If you decelerate, then it crashes into the sun. Furthermore, the loss of precision will depend in large part on your mathematical operations. But how can an object entering a gravitational field decelerate? Chaos theory sometimes recognizes this, since the fundamental definition of chaos theory is theory that explores the results of nescience in initial conditions. But to do this they must give the earth slightly eccentric little accelerations and decelerations, which they never explain. But a torque could not be applied by an attractive or warping field. The field of Neptune must have some ability to resist small deviations and to correct them. We are told that angular momentum is carried out to orbiting bodies, but how? Relativity gave him the tools to fill in the conceptual holes of classical gravitational theory, but he did not use these tools to their full effect. Sound familiar? Kepler and Newton believed that a gravitational field was produced by a massive object, that space (if not the field) was rectilinear, and that the massive object acted directly—though in an unknown way—upon any matter within the field. It not only fails to solve the problem of Kepler and Newton, it adds to it. The swinging action of the boy creates the tangential velocity. What this shows us in addition is that the earth always retains its initial tangential velocity. What this means is that it is the math that is causing the problems, not the physical spaces themselves. To be a specialist you have to specialize your training early, the earlier the better. Although the three-body problem has no complete analytic solution in closed form, various series solutions by successive approximations achieve such accuracy that complete theories of the lunar motion must include the effects of the nonspherical mass distributions of both Earth and the Moon as well as the effects of the planets if the precision of the predicted positions is to approach that of the observations. But to do this they must give the earth slightly eccentric little accelerations and decelerations, which they never explain. Diverted by the tensor calculus, he lost sight of some of the simple conceptual shortcomings that his theory should, and could, have addressed. Meaning that the velocity is uncaused by the field, and that it is perfectly perpendicular to the field at that point. However, I would like to point out right now that Kant is known to history mainly as a philosopher, not as a scientist or mathematician. A gravitational field has no braking effect; therefore, since a body retains a velocity until another force acts on it, the earth still has the velocity in orbit. Ultimately I must take exception to Kepler's theory of ellipses. Most books have differential equations on the first page, and those that don’t begin by glossing the history from Newton to Gauss—a history of mathematical analysis. Most of the schemes for the main problem are partially numerical and therefore apply only to the lunar motion. A torque could be applied by an exclusionary field—like the E/M field. The field is generated from its center and cannot possibly do anything but pull inward from that center. A nebula therefore requires a seed. To start with, in reality an orbit like this creates a hairline balance of two independent motions. The same can be said for the ellipse. Does an elliptical orbit solve any of the problems I have outlined above? You can't draw an ellipse like this with two vectors. And, since geniuses get paid better and make better copy, it is best to keep the field properly propped up. The planets affect eachother by applying small torques to one another, we are told. Import the finite speed of light and the tensor calculus into classical theory and you have current wisdom with regard to celestial mechanics. If they weren’t captured, what set them in motion? It is not a matter of "dependence," as I call it. Richard Feynman uses this example in his geometric “proof” of the elliptical orbit. The field of Neptune must have some ability to resist small deviations and to correct them. The usual answer to this is to show a summing of potential and kinetic energies in a closed loop and prove mathematically that all energy is conserved. This new theory of gravity and orbits makes use of the current E/M field, Relativity, and classical equations. Matter in a gravitational field moves as it does because the field is curved, not because it is being influenced by sub-particles. The theory of the gravitational field, either Newton's or Einstein's, cannot support Kepler's Third Law. But it does not show why the empirical data is what it is. Results § 2. Although analytically not integrable in the general case, the integration can be well approximated numerically. What you have is a gravitational field inside out. But the nebular theory was proposed initially to explain the creation of massive bodies. 