Why the Eternal Ellipse?

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• #10804

The ellipse is a central orbital theme in TUB. I think it wise to explore this fact in a discussion to see what we can discover about the eternal ellipse.

The elliptical orbit is fascinating because, geometrically, it has two foci. One is the larger mass and the second focus is empty. Can your fellow scientists, Nigel, offer some explanation for this? I cannot find anything in gravitational theory that can explain the elliptical orbit that jives with the inverse square law. When an planet reaches its farthest distance from the Sun, what increase in gravitational pull overcomes the inverse square law to pull the orbital back towards. the Sun? Alternatively, the planet at its nearest approach to the Sun seems to experience less gravitational pull to keep the orbital from giving way to the inverse square law and crashing into the sun. Neither Newton nor Einstein have answers for this.

#10820

I cannot find anything in gravitational theory that can explain the elliptical orbit that jives with the inverse square law. When an planet reaches its farthest distance from the Sun, what increase in gravitational pull overcomes the inverse square law to pull the orbital back towards. the Sun? Alternatively, the planet at its nearest approach to the Sun seems to experience less gravitational pull to keep the orbital from giving way to the inverse square law and crashing into the sun. Neither Newton nor Einstein have answers for this.

Newton is the one who did answer this if you want to look into it further. The insight that planetary orbits are elliptical came before him, it goes back to Kepler and his first law of planetary motion.  Newton then showed from the universal laws of motion that elliptical orbits are exactly what you get from gravitational forces.

#10834

Newton then showed from the universal laws of motion that elliptical orbits are exactly what you get from gravitational forces.

I don’t think so. Force of gravity ≅ M1 * M2 / d^2. This is Newton’s gravity equation. You can see clearly the inverse square law is in this equation but TUB tells us that this so called law is only a rough approximation and that the diminution of gravity has much to do with the properties of space. To address the problem here you must defend the indefensible. An elliptical orbit has an aphelion and a perihelion. That means that when an orbital is at its furthest away from the major mass, it must experience a much diminished gravity according to Newton’s equation shown above. What force brings the orbital back to the major mass to complete the orbit? Is the gravitational force variable throughout the orbit? Absolutely nothing that Newton provided explains this.

In Newton’s and Einstein’s time we did not know of space expansion. The Cartesian coordinates we still use today depicts an unbounded cube, an absolute space. This is a background that does not move. If we may use TUB as a reference here, we are told that space moves, and it is not absolute and not a boundless cube. This is a major revelation! Einstein’s gravity is caused by mass distorting the geometry of space. TUB states that gravity is the sole control of matter-energy. How can mass control gravity? this is contrary to TUB. This is a major revelation! And this is just for starters. Houston, we have a problem.

Newton is the one who did answer this if you want to look into it further.

I’ve spent many years looking into it and it looks pretty ugly.

#10855

Here is one good paper to simplify it down as far as maybe it can reasonably be simplified, “Teaching the Kepler laws for freshmen”:

http://arxiv.org/pdf/0707.4605.pdf

“It is hard to exaggerate the importance of the role of the Principia Mathematica in the history of science. The year 1687 marks the birth of both modern mathematical analysis and modern theoretical physics. As such the derivation of the Kepler laws from Newton’s law of motion and law of universal gravitation is a rewarding subject to teach to freshmen students. In fact we were motivated for our work, because we plan to teach this material to high school students in their final grade. Of course, the high school students first need to get acquainted with the basics of vector geometry and vector calculus. But once this is achieved there is nothing in the way of understanding our proof of Kepler’s law of ellipses.”

You can find a lot of other proofs through googling:

They really are called proofs for a reason, it’s inexorably, mathematically the case that the law of universal gravitation from Newton results in elliptical orbits (circular orbits are simply a special case of elliptical orbits where eccentricity = 0).

Newton not only proved this but he proved that the only way orbits could be ellipses would be if gravity were an attractive force following an inverse square law.  You’re saying that the inverse square law means that elliptical orbits don’t make sense. Newton proved that you can’t get Kepler’s laws of elliptical orbits any other way!

As the PDF above summarizes, “Using Euclidean geometry Newton derives in Proposition 11 that the Kepler laws can only hold for an attractive 1/r^2 force field. The reverse statement that an attractive 1/r^2 force field leads to elliptical orbits Newton concludes in Corollary 1 of Proposition 13.”

#10863

Hi tas.
I will not argue that Principia is the scientific bible. I’m saying that this scientific scripture is false.

