Harmony in the Heavens - a Physics Preview

The ancients spoke of a harmony in the heavens. They imagined a divine hand of creation and believed that all planet orbits were perfectly circular, for God would have it no other way. Even Johannes Kepler sought evidence for divinity, but instead found that the planet orbits were ellipses, with the Sun at one focus. The idea of a perfect, divine, Euclidean like harmony of form, was lost, and replaced with Kepler's clockwork order, and Newton's universal law of gravitation.

Like the Early Greeks before them, Kepler and Newton attributed the (clockwork) order to a divine hand. In 1713, Isaac Newton wrote the Scholium for the second edition of the Principia. Newton wrote, " This extraordinary arrangement of the Sun, the planets and the comets can only have originated in the design and domain of an intelligent and powerful being. This Being governs everything, not as the soul of the world, but rather as the lord of all that exists." The mystic today, like the mystics of yesterday, believe in a creator, and view the economy of stable system action as proof for its existence. It is not within my range of expertise or knowledge to determine the ultimate cause of the order we see in the universe. However, I can show that the order we see is one order that does not arguably speak to a divine hand.

But the planet orbits are not perfect circles. They are ellipses with the Sun at one focus. Even so, these planet trajectories share the property that defines the circle economics. The circle is the shortest closed line length that surrounds the largest area. For maximum return of area on line length expenditure, you can't do better than a circle. The economic of the circle is described by the ratio of its circumference and its area. Different sized circles will have different magnitudes, but for any given size area, the [circumference/area] ratio is more economic than is any other, like, given, closed, area surrounding, line length relationship.

In a given perfect circle, this relationship remains constant over any circumference segment length, taken at that circle. when the segment ratio is taken against the accompanying, radially subtended, pie slice shaped area. That is to say, if you select a circumference segment length of half the total length, the line drawn from each segment end to the circle center will cut the circle in two. If you chose a segment one quarter the total circumference length and draw a line from each end to the center of the circle, you will quarter the circle. In short whatever proportion of the circumference you chose as your initial line segment length, the area it radially subtends, to the center of the circle, will represent the equivalent proportion of the total circle area. This is a property attendant to the symmetry and economics of the circle. The constant economy at any length of the circle curve and its radially subtended area.

Consider: we see this same property in the planet orbits, in terms of time. It is called Kepler's Law of Areas. If the planet orbits were perfect circles space (distance), then Kepler's three laws would be redundant. Kepler discovered that the motion of the planet changes, in such a manner, as to maintain the temporal economic ratio of the planet trajectory and the radially subtended area. However, Kepler did not recognize his discovery in this particular way. Kepler noted that for any given time period, the planets speed up or slow down, in order that they cover the trajectoral distance necessary to radially subtend equal areas of the trajectoral conic.

With respect to any given time interval taken at any location on the orbit trajectory, the accompanying subtended pie shaped area of the ellipse will be constant. This is a ratio between the planet trajectory length and the radially subtended pie slice shaped area of the ellipse, that holds for any trajectory segment length, and its radially subtended, pie shaped area, per unit time.

The economic property that defines the Euclidean circle, also applies to the orbital action of the planet. The action of the planet mimics the economics of the circle, when we take the circumference in units of time. The value of the radial distance between the center of the planet and the center of the Sun [r], and its ratio to the orbital velocity of the planet, when converting from the solar (motion and time), to the Euclidean (static order of form) coordinate system, translationally reduces to a property of [r] and the circumference of the circle.

With the perfect spatial symmetry of the Euclidean circle we can take our economic property in the form of the ratio of the circumference to the radius. In the planet orbit ellipse the value of the line length drawn from the planet center, to the center of the Sun, when taken as a ratio with the instantaneous orbital velocity of the planet, provides us a frame that is translationally equivalent, to the Euclidean frame, in terms of economics.

Mainstream science does not see it this way. In mainstream terminology one would say that the period of the planet revolution is a function of the long axis of the ellipse.To this academic body there exists no special relationship, shared between the different planets, that connects the ratio of [r] to the orbital velocity. This is probably because it is not apparent that a direct proportional equivalence exists between one planet orbit's [r-v] magnitude as compared to another planet orbit's [r-v] magnitude. But the radial sweeping out area of the celestial conic trajectory, and the translationally equivalent, Euclidean circle circumference segment length's radially subtended area, is the connection that defines the economic property in each frame. The Euclidean circle, circumference to area ratio magnitude, varies for different sized circles. However, we can see the invariant relationship that exists between the circle's circumference/radius ratio [2pi] , even across different sized circles. The relationship in the Euclicean frame is in the fact that this specific proportional magnitude is the limiting defining property for the economic enclosure of space. The ratio becomes the constant temporal rate of sweeping out area, in the Solar frame. Or a function of the long axis of the ellipse. We have dressed this consistent economic action, according to our subjective world view, by inserting mass as the velocity partner, and calling the constant sweeping action, angular momentum. The mainstream interpretation of the law of areas largely overlooks the economy of action it necessarily derives from. But, while failing to rigorously apply the rational use of the English language to their thought processes, the physicist mathematician did not fail to apply his feeling of being pulled toward the Earth, to the economic orders of form, and subsequently declare that the force he feels is the cause of the clockwork order in the sky.