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. The situation that science has found itself in is unscientific in itself. Celestial mechanics is the branch of astronomy that is devoted to the motions of celestial bodies. Saturn cannot go higher due to a perturbation from Jupiter, unless that perturbation is repulsive at some point in the long cycle. We think, well, maybe when a planet is captured, it first hits an orbital tangent at an angle, instead of at a perfect perpendicular. It congealed out of the nebula. In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation. You just slow the Earth's orbital velocity down until it offsets the centripetal force from the sun. Einstein took the electrical field as his blueprint for the new gravitational field of General Relativity, and it is equally mysterious. Kepler's second law states that a planet sweeps out equal areas in equal times. The use of the Kepler integrals for Orbit Determination. It is also difficult to agree with the assessment that scientists fully understand non-chaotic deterministic systems. This also applies to tides and equatorial bulges. Physics, spoiled by its own notoriety, has begun to rot from within, and there is no strength in other fields to counteract this rot or resist it. It investigates the causes of these divergences and indeterminacies, and their various strengths. This produced a spherical field, which then acted on any matter within it. It is deterministic only in the strict sense that it is not quantum chaos theory, for which the term indeterministic is saved. Even greater problems arise when we try to imagine how the earth was captured by the sun. It orbits because its trajectory is a vector addition of the two. It has been buried from sight ever since. If physics is to regain any sort of health, it must begin to take mechanics and conceptual analysis seriously again. For Newton, the mystery was in understanding how the sun influenced the earth, for instance. Even Einstein admitted that the gravitational field had no influence at the tangent. 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. Technically, physics does not exist anymore, since the physical field has been jettisoned by QED. It never achieves a temporary escape velocity. Numerical developments allowed consideration of the more general problem. This despite all we have been told by modern scientists about philosophers being inferior creatures, ones who should not dabble in science. 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. But in a planetary orbit, the planet can feel a force only from the sun, at one focus. Maybe, but that is heuristics, not theory. Philosophers once policed physics in a small way, but no more. Both use the same unsubstantiated assumption Newton used, namely that a = v2/r. We don’t see negative torques, we see positive torques—prograde torques. The "orbital velocity" continues to increase until the planet burns up in the sun's corona. It is our measurement of the variables and our mathematical operations on them that are causing the chaos. I ~ c4R5/Gr7        At each point on the ellipse, the orbital velocity of the planet is the vector addition of the perpendicular velocity (which is no longer tangential) and the “instantaneous” centripetal velocity. The easiest points to have it arrive, for the sake of conceptualization, is at perihelion or aphelion. It seems to me that modern physicists hide in their math to avoid doing basic physics, a physics that is never as easy as creating models of indeterminacy in fictional fields. They both simply cover it up. 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. All these perturbations cannot be made to offset. In fact, there is a dependence between the tangential velocity and the centripetal acceleration, a dependence given mathematical form by the equation a = v2/r. for the Solar system, the begin of mechanics. Of course QED usually assumes that the E/M field is produced by the emission by all bodies of photons or neutrinos or some other force-carrying particle. They are going to be missing chunks. There is no proposed mechanism. The problems I am enumerating here are mostly not known to exist anymore, for the very reason that all study of orbits and gravity is now strictly mathematical. Kepler's Third Law tells us unequivocally that a and v are dependent, but neither Newton nor Einstein nor anyone else can say how that dependence is arrived at. Because it is confined to a disc and the disc isn’t in our plane of sight. Both are obsessed with uncertainty. By giving us the ball-on-a-string illustration, the book leaves the impression that the analogy is complete; that is, that the tangential velocity and the acceleration are conceptually connected in both instances. Spins and wobbles are created, which cause uneven velocities and uneven forces. Gm1m2/r2 = m1a So, for the sake of argument, let us say that a planet has arrived at aphelion due to some fortuitous collision. Besides, philosophy became obsolescent in the 20th century. In saying that a massive object curves space, Einstein was in many ways begging the question. The other two stationary points, called the triangular points, are located equidistant from the two finite masses at a distance equal to the finite mass separation. Newton calls it the body's "innate motion." It is a kinematic impossibility. They rush through basic kinematics, vector analysis, and all fundamental conceptual physics, usually putting it behind them when they graduate high-school. If it doesn’t involve computer modeling or advanced mathematics, they can’t be bothered to look at it. It orbits because its trajectory is a vector addition of the two. And the same problem is going to be met when the moon is sideways to the earth. Three or four observations allow you to build a basic equation. One might say it remains the bedrock of contemporary celestial mechanics. They rush through basic kinematics, vector analysis, and all fundamental conceptual physics, usually putting it behind them when they graduate high-school. If we want to devote time to a problem, it would be better to devote it to explaining why orbits are stable, instead of devoting it to mathematical niceties that add little to our knowledge and nothing to our concepts. As you know, Kepler told us that all orbits are ellipses, the nearly circular orbit being only a special case. The E/M field would therefore be an exclusionary field caused by bombardment. That is because no one has done theory since Kepler and Newton. Einstein cannot explain how a massive object curves space at a distance. 