42:11.5 Linear-gravity response is a quantitative measure of nonspirit energy. All mass—organized energy—is subject to this grasp except as motion and mind act upon it. Linear gravity is the short-range cohesive force of the macrocosmos somewhat as the forces of intra-atomic cohesion are the short-range forces of the microcosmos. Physical materialized energy, organized as so-called matter, cannot traverse space without affecting linear-gravity response. Although such gravity response is directly proportional to mass, it is so modified by intervening space that the final result is no more than roughly approximated when expressed as inversely according to the square of the distance. Space eventually conquers linear gravitation because of the presence therein of the antigravity influences of numerous supermaterial forces which operate to neutralize gravity action and all responses thereto.

“Using Euclidean geometry Newton derives in Proposition 11 that the Kepler laws can only hold for an attractive 1/r^2 force field.

The foundation of Euclidian Geometry rests on 5 axioms. Axiom number 5 is that regarding parallel lines. This axiom, in particular, forms the cornerstone of remainder of “The Geometry”, including non-Euclidean geomtery.

The theory of parallel lines accepts as its sine qua non the concept of absolute space. Space must be absolute and infinite for a pair of parallel lines never to meet.

TUB makes a big deal about stating that space is sub-absolute and it even moves. This alone blows up the entirety of Euclidean geometry, and along with it Newtonian propositions. Did Newtonian space move? No, Newtonian space was absolute. Was Newtonian time relative? No, it was absolute. Was Newtonian light finite? No, it was infinite.

Was Einstein’s concept of time circular simultaneity? No, it was relative but linear. Was Einstein’s concept of space sub-absolute? No, it was absolute but flexible in the presence of mass. Did Newton’s or Einstein’s concept of space move? Absolutely Not!

Newton flatly rejected the logarithmic spiral ellipse for reasons that had to do with his contention that the orbits would spiral into the Sun or out into space. Newton provided a rigorous proof in Principia that disallowed a logarithmic ellipse owing to his proof that an inverse cubic law would have to be in effect and this would not be consistent with Earth-Moon observations. It is true that the poorly understood gravity attenuating properties of space provide the inverse square of distances between masses to roughly approximate the lessening in gravitational force. Still, this does not provide any cover for Newton’s folly. Sure, Newton described that elliptical orbits but this was simply mathematics he inherited from Descartes. Newton did no physics here because he failed to show the differential forces that cause an orbital to follow such a path of infinitesimal changes in radius of curvature that is required to follow an elliptical orbit.

Either we pay more attention to what TUB is telling us or we keep on going down this path of false science. They both cannot be right in the points I made above.

#10874

I will restate my previous discussion and I will not have to take anyone back to high school math. In fact, I will use only elementary arithmetic to make my point.

Newton’s law of gravity is F = G [M1*M2/d^2] where F is the force of gravity, G is the gravitational constant, M1 and M2 are the masses incolved in a two body system and d is the distance between them at any one point.

In the elliptical orbit of the Earth around the Sun what changes?

Answer: F and d only. In Newton’s equation the force of gravity changes as the inverse of the distance between the masses changes.

In the elliptical orbit, there are two extremes. One where the Earth comes closest to the Sun and the other where the Earth is furthest away from the Sun.

At which extreme is the gravitational force greatest and at which extreme is it least?

Answer: F is greatest when the distance is least and visa versa. And the forces are very very different because d is a squared value.

By forth grade I could easily do this arithmetic when I learned to answer < and > problems.

Gravity being an attractive force, the question remains as to what brings the Earth back into orbit once it has reached its furthest extreme in distance from the Sun? What keeps the Earth from crashing into the Sun when it is at its closest to the Sun and the force of gravity is greatest?

Newton does not address this glaring, obvious problem and no one has since Kepler’s discovery. It is simply astounding to me that this is overlooked and for so long.

I suggest we first get acquainted with simple math before we muddle the waters with the calculus.

#10933

Maybe I can help clarify it for you by instead of starting in the orbit being flung away from the sun, start with the state of the object in orbit at its furthest point, at aphelion.  Imagine the sun and instead of a planet in orbit let’s imagine something smaller, a boulder.

Aphelion is the point precisely where an object has neither motion toward or away from the sun.  If the boulder were to be placed say 1 billion miles away from the sun and with no other motion of its own, even though the inverse square law says that gravity must be very weak out there, it still is a force acting on the boulder, and the boulder will begin to accelerate toward the sun.  Since it has no other motion relative to the sun, it just accelerates faster and faster until it hits the sun.

