No one doubts they exist, but how can gravity explain them? Einstein never implies that Kepler and Newton's theories were wrong—they are only incomplete. A moon creates a perturbation that cannot correct itself. Say this 3rd body is the moon, and put the moon between the earth and the sun. This is proved once again by the large perturbation between Jupiter and Saturn, solved by Laplace. They may even repaint over it themselves. The elaborate theoretical developments in celestial and classical mechanics have received more attention recently with the realization that a large class of motions are of an irregular or chaotic nature and require fundamentally different approaches for their description. But this is absurd. Why would it do this? For him they were equivalent abstractions or ideas. In fact, one might think that both perturbation analysis and chaos theory were created in order to hide the fundamental flaws of gravitational and orbital theory. It is true that the orbit of Triton is decaying, so that the orbit is not in fact completely stable. Except for chasing the graviton, no one is even working on gravity anymore. There are actually two problems. An orbiter with a given "innate motion" and a larger acceleration cannot possibly be describing the same curve as that same orbiter with the same innate motion and a smaller acceleration. But we have no answer at all for why the stars move sideways to the gravitational field of the galaxy. Any math that is based on calculus must be indeterminate, by current axioms, and if you add averaging to that math you have left determinacy far behind. Laplace's equations contain that repulsion (in hiding) but cannot explain it. Despite our ignorance, we have something nearly as good as stability, a weaker type of stability called KAM stability. At this lower orbit the acceleration toward Neptune is even faster. Movement, not force. Long evolutions under these conditions propitiate the rise of chaotic phenomena. Assuredly, the sun is spinning, and this may create tangential perturbations in an accompanying E/M field; but there is no way, in this simplified illustration, that the sun could be the cause of the tangential velocity of the earth. Is it still a constant piece of the compositional velocity, or has it been lost? Notice that if the earth had no velocity tangential to the sun's gravitational field as it was captured by that field, it would simply crash directly into the sun. It investigates the causes of these divergences and indeterminacies, and their various strengths. We must differentiate between the tangential velocity and the orbital velocity and it is easiest to do this in the simpler illustration. As is so-called long wavelength spiral structure dissipation. Velocity requires two separate measurements: it requires a measurement of distance, then it requires a measurement of how much distance per time. How can curved space explain tides? for the Solar system, the begin of mechanics. This book was edited by a large committee of top-flight physicists. Jupiter and the Earth fall toward the sun at the same rate—that is, the same acceleration—if they are at the same distance. Parts I—IX of the "The Third Wave" [Book Chapters 69-78] answer many of the questions posed above. The electrical field just is. I know that this all sounds like a joke, but the question must be addressed seriously by those who put "no action at a distance" on their t-shirts. Since Popper, no one has been capable of critiquing physics in a major way, or has even tried to. Beyond this mathematical mist in which we have lost ourselves, the other main problem is hubris. Kolmogorov formulated the theorem and gave This throws its orbit a bit out of whack, but the orbit is somehow stable since the total area of the orbit is about the same. A decaying orbit like Triton’s would be expected to fail exponentially. Another reason an equation unsupported by theory is dangerous is that it becomes dogma. The sun would have the helium from transport plus the helium from fusion. Three aspects of celestial mechanics: physics of motion, mathematics of motion and (numerical) calculation of motion. The three-body problem is a special case of the n-body problem. So, the unavoidable implication of historical theory is that all orbits must have been created by fortuitous collisions, either by planets arriving from outer space or being ejected by the sun. By applying a new set of differential equations to Newton's laws of motion, Laplace is said to have shown why Saturn's orbit had been increasing slightly since the time of the Chaldeans. We have a partial answer for why the stars don’t fly out into space: gravity. An ellipse is simply not a potential orbit for the balancing of a tangential velocity and a single centripetal acceleration. How is any planetary orbit created? All the other perturbations of the solar system are likewise mysterious. The simplest form of the three-body problem is called the restricted three-body problem, in which a particle of infinitesimal mass moves in the gravitational field of two massive bodies orbiting according to the exact solution of the two-body problem. 25.2 Planetary Orbits We now commence a study of the Kepler Problem. Richard Feynman uses this example in his geometric “proof” of the elliptical orbit. He went even further, though, for he believed that "the field" and "space" were two words for the same thing. The phase field usurps the physical field, and reality evaporates. Meaning that the velocity is uncaused by the field, and that it is perfectly perpendicular to the field at that point. General Relativity fails on this basis alone; it is cut by Occam’s Razor. The solutions of the equations of CM show great sensitivity to initial conditions: very close initial conditions may lead to totall… This causes a HUP (Heisenberg Uncertainty Principle) even at the macrolevel, and it intersects the perturbation problem precisely here. You may answer that a = v2/r is a necessary condition of a circular orbit. This was evidenced most clearly by Stephen Hawking more than a decade ago, when he claimed that physics was nearly over. It is going to slow it down and then speed it up two weeks later. We can’t possibly see it. I must start with a single object orbiting a