# celestial mechanics problems

The approximate nature of Keplerâs laws. It is impossible since the perpendicular vector has to stay the same length all the way around. Most books have differential equations on the first page, and those that dont begin by glossing the history from Newton to Gaussa history of mathematical analysis. First a solar disc is created, then this disc accretes into planets over millions of years. This is not to say that ellipses don't exist. It is mostly a tying together of existing theory, not a GUT that jettisons the whole Standard Model or proposes mysterious new strings, branes, etherons, or supraluminal velocities. Finally, let us look for the "equivalent" circular orbit. They are going to be missing chunks. We think, well, maybe when a planet is captured, it first hits an orbital tangent at an angle, instead of at a perfect perpendicular. The question is, can we connect up the ellipse? Why would it do this? Celestial Mechanics, An Introduction to Modern Astrophysics 2nd - Bradley W. Carroll, Dale A. Ostlie | All the textbook answers and step-by-step explanations People have always accepted this diagram on faith, but it is a false diagram. 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. Now, if we look ahead on the ellipse, we can see that the path begins to curve toward the sun, decreasing the orbital radius. A balancing of instantaneous velocities cannot explain it, since even if Triton happened to intersect its future orbit at exactly the right distance and at a precise 90o angle, many other factors would also be involved. The velocity variable in a=v2/r must then be this new orbital velocity. A gas is either in a state where thermal forces are ascendant or where gravitational forces are ascendant. 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. It is a sort of obscurum per obscuriusexplaining the obscure by use of the more obscure. It not only fails to solve the problem of Kepler and Newton, it adds to it. It has slowed down and gone lower, therefore we would expect a multiplied affect. For given values of this constant it is possible to construct curves in the plane on which the velocity vanishes. But there is no plane of orbit that is self-correcting in this situation. The only possibility appears to be a fortunate collision that accidentally throws it into the perfect spot. They prefer the chaos in their models, which is in some sense controllable and finite (if only because it can be stopped by turning off the computer) to the chaos in their basic theories, which was created by them and their precursors, and which cannot be turned off except by making better sense of it. Philosophers once policed physics in a small way, but no more. It has its initial velocity, and that is all. Then let a = v2/r Poincaré showed that perturbation series are often divergent and therefore they are valid only over short time spans. But nebular theory never answers the first questionthat being how could a pre-collapse nebula have angular momentum? Richard Feynman uses this example in his geometric proof of the elliptical orbit. A torque could be applied by an exclusionary fieldlike the E/M field. It investigates the causes of these divergences and indeterminacies, and their various strengths. This book was edited by a large committee of top-flight physicists. Maybe it formed by simple accretionnot gravity but random collision. If we do that then aphelion becomes the radius of the circle, and we have our circular orbit. 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. 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). It cannot look at real problems; it must invent fictional ones to divert it. To confirm this, we look at the emission lines created by a stellar wind. 25.2 Planetary Orbits We now commence a study of the Kepler Problem. Is it still a constant piece of the compositional velocity, or has it been lost? Another reason an equation unsupported by theory is dangerous is that it becomes dogma. And the same problem is going to be met when the moon is sideways to the earth. If we rigorously study the variable assignments of Kepler and Newton, what we find is this shape, not the ellipse:You see, the curvature cannot be the same on both sides if the innate motion or tangential velocity is a constant. Until orbital physics is prepared to admit that it is mainly heuristics, it will never build beneath itself the necessary conceptual framework. His assumption has never been seriously questioned. 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 directlythough in an unknown wayupon any matter within the field. Beyond this mathematical mist in which we have lost ourselves, the other main problem is hubris. Perturbation analysis hid the flaws of classical theory, and chaos theory came along later to help hide the newer flaws of GR. Why would it do this? Theory of perturbations § 1. 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. What, exactly, caused Triton to settle into its current orbit? 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). To sum up: the problem with nebular theory is that it 1) utterly fails to explain how a gas sets up around a center, 2) fails to explain low angular momentum at the center, as in the case of the sun. I have said the tangential velocity is equal to the initial velocity of the planet, before capture by the field. Laplace next turned his attention to celestial mechanics. He had nothing to add but an updated proof. Since then the science magazines have followed suit, encouraging a smug self-satisfaction while at the same time promoting increasing levels of obstruction. But a torque could not be applied by an attractive or warping field. A sub-field of physics that thinks that it is perfect or near-perfect will not make any effort to improve. 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. [GR has some mathematical failures, toothe most important of which is the failure of gammabut those are addressed in other papers.] Yes, the force is different, but the acceleration is the same. It is simply unsupported. Otherwise no body could ever be captured in the first place. You cannot physically measure at a point or an instant, and this must affect all your final numbers. And this is not even taking into account the sun's effect on the moon's orbit, which causes further uncorrectable perturbations. Three or four observations allow you to build a basic equation. The theory of the gravitational field, either Newton's or Einstein's, cannot support Kepler's Third Law. They both would have had some spin. The electrical field just is. Captured satellites must have been captured as I stated aboveby decelerating into orbit. 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. This is the theory of how the solar system was created. These cannot be done simultaneously. Next, since all the orbits of the planets are nearly circular, let the distance travelled in each orbit equal the circumference of the orbit: It is also difficult to agree with the assessment that scientists fully understand non-chaotic deterministic systems. I have listed many of the holes in orbital theory above, but every modern theory is full of invisible holes. Another problem is that even the current model believes that some satellites, like Triton and Phoebe, are captured satellites. Can we draw the line all the way back to aphelion? Its mathematics becomes its reality. There is no margin of error. Most books have differential equations on the first page, and those that dont begin by glossing the history from Newton to Gaussa history of mathematical analysis. Specifically, the lack of angular momentum in the Sun is explained in Part IV. The orbiting body is assumed by Newton to have a velocity due to "its innate force." Three or four observations allow you to build a basic equation. His popular book was a sign of the times, and a sign of things to come. 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. Even General Relativity only recast the old concepts in new but basically equivalent terms. So far so good. We are told that angular momentum is carried out to orbiting bodies, but how? It investigates the causes of these divergences and indeterminacies, and their various strengths. Preliminary results from mechanics § 3. Even if we assumed that all the helium in the pre-collapse nebula were initially positioned at the center of the cloud, and that it all was transported to the outer planets during system formation, even then that small amount of helium could not have carried all the angular momentum away from the sun. The tangential motion and the centripetal motion must be perfectly balanced or the orbit will deteriorate immediately in one direction or another (inward or outward). 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. This phase space and these grains were formed by accretion as well and perpendicular and! No change over an instant, and it is going to pull the earth to the of. The three-body problem of celestial mechanics both use the same celestial mechanics problems assumption used... 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