An object with a certain amount of velocity at aphelion that is perpendicular to the sun however won’t proceed directly in a line to the sun but will arc toward it. For many low values of this sort of sidewise velocity, the object will not be able avoid the sun, it will bend closer and closer as it approaches and it will still hit the sun on a collision course.

But I think you should be able to see that there always will be some value of perpendicular velocity high enough at aphelion, which if the object has it, means that though the object falls to the sun and accelerates in velocity faster and faster toward it, in the end it doesn’t quite collide with the sun but instead skirts around it.

For any object that does this, as it now flies away from the sun, the very same gravitational force that accelerated the object in falling toward the sun now decelerates the object as it speeds away.  I think you should be able to see that this must be a symmetrical process in the absence of any other forces, due to conservation of energy.  For any object at its aphelion, at that point the object has maximum potential energy.  It’s like if you are standing on a bridge attached to a bungie cord and haven’t yet jumped. As the object then falls toward the sun, the potential energy is converted into kinetic energy in the form of higher and higher velocity.  At perihelion there is maximum kinetic energy — maximum velocity — and no more potential energy.  (The reason it doesn’t fall and hit the sun though being so close and F from gravity being at a maximum is that simultaneously it has a much higher velocity now, too fast to collide.)  It should be clear that this kinetic energy is destined to be converted back to the state of being potential energy at the aphelion.

When you jump off a bridge with a bungie cord, I’m sure you understand that you can’t bounce back up higher than the bridge on the return trip.  It’s the same for an object in orbit.  If an object has an aphelion it can’t go around and in another orbit escape further past it (unless some force acted on it other than the sun’s gravity).  It’s not a mystery why at the far end of its orbit it bends back to start another orbit, even though the force of gravity is weakest.  The object never had enough velocity to begin with to escape, it was always destined to bend back. The math does show that rigorously and also that the shape of the path that is traced by the object is an ellipse when the attractive force is following an inverse square law.

There are of course many trajectories and starting velocities that lead to the scenarios you describe, of objects falling into the sun or objects going off into the deep and never coming back.  What we see in the solar system right now is the end result so far of billions of years of those objects being lost.  Those happen but they aren’t orbits.  What we see are the objects that did have the right trajectories and velocities to be in stable orbits so that’s why they’re still here.

#10941

Hi tas.
I agree that all experiments and observations have confirmed Kepler’s equation for the ellipse. What I am saying is that the accelerations and velocities in the elliptical orbit were impossible to explain with the gravitational field. In other words, we have the correct math, the correct shape , but the wrong mechanics. We have a real problem here because the accepted kinematics cannot support the motions in the field. A set of equations without mechanics is not physics, it’s heuristics.

Newton used the term “innate motion” as the velocity of the orbiter carried into the orbit from prior forces caused by the formation of a nebula or solar disc, but it cannot be caused by the gravitational field of the current orbit. There is simply no mechanism to impart tangential velocity by a gravitational field. Both Newton and Einstein knew this. There is no possible way to generate a perpendicular force from the center of a spherical or elliptical gravitational field.

The orbital velocity of an orbiter at any point in the orbit is the vector addition of the two independent motions; that is to say, the centripetal acceleration at that point in the field and the perpendicular velocity, which is a constant.
The orbiter must retain its innate motion throughout the orbit, no matter the shape of the orbit, otherwise its innate motion would dissipate the the orbit would become unstable. The orbiter must then always retain it innate motion over each and every differential. Take the two most important differentials, those at perihelion and aphelion and compare them. We see that the tangential velocities due to innate motion are equal. But the accelerations are vastly different, due to the gravitational field (inverse square law). And yet the ellipse shows the same curvature at both places. The ellipse being a symmetrical construct, this is a physical impossibility. Given the motions, the ellipse is impossible to explain.

The logical creation of an ellipse requires forces from both foci, but one of our foci is empty. Modern analysis conflates orbital velocity and tangential velocity. But the tangential velocity does not curve. These elliptical orbits cannot be explained with the theory we currently have. We have a huge theoretical hole because the theory of the gravitational field cannot explain the most basic math it contains. Current theory attempts to plaster up that hole by summing the closed circuit, showing that everything resolves. But this proves nothing, since they cannot help but resolve. This is a closed circuit by definition. It would be very surprising if the sums did not resolve. We are talking about differentials here. The differentials betray huge holes in the theory. These differentials can be summed to show a circuit, the variance they contain cannot be explained by the gravitational field for the innate motion.

To make the ellipse work, you have to vary not only the orbital velocity, but also the tangential velocity. To get the correct shape and curvature to the orbit, you have to vary the object’s innate motion. But the object’s innate motion cannot vary. The object is not self-propelled. It cannot cause forces upon itself.

