically null results. If your addition of small chaotic perturbations can in some cases model the advance of Mercury's perihelion, by example, that's would be a very valuable result. And the line of research in itself is very interesting. At a given point, you would have to consider too how those chaotic effects could take place in the solar system. And of course, I think that it would be also very interesting to know what kind of effects you have modeled, or produced. Regards, Mauro On 09/22/2010 06:13 PM, OrionWorks - Steven V Johnson wrote: Mauro, Thanks for pointing me to the analysis work of Mathis. At present, I don't know if I can make practical use of his mathematical findings or not. It's probably going to make my brain hurt for quite a spell while attempting to get the gist of it all. To clarify what I have been doing: For several years now I have been researching what I have assumed is probably considered by most an uninteresting aspect of Newtonian based Celestial Mechanics, (CM). More to the point, I have focused primarily on computational feed-back loops where chaos is introduced into the solution. I've been plotting the chaotic results for some time now. No doubt, much of this work is related to emergent behavior, fractals, and what-not. It would not surprise me if some of Wolfram's work may have occasionally touched on what I have been studying. (Mike Carroll brought Worlfram's work to my attention.) Serendipitously, I recently discovered that Wolfram used his Mathematica software to study the characteristics of the empty foci belonging to a classic elliptical shaped satellite/planetary orbit. I was gratified to discover that the results Wolfram's Mathematica produced seemed to mirror some of my own independently researched findings. I have assumed (perhaps incorrectly) that the specific CM branch I'm studying (the chaotic aspect) is probably considered uninteresting and not of much practical value to most scientists researchers. I assume so because of the fact that when it comes to accurately plotting the orbits of celestial bodies like planets, moons, and satellites the last thing one wants to do is introduce the effects of chaos into the algorithm! For obvious reasons the effects of chaos must be kept at a minimum in order to accurately plot a future position of a celestial body. This is accomplished by making sure the computational iterative samples one feeds into the algorithm are sufficiently small, from plotted point to the next plotted point. Things can quickly get squirrely as one's satellite approaches the main attractor body, and the plotted point-to-point positions increase in distance from each other geometrically. But there by the Grace of God go I. I've discovered that within the unpredictable realms of chaos a wealth of strange and weird-like behavior is worth exploring. At the razor's edge, where the boundary between Order and Chaos meet, I find tantalizing behavior. My chaotic research continues. I hope to eventually put some of my findings out on the net. Much more work needs to be done... It's daunting. Regards Steven Vincent Johnson www.OrionWorks.com www.zazzle.com/orionworks
Re: [Vo]:Mercury's perihelion precession, a question for Vort
On 09/22/2010 07:47 PM, Mauro Lacy wrote: Hi, I'm in the same situation at the moment regarding the work of Mathis. I've just found out about his, at least at first sight, surprising and impressive body of work, when doing research to answer your question. Well, it's certainly not very difficult to recognize the work of a genius.