Newton's third law dealing with mass, which applies economically (a common delineator here), and is conserved at the local (earth centered) terrestrial frame (and presumably at any other local, planet centered point within the solar object-space frame), was generalized to the broader solar centered frame, and from there to the celestial frame, and finally to the entire universe, where it remains to this day. It is so incipient to our thinking that we have created absurdly impossible theoretical structures that are ultimately based solely on this assumptive generalization (See Gravity, this publication).

We discover remote systems in the universe that have extraordinary properties that indicate something other than gravity is at work, and we fail to recognize this in our zeal to confirm our gravitationally based idea of black holes. Which idea incidentally, would cause any rational thinking animal to reevaluate the sequence of thought that brought it there.

We explained the law of areas by assuming that every planet experiences a constant linear acceleration tug toward the Sun, while the Sun in turn, experiences the same tug from each planet. This idea of centripetal acceleration is the inverse of the square of the radius [r]. It is also the rate at which a sphere's surface expands with the length of its radius [r]. From here everything follows mathematically from the properties of the order of form. One can regard the centripetal acceleration of the planet as the cause of the ellipse which is a function of the long axis. So setting the mass force of the Sun equal and opposite to the mass force of any planet makes them directly proportional to each other and inversely proportional to their distance apart, measured at center. All of these critical properties, including the measure from center, speaks to the trajectory of the planet, which is an ellipse in space and a circle in time.

Although I can show that the idea for a universal gravitational attraction between all objects in the universe is a grossly assumptive unfounded generalization, I cannot prove that the assumptive generalization for gravity is invalid, except by noting that the constant acceleration at free fall is independent of mass magnitudes. But it is clearly shown by reason alone, that the assumptive generalization for the force we feel and quantify locally, is hardly written in stone. In fact, I will show that it is very shaky and highly unlikely. Why should the order we see in the universe be caused by a local effect we feel at the terrestrial frame? What is so special about us, that we can elevate our local determination of rest mass and set the universe accordingly?

The ancients had a technique for a mathematical proof that argued logically, step by step, from a premise, and if they could force a ridiculous conclusion from that argument, they could prove the falsity of the original premise. Mass derived gravity has been taken to its logical consequence in tandem with our poorly defined but highly scientific quantity we call visible light, and has given us the black hole, which even leads us to warped space and other infinitessimally small universes. We have allowed any absurdity its day of fame, by referencing the uncertainty principle, which allows for many conundrum events and is based only on our ignorance. We even have the audacity to justify certain absurdities by stating that "the theory of relativity does not forbid it", just as though the universe can do anything that is not forbidden by a theory developed by man. As though our inability to determine an event provides the latitude to justify and explain the absurd? Look, I know that gravity is a fundamental part of our experience and I know how difficult it is to release it as a fundamental property shared between all objects in the universe. You might even want to bring in Henry Cavendish and his thin gossamered torsion device to cite as proof for the force between masses. But this too only shows (in the best interpretation for gravity) that a relationship between objects over distance exists. It does not necessarily speak to any effect we feel, but only to the principle of least action. It is rigor we want prior to our assumptions, not after we have erroneously embarked on a path to nowhere. I have to avoid these occasional outbursts. Its just that when I get to the absurd conclusion part, I realize that its not going to cause a change in our thinking. So I rant and rave for a moment..

Newton's third law generalization to the solar system is not based on congruency of form, but rather, it is based on similarity of form. The economic action in the sky must show the same structural economy as economic action anywhere in the universe. This similarity that is common to economic action allows our idea of gravity to work anywhere an economic order of form exists, with but one stipulation that derives from the local terrestrial frame. The equivalence of mass magnitudes in free fall, is the property that allows us to use a balance scale, a fulcrum and lever, an inclined plane, and every other power leveraged tool that aids us in countering the attraction we have by virtue of rest mass, to the Earth. So it seems reasonable to consider inertial mass equivalent to gravitational mass and even declare that the force of gravity is universal, where every object attracts every other object with an equal but opposite force magnitude, proportional to local inertial mass magnitudes..

But the planet mass cannot figure as fundamental to its orbital invariance (See excerpt 1.3). If anything, the irregularities and perturbations of orbit, may be the planet's actual contribution to invariance, due to its initial variable mass aggregation during planet formation, and its changing mass thereafter. The consistent action is the angular velocity of the radius, as measured from the Sun. Our inclusion of mass, assigns the Sun an angular momentum whose magnitude derives from our measure of local inertial rest mass magnitudes, which we set equivalent to a force we feel as weight, and call gravity.