I am not claiming that Kepler’s or Newton’s math is wrong. I am not claiming that the planets do not draw ellipses. The problem is with the underlying mechanics. The gravitational field, as it is currently defined, cannot support the shape or the equations. We need a unified field that can explain them.

TUB provides a hint for us to resolve this problem. I will post it here to get you thinking.

11:8.9 Paradise is the absolute source and the eternal focal point of all energy-matter in the universe of universes. The Unqualified Absolute is the revealer, regulator, and repository of that which has Paradise as its source and origin. The universal presence of the Unqualified Absolute seems to be equivalent to the concept of a potential infinity of gravity extension, an elastic tension of Paradise presence. This concept aids us in grasping the fact that everything is drawn inward towards Paradise. The illustration is crude but nonetheless helpful. It also explains why gravity always acts preferentially in the plane perpendicular to the mass, a phenomenon indicative of the differential dimensions of Paradise and the surrounding creations.

#10942

Well, I feel I’ve reached the point where I can’t do much more than restate what I’ve already said, so I’ll let you continue on with your own endeavors.  In your explanations are some pretty significant misunderstandings on this topic (like that “ellipse requires forces from both foci” and “elliptical orbits cannot be explained with the theory we currently have”), so I’m not going to be able to try and follow your logic extending beyond these.

The only force you need in order for there to be elliptical orbits is attraction according to the inverse square law F = G*(m1*m2/r^2).  I know you don’t believe that and think there’s a mysterious shocking hole that has gone unnoticed, but there really isn’t.

Take the two most important differentials, those at perihelion and aphelion and compare them. We see that the tangential velocities due to innate motion are equal. But the accelerations are vastly different, due to the gravitational field (inverse square law). And yet the ellipse shows the same curvature at both places. The ellipse being a symmetrical construct, this is a physical impossibility. Given the motions, the ellipse is impossible to explain.

This is untrue.  Given the motions, and the inverse square law, an ellipse is the only orbital path that can result.

I am not claiming that Kepler’s or Newton’s math is wrong. I am not claiming that the planets do not draw ellipses. The problem is with the underlying mechanics. The gravitational field, as it is currently defined, cannot support the shape or the equations.

But of course then you are saying Newton’s math is wrong.  What he showed is that based on a mechanic of universe gravitation with an inverse square law where F = G*(m1*m2/r^2) then what results are elliptical orbits.

#10947

This is untrue.  Given the motions, and the inverse square law, an ellipse is the only orbital path that can result.

This can give you an ellipse on paper, but you need forces to actually draw an ellipse mechanically by celestial orbs.

I cannot emphasize this enough. This is math, not physics. Your pencil can do this by the force of your hand but where are the forces in the solar system and elsewhere? Newton’s math is not necessarily wrong, they are just missing the mechanical forces that cause and that is pure heuristics. There is a disconnect between the math and reality.

I know you don’t believe that and think there’s a mysterious shocking hole that has gone unnoticed, but there really isn’t.

Oh yes there is. When Feynman’s famous explanation of the ellipse uses the visualization of string and two thumbtacks, this visualization requires two foci. It cannot work with an ellipse and only one focus.

#47477

it’s the perfect shape for the ellipse of all the other spheres’ orbits in creation.

105:0.1 (1152.1) TO EVEN high orders of universe intelligences infinity is only partially comprehensible, and the finality of reality is only relatively understandable. The human mind, as it seeks to penetrate the eternity-mystery of the origin and destiny of all that is called real, may helpfully approach the problem by conceiving eternity-infinity as an almost limitless ellipse which is produced by one absolute cause, and which functions throughout this universal circle of endless diversification, ever seeking some absolute and infinite potential of destiny.

The ellipse is a central orbital theme in TUB. I think it wise to explore this fact in a discussion to see what we can discover about the eternal ellipse. The elliptical orbit is fascinating because, geometrically, it has two foci. One is the larger mass and the second focus is empty. Can your fellow scientists, Nigel, offer some explanation for this? I cannot find anything in gravitational theory that can explain the elliptical orbit that jives with the inverse square law. When an planet reaches its farthest distance from the Sun, what increase in gravitational pull overcomes the inverse square law to pull the orbital back towards. the Sun? Alternatively, the planet at its nearest approach to the Sun seems to experience less gravitational pull to keep the orbital from giving way to the inverse square law and crashing into the sun. Neither Newton nor Einstein have answers for this.

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