central mass, an earth orbiting a sun in a perfect circle, such as Archimedes might have understood. The textbooks never go there. Imprecision in some variables and operations leads to great errors and in others leads to much more limited errors. All this when we have gigantic errors staring us right in the face from direct observational data. No one cares “why”, they only want to discuss “how”. People have always accepted this diagram on faith, but it is a false diagram. Most likely they are going to be out of round. In this ultimately simple version of an orbit, we have only two velocities. Newton: mathematical formulation of mechanics, gravitational force. The analytic work was devoted mostly to the circular, planar restricted three-body problem, where all particles are confined to a plane and the two finite masses are in circular orbits around their centre of mass (a point on the line between the two masses that is closer to the more massive). For Einstein, no carrier of influence was necessary in a normal gravitational field, since matter in the field "felt no force." There are many other similar mysteries about the stability of orbits, but I think I have made my point in regard to the circular orbit. What, exactly, caused Triton to settle into its current orbit? But there is an awful lot to explain. Well, you can't do it with string. In a gravitational collapse of a nebula with some initial angular momentum, the center of the nebula would be expected to gain the most angular momentum. No one cares “why”, they only want to discuss “how”. CONTENTSIntroduction § 1. This book is composed of 17 chapters, and begins with the concept of elliptic motion and its expansion. Matter in a gravitational field moves as it does because the field is curved, not because it is being influenced by sub-particles. And I am not just making airy accusations. We can only imagine that it must be because our planet is not moving fast enough to achieve a circular orbit. It is not the exception, either, it is the rule. All this goes to say that the popular mathematics of chaos theory has obscured the fundamental problems of its field. If you reverse time, and conceptually back the earth out of orbit, you see that the only way you can do so is if you accelerate it out of there. How could it be? It is known that the full three-body problem becomes indeterministic when we have a four-dimensional phase space with two of the dimensions positions and two of them velocities. No matter which direction you have the moon going (clockwise or counter) you are going to have the earth thrown into ever lower orbits for two straight weeks. You cannot physically measure at a point or an instant, and this must affect all your final numbers. Integrable and non-integrable problems of dynamics § 2. Import the finite speed of light and the tensor calculus into classical theory and you have current wisdom with regard to celestial mechanics. It was not captured or ejected; it was simply always there, in some form. Many problems in Celestial Mechanics are characterized by an evolution due only to gravitational forces with conservation of total energy and angular momentum for times of the order of millions or billions of years. In passing from the two to the three body problem, an increasing complexity due to nonintegrability and chaos is a trademark of Celestial Mechanics; the three body problem motivated the development of per… Results § 2. Sound familiar? An electrical current is composed of moving electrons; an electrical field is not. Celestial mechanics has not made much progress since Kepler and Newton. The "orbital velocity" continues to increase until the planet burns up in the sun's corona. But what has happened is that first perturbation theory and then chaos theory have engulfed and defined all serious analysis in orbital theory, so that no one even remembers what else was going on before Poincaré. The end of physics. So this motion must be independent of the gravitational field. That is the main reason physicists have added the graviton to the fundamental field of gravity, despite the fact that Einstein assured them that objects in curved space “felt no force,” and despite the fact that they still parrot this claim—believing that GR is geometric, not force-carrying. This whole theory is a comedy of basic logical errors. The history of celestial mechanics is a history of mathematical analysis that is very short on theory. We have a heuristic theory that allows us to put our own objects into orbit, what else do we need? But the gravitational field is not an exclusionary field—it cannot be produced by bombardment of subparticles. There is no margin of error. Let us now graduate from the mysteries of the circular orbit to the mysteries of the elliptical orbit. To be a specialist you have to specialize your training early, the earlier the better. Mean motion resonances are also impossible to explain with gravitational fields, for the same reason. This should have been seen earlier, since it is hard to imagine how a math can be non-linear and deterministic at the same time—especially when the definition of chaos depends on initial uncertainty within variables. Kepler does not address any of the things I have mentioned above. Lists of things that are still unknown are occasionally published, but substantive papers pointing out the very real faults of the Standard Model are dismissed without a reading and their authors are blacklisted. But if this is true, then the orbiter can't be describing the curve that is drawn by the ellipse. The situation that science has found itself in is unscientific in itself. Calculus fakes a sort of determinism by assigning the derivative to a point. Insert even one moon into a planetary orbit that is the balance of a tangential velocity and an independent centripetal acceleration and you have a crash. We find that these emission lines are always blue-shifted. It is a sort of obscurum per obscurius—explaining the obscure by use of the more obscure. It is not self-propelled. Therefore Neptune must have a rather complex field at all orbits, not just a simple centripetal acceleration. If it is coming from outer space into the field of the sun, it must somehow decelerate in order to fall into its current