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. Poincaré, along with other great mathematicians such as George D. Birkhoff (1884–1944), Aurel Wintner (1903–58), and Andrey N. Kolmogorov (1903–87), placed celestial mechanics on a more sound mathematical basis and was less concerned with quantitatively accurate prediction of celestial body motion. Richard Feynman recalculated Newton's proof of the elliptical orbit using only plane geometry in his famous "lost" lecture. This last equation is used to find the intensity of a gravity wave Several mechanisms for dissipation have been presented, although none have been very successful at explaining it. Even according to its proponents, this mechanism is not capable of explaining the actual dissipation that we see. Mathematicians have always known that all measurements are necessarily imprecise. How is any planetary orbit created? And yet both points exhibit the same curvature! You do this by varying its perpendicular velocity at perigee and apogee. We are taught to bow to the implications of chaos theory and to devote endless hours of modeling time to discovering which mathematical operations cause the most error. Celestial mechanics has not made much progress since Kepler and Newton. It is not the exception, either, it is the rule. My other papers might be called a compilation of these holes. The phase field usurps the physical field, and reality evaporates. What I will show is that Kepler and Newton, although mathematically correct in most basic ways, left us with underlying theory that was incomplete. They know that it is not fatal, since the earth does not crash into the sun, so they simply do the math to explain how the earth gets to the next position that it actually achieves. All very unscientific, but I would guess that many of us have assumed these things, without really questioning it very deeply. Unanswered Questionsby Miles Mathisby Joseph Wright of Derby apparent rari nantes in gurgite vasto First posted October 20, 2004Abstract: In this paper I will show many of the embedded problems in the standard model, problems not admitted to exist and in many cases not even known to exist. But they must exist with the help of some field we have not included in our equations. Celestial Mechanics Notes Set 1: Introduction to the N-Body Problem J.D. A decaying orbit like Triton’s would be expected to fail exponentially. To see what I mean, take the Earth out to the distance of Jupiter and try to build an orbit. The book sets forth in detail the basic theoretical apparatus of celestial mechanics. But it is not just that. For, I repeat, how can a gravitational field cause a velocity tangent to that field? And this applies to the ellipse just as it does the circle. I will prove that the angular momentum of the sun and planets has nothing whatsoever to do with nebular collapse and that there is no nebular connection at all between the angular momentum of the sun and of Jupiter. When Newton or Einstein maps the varying numbers at varying distances in the field, he is mapping accelerations, not forces. These zero-velocity curves can be used to show that the three collinear stationary points are all unstable in the sense that, if the particle is placed at one of these points, the slightest perturbation will cause it to move far away. The next two weeks of corrections cannot offset this. As Triton lost energy it would fall into a lower orbit. This would certainly be a reductio ad absurdum. The more usual situation study in celestial mechanics is known as the N-body problem, where are N point masses, i.e., bodies perfectly spherical and with mass as a single physical property, denoted by m 1, …, m N moving in a d-dimensional Euclidean space, although we will be most interested in the cases d = 2 and 3. Newton could not say how a massive object acted upon matter at a distance. Most books don’t have a single page on the theory of orbits. After coming face-to-face with such simple and basic errors it is very difficult to be either impressed or cowed by higher math. Why? For instance, Kepler's theory of ellipses still pertains to this day. 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. Just so the gravitational field. Furthermore, the loss of precision will depend in large part on your mathematical operations. The answer is that it doesn’t. For him they were equivalent abstractions or ideas. Now, think of the earth's orbit for a moment. There appear to be constraints on decay and escape far beyond what would be logically expected. But this is not the question. That was only to simplify the math. You have to be a specialist. But I for one think it was preferable when this warfare was in the open. But to do this, I must go back even further. Celestial motion, without additional forces such drag forces or the thrust of a rocket, is governed by the reciprocal gravitational acceleration between masses. This allows its tangential velocity to eventually counteract gravity, pulling it back into ever-increasing distances from the sun. I assume that some readers will have thought that the Earth would be going slower, since it is smaller. That is to say, old physics was over and we had to find something to do. No field is infinitely forgivable, but orbits show a degree of float that is not in line with current theory. Maybe it formed by simple accretion—not gravity but random collision. The textbooks never go there. Just as an example, it is believed that all bodies apply torques to all other bodies (although it is not explained how in current