After having been kicked out of Dr. Mills Yahoo Classical Physics group earlier this year I came to the realization that I should probably spend more time focusing on my own personal research work rather than wasting endless hours indulging in circuitous conjecture that never gets resolved. Resolution will only happen when (and if) Dr. Mills can pull his CHIT technology together and demonstrate a working prototype that generates electricity from the breakdown of water, some powdered metal, and the CHIT catalyst. After that defrocking, combined with some additional self-reflection I decided to unsubscribe from Vortex as well. This additional self-imposed banishment was also done to help encourage me to redouble my efforts to work on my on-going Kepler project. That I have done.
As 2015 comes to an end I decided to briefly re-subscribe to Vortex... just long enough to give a brief update to the Collective on how my research is going. So. here goes: Back in October I experienced a minor epiphany concerning my Kepler research. It occurred at my local Noodles and Co restaurant while scarfing down a chicken Caesar salad. I was pouring over some Mathematica generated graphics depicting plotted orbital positions and accompanying velocity vectors. I suddenly noticed an interesting correlation having to do with the two foci that make up a typical elliptical orbit. My epiphany came from looking at the following link over the duration of several years. See: http://www.physics.csbsju.edu/orbit/orbit.2d.html These simple Mathematica graphics were generated from the physics department of College of Saint Benedict (Saint John's University) located in Minnesota. Besides Wikipedia, additional useful resources for understanding much of the physics behind Orbital Mechanics can be found at: http://www.jgiesen.de/kepler/ and http://www.stargazing.net/kepler/kepler.html The subtle information pertaining to my personal epiphany is embedded in the geometry of the Mathematica diagrams. It's related to how we apply "Kepler's equation" in order to plot the position of planets traversing an elliptical orbit. The new information isn't obvious at first sight. In fact, it took me years to notice the startling new correlation. As best as I can tell none of these orbital mechanical websites have carried through and rearranged the geometry of some of these Keplerian diagrams in a manner that I think Kepler would have eventually found himself doing had he lived long enough to do so. Based on my own research I think it wouldn't have taken Kepler not all that much more observational powers to have discovered three more Keplerian laws, additional laws that are just as important as the 1st, 2nd law and 3rd laws. What stopped Johannes was the eventual morality we all must face: Short lives. and perhaps not having sufficient computing power at his quill to plot out a few additional theoretical orbits to verify certain suspicions he may have speculated about. As we all know Kepler's 1st law of planetary motion states: "The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses)" Over the centuries there has been conjecture as to what might be happening at the other (empty) foci. Does this seemingly unused focal point exhibit any kind of particular Keplerian law of the same caliber as Kepler's 1st law? As best as I can tell nobody has managed to uncover a unique Kepler law that specifically uses the other empty foci in an exclusive manner similar to Kepler's 1st law. Over the centuries respected researchers have puzzled over this enigma including Richard Feynman. You can view some of Feynman's ponderings on the matter out at: http://tinyurl.com/qzcrpoy The best representation, to date, that I know of that tries to employ the other "empty" foci is the string tied into a loop method which is then placed around two separated thumbtacks. The two thumbtacks represent the two foci of a hypothetical ellipse arrangement. This allows one to trace out an ellipse when a pencil is placed between the two tacks and the string is held tight. It's quite clever in all honesty! Nevertheless, this arrangement does not reveal anything exclusive as to what the empty foci might reveal in its own right, similar to what Kepler's 1st law reveals. I confess, WHAT THE EMPTY UNFILED FOCI MIGHT REVEAL HAS BEEN AN OBSESSIVE CURIOSITY THAT HAS SUCK WITH ME FOR, FOR DECADES. And now, in my early 60s, I think I have managed to uncover the mystery of what the so-called empty foci represents. I admit it is probably arrogant for me to say this (and it's still possible I may be proven wrong) but I believe I know exactly what kind of information the empty foci reveals - in Keplerian terms. In order to explain it in Keplerian terms I believe it will be important for me to establish three additional honorary Keplerian laws. The first two of these new laws are based on well-known orbital mechanical principals. Well. I