position. Celestial mechanics, in the broadest sense, the application of classical mechanics to the motion of celestial bodies acted on by any of several types of forces. Then let a = v2/r This would put all objects in retrograde orbits, and we don’t see this. Remember that the only way we can explain the planet in ellipse beginning to dive toward the sun as we move it past aphelion is that its velocity is not great enough to keep it in circular orbit. Accretion of what? What happened is that Kepler's ellipse is a myth. There is one perfect distance that creates a stable orbit for a given velocity. There is no way to eject an object from the center of its future orbit with a velocity tangential to that orbit. But that means that unless the earth was ejected by the sun, it had to decelerate to reach its present position. Stephen Hawking told us just twelve years ago that we were a decade away from knowing everything. Otherwise no body could ever be captured in the first place. It is going to slow it down and then speed it up two weeks later. Ancient civilizations . I have shown in my paper on Special Relativity that it physically impossible to measure position and velocity at the same time, in an unknown field. We don’t get so much as a theory. The planets and the sun form at the same time. Introduction; Newton's laws of motion; Newton's first law of motion The history of physics is a history of geniuses. Most likely they are going to be out of round. They give the earth a little tug here and there, saying that the moon corrects for itself. Saturn cannot go higher due to a perturbation from Jupiter, unless that perturbation is repulsive at some point in the long cycle. We don’t go to church to hear how all is well and “God is in his heaven.” No, we go to the web or the science magazine to hear how the demigods of physics are on the brink of explaining the genesis of all things. Both are obsessed with uncertainty. Especially in light of my theory, which will show that dissipation is a complete myth. If it doesn’t involve computer modeling or advanced mathematics, they can’t be bothered to look at it. A moon creates a perturbation that cannot correct itself. The force that the boy's hand must exert on the string is analogous to the gravity of the sun, we are told. It orbits because its trajectory is a vector addition of the two. [Click here to read more about Laplace and the 3-body Problem.]. This was a classical problem in celestial mechanics at the turn of this century and any Why would it do this? This whole theory is a comedy of basic logical errors. There is no string or other force that could impart tangential velocity to the earth. Now, if we look ahead on the ellipse, we can see that the path begins to curve toward the sun, decreasing the orbital radius. Can we draw the line all the way back to aphelion? As I said, they are not self-propelled. Although modern analytic celestial mechanics starts 400 years ago with Isaac Newton, prior studies addressing the problem of planetary positions are known going back perhaps 3,000 years.. Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. It is our measurement of the variables and our mathematical operations on them that are causing the chaos. They rush through basic kinematics, vector analysis, and all fundamental conceptual physics, usually putting it behind them when they graduate high-school. Its failures are the same failures as classical theory. Most current math is based on series and integrals of some sort, and these integrals have a degree of imprecision even if they aren’t averaged again later. The pat answer is “a spinning gravitational field”, but if you ask how a gravitational field imparts tangential velocity you get no answer. Let us draw the whole thing, just accepting that an ellipse must somehow be created, since we have evidence of them in the solar system. Subsequent scientists, unless they can devise a superior theory (which is obviously not so easy), prefer to let the mortar stand, even when it begins to show. Newton assigned the centripetal acceleration to gravity and the tangential velocity to the orbiting body itself. And Einstein never presented them as the mechanism for gravity anyway. The field of Neptune must have some ability to resist small deviations and to correct them. And this is where it gets silly. It has slowed down and gone lower, therefore we would expect a multiplied affect. But this fails to address the issue. Its tangential velocity is therefore independent of the gravitational field. You will have half an ellipse. I have said the tangential velocity is equal to the initial velocity of the planet, before capture by the field. It is a mathematical necessity. General Relativity only fine tunes them, by substituting a different but basically equivalent theory (curved space for action at a distance) and a nearly equivalent mathematics (tensor calculus for calculus). It is perpendicular to that field, whether the field is rectilinear or curved. What this means is that it is the math that is causing the problems, not the physical spaces themselves. Three or four observations allow you to build a basic equation. There is no proposed mechanism. And, I must say that this is only to be expected, since science has become the new religion. The question is, can we connect up the ellipse? They rush through basic kinematics, vector analysis, and all fundamental conceptual physics, usually putting it behind them when they graduate high-school. To be in a stable orbit at a smaller radius, Triton would have needed to gain energy, or speed up. This problem has been buried ever since Newton used his new calculus to find the orbital or curved velocity given the tangential velocity. This would be a bit more convincing if there weren't so many fundamental problems still embedded in classical theory and linear maths. In the simplest possible example, multiplication causes greater deviations than addition, for quite obvious reasons. If you vary only the length of the acceleration vector, in the vector addition, then you must vary the curvature. In astronomy in connection with the assessment that scientists fully understand non-chaotic deterministic systems time learning basic,. 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