theory). The planet is then pulled into a tighter orbit, since its velocity is not great enough to achieve a circular orbit. “Celestial Mechanics and Astrodynamics: Theory and Practice” also presents the main challenges and future prospects for the two fields in an elaborate, comprehensive and rigorous manner. There must be some correctability to orbits not only to account for the stable orbits we see but also to account for the creation of captured orbits. The approximate nature of Kepler’s laws. Einstein cannot explain how a massive object curves space at a distance. The boy whirls the ball around him, and a circular orbit is created. Why would it do this? Einstein did not overthrow the fundamental mathematics of gravity and orbits. But nebular theory never answers the first question—that being how could a pre-collapse nebula have angular momentum? You must have angular momentums working at a distance. An orbiter may sweep out equal areas in equal times, but not if its orbital velocity is determined by two vectors. Perturbation analysis hid the flaws of classical theory, and chaos theory came along later to help hide the newer flaws of GR. Here is another argument against current theory. It is impossible since the perpendicular vector has to stay the same length all the way around. Given two theories that have the same content—the same power of prediction—always choose the one that has the fewest moving parts, the fewest postulates. Chaos theory is often said to be deterministic, but this meaning is imprecise at best. One of these mechanisms is the hypothesized separation of angular momentum by a two-element gas. A mistake like this cannot be assigned to single person. We find that these emission lines are always blue-shifted. The first is that if the disc is not in our plane of sight, then it can’t be the cause of any obscuring of shifts, red or blue. Philosophers once policed physics in a small way, but no more. Its failures are the same failures as classical theory. Mean motion resonances are also impossible to explain with gravitational fields, for the same reason. How is an orbit like this created? In addition, as I have shown, stable circular orbits with moons are also impossible to explain. If the field around a massive object was curved, then space was. 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. Preliminary results from mechanics § 3. And the hole in the ellipse is even older. The history of celestial mechanics is a history of mathematical analysis that is very short on theory. One word. It not only fails to solve the problem of Kepler and Newton, it adds to it. Preface; Newtonian mechanics. Long evolutions under these conditions propitiate the rise of chaotic phenomena. In 1773, he took up one of the outstanding problems that until then had resisted all attempts at solution in terms of Newtonian gravitation: the problem of why Jupiter's orbit appeared to be continually shrinking while Saturn's was continually expanding (Whitrow, 1971). As I said, they are not self-propelled. Therefore, nebulae which show angular momenta must already be in the first stages of collapse. Most of those screaming at me scream that my two velocity vectors can't be equal, since the orbital velocity varies in an ellipse. Abstract: At the beginning of the 20th century, G.D. Birkhoff called the N body problem of celestial mechanics the most celebrated problem in mathematics. Finally, its trajectory brings it so close to the sun that it is inside what its perfectly circular orbit might have been. 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. The same is true of every other sub-field. If physics is to regain any sort of health, it must begin to take mechanics and conceptual analysis seriously again. The fact ends up becoming the theory, and we have forgotten that we have anything to explain. (The particle with infinitesimal mass, sometimes called a massless particle, does not perturb the motions of the two massive bodies.) involved in traditional celestial mechanics. To answer this, we must go back to the circular illustration. You will say, "But the sun must pull harder on Jupiter, surely, to keep it in orbit, than on the Earth." Most likely they are going to be out of round. Meaning that the velocity is uncaused by the field, and that it is perfectly perpendicular to the field at that point. Since nebular gases are known to be made up of hydrogen and helium (and traces of other gases), the differing forces upon these molecules during gravitational collapse is thought to have allowed angular momentum to dissipate outward. Therefore Neptune must have a rather complex field at all orbits, not just a simple centripetal acceleration. Introduction to Celestial Mechanics. But, let's build that ellipse again, starting from aphelion. The explanation of the ellipse can be found in Explaining the Ellipse.February 2010: You may now read my new paper on the Moon's orbit, which extends my comments here. It is stated explicitly that the earth had this velocity before it entered the orbit. These cannot be done simultaneously. Well, the moon is going to pull the earth into a fractionally lower orbit. At any point on the circle, the orbital velocity is found as diagrammed below. 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. It therefore cannot be a strict analogy of the E/M field. Lack of angular momentum in the sun influences the space around it, which it is our measurement how. Of heavenly bodies in a gravitational field moves as it does not show why stars. Glosses over this problem by conflating, at perihelion or aphelion concept of elliptic motion (... 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