should really say these are mathematical principals well known to those who have studied the characteristics of orbital mechanics, but not necessarily to the general public. In order to reveal the third new law, the law which explains what the so-called empty foci represents, I will need to first define these two additional laws as important support to the third law. These are laws that in my opinion Kepler, himself, would have published if he just had more time, and perhaps more computing power at his fingertips. In a sense, it sometimes feels as if I'm doing this in a posthumous fashion, sort of in honor of Kepler. So, what does the empty foci reveal? In a nutshell: The empty foci reveals velocity vector information that is both directly linked and correlated with each planetary position within the elliptical path taken. PLEASE NOTE: Do not confuse my use of the term "velocity vectors" with what has been defined as "angular momentum." That is a completely different animal - another exotic creature that I might possibly tackle at a later date. This velocity vector information I refer to is not necessarily obvious at first sight - not in Keplerian terms. I need to stress that this information is not something that has not already been meticulously published nor plotted out in various permutations involving mathematical / derivative / integral / parametric equations. In fact, I will need to resort to using a number of these known equations in order to computer animate the movement of my planets. That said, due to my own initial ignorance of orbital mechanics I often ended up having to self-educate myself of the basic principles associated with orbital mechanics. This often resulted in me in self-discovering certain facts on my own and from such an obtuse observational perspective that it's still possible I might end up contributing a few new equations to the current mulligan stew. A crucial point I'm trying to make here is that I believe we need to rearrange some of the geometry currently used in order to make the three new Keplerian laws pop out in glaring obviousness. IMO so much more of what currently makes up the fundamental architecture of orbital mechanics can be revealed through the use of simple geometry. Doing so, I think, would be more intuitively understandable for many. The three new Keplerian laws are all there, visually speaking! As I see it, the way we have currently exploited some of the mathematical equations used to define orbital mechanics has unfortunately ended up compartmentalizing too much of the information and in a sense obfuscating what I would describe as an utter simplicity I suspect Kepler had intuitively sensed. I hope I can reveal some of that utter simplicity within the simple geometry of the ellipse itself. I suspect Johannes was endeavoring to do just that, if only he had had more time. Some Spin Off Speculation: At this early stage, I don't know if this will eventually pan out or not, but the speculated addition of these potential additional Keplerian laws might suggest that, in quantum mechanical terms, it might be possible to measure BOTH the position and velocity of sub-atomic particles simultaneously. According to quantum mechanics as it is currently taught, that is a definite no-no. But if both the position and velocity could be mapped out simultaneously, could this have useful industrial applications? It's going to take me some time to generate the appropriate code and animations to do it proper justice. I've been working full-time on this project since last April. My hunch is that I'm in for the big haul for at least another year or two of meticulous analysis and coding before my findings are sufficiently refined to a point that it's ready to be placed out on-line for others to ponder. Why so long? Hey! Your're all Vorts, right? You should all be aware of the inevitable delays that come with any worthy project! Think of Steorn, Rossi, Mills. While most of these individuals and/or their organizations continue to show signs of definite progress, to the best of my knowledge none of them have yet to break out of the pack and sprint to the finish line as the clear winner. As for me and my own endeavors, what I've learned about retirement is that it doesn't necessarily translate into acquiring oodles of free-time at my disposal. One word explains it all: HoneyDo! In the meantime, I continue to passively check in on the Vortex archives, sometimes daily. Typically, I check subject lines for relevance. Next, I like to check out what Jed Rothwell may have felt compelled to comment on, or perhaps just to simply to announce for the benefit of the Vort Collective. If I find both Jed and Jones posting repeatedly in same subject thread, I know I'll be interested! And now, back to work... and a little NY Eves celebration. c u all in 2016! Regards, Steven Vincent Johnson OrionWorks.com zazzle.com/orionworks