In a circular trajectory, with say, a rock on a string, the mass and the velocity of the rock speaks to its momentum, independent of the string. In the planet orbit, the value of [r] and its angular velocity, speak to the constant rate of sweeping out area. Niether the mass of the Sun, or the mass of the planet, figures as a component of this action. If mass did figure as a component of the constant angular velocity of [r], we could not orbit satellites on the basis of the value of [r] and orbital velocity alone, nor could we have the constant acceleration across mass magnitudes during free fall. The velocity of the planet varies to meet the Sun centered constant. The momentum of the planet speaks to a separate and distinct variable quantity that arises from the motion and mass of the planet itself. The variable momentum of the planet [mvr] is conserved because the mass of the planet is paired with the velocity of the planet [s/t] or [s/r] which is constant over one complete cycle and any proportional temporal portion of that cycle. The economic behavior of inertial mass in the terrestrial frame and the economic behavior of inertial masses in the solar frame, coupled with our sensory detection of our own weight and its quantitative equivalence to terrestrial rest mass, causes us to define the universal order, in terms of an aspect of that order we feel as force. Our own weight. What we feel locally as a result of the universal order varies according to our weight. A fat man experiences more inertial mass than a thin child.


The Finger Points to Centripetal Force Origin	The Finger Points to Centripetal Force Origin

The direction of the centripetal force vector points to the center of orbit. A centripetal force was used by Newton to help explain his gravitational concept. Newton was probably influenced here by Huygen's idea for centrifugal force. The significant property to note is that the centripetal force vector changes orientation according to the location of the stone. This force is quantified in terms of the stones inertial mass. What do we call the force that holds the string to center? Centripetal. Where does its vector point? To center. Its orientation changes according to the stone's location. The anchor for this force is a theoretical sky hook that somehow, mysteriously arises from the property of mass.

Consider again the rotating rock on the string. The centripetal force vector is toward the hand along the direction of the string. We can use this definition of the force and enjoy the benefit of the time distance properties of the stone trajectory if maintained as constant. However, the equal and opposite property of the force only occurs at near the point the string breaks. In such a system, the slightest invariance could result in system degradation. Equal and opposite could not long maintain a mutual attraction. It works fine operationally applied to an already time-space ordered stable system of economic actions, but try to construct such a convenient system mathematically. It makes the solving of the three body problem from the in place system a matter of childs play. Equal and opposite speaks to the behavior of momentum in the mass equalized horizontal to free fall direction. There is an attraction toward the planet that keeps it together. Our definition of centripetal force to describe it, fails. We created the gravitional force after our own image.

The Stone's Inertial Force [ma] is Equal and Opposite to the Centripetal Force. In these three diagrams with the pointing finger, the only real force we have is the stone's inertial mass. Centripetal Force in this context is nothing more than an imaginary sky hook that enables the math to operate in terms of time and space.

With the little man above pulling in the same direction as his inertial force vector in the finger diagram to the left, we see an apparent contradiction. The centripetal force in the diagram above, that counters the mans inertial mass is oriented transverse to the stone's inertial force vector. And if we reexamine the first spinning stone diagram, where the bow is tied to the finger. We see the direction of the centripetal force is transverse to the plane of the string. What happens if the giant above acts on Newton's third law by pointing his finger straight out. The little man goes flying.

...the only thing that figures in a stable orbit is the planet orbital velocity and the distance between the planet center and the center of the Sun. Isaac Newton added the quantity called mass to this coordinate system, largely based on the conserved dynamic quantity called momentum, involving the behaviour of mass at the transverse to free fall direction, near the surface of the Earth. The measure of mass components transverse to free fall direction, and their proportionally constant behaviour, is a consequence of the constant acceleration of gravity across mass magnitudes at rest or in motion. This equalizing influence levels the playing field for the local terrestrial masses. What we learn in this field of action is that all unstable processes seek equilibrium in the most efficient manner...

... Kepler gave us another ratio. The period squared, taken against the radius cubed, of each planet, is also constant. A line length squared, gives us a square. If we take the square to the next power, it provides us a cube. The square of a circumference derives from a sphere. The cube of a radius derives from a sphere. An economic circle is a plane of the sphere... What then does the ratio T²/r³ represent? A sphere is the economic enclosure of volume as the circle is the economic enclosure of area. Does this speak of a universal gravitational constant, or does it merely denote the mathematical property of an extended, spherical, economic order of form?

This is one of my ongoing but unfinished sections. I admit that it is a mess. I've posted this to allow anyone that is interested to participate or to follow the progress of its development. My unfinished work is not a pretty sight but ideas are usually presented in finished form and many persons never realize the process or the work that goes into such a piece. My greatest idol in science is Kepler. He presented his work to my way of thinking, in the true spirit of science. Complete with all its flaws of development. We do not see that anymore, in part because everything is presented solely in terms of the mathematics and the simplistic elegance of the final equation. Its a distinctly different process that allows operational answers absent conceptual understanding. A convenient short cut that circumvents reason. But the mathematics is the handmaiden of reason and not its master.

Posting it also forces me to deal with it expediently and get it coherent. The direction I'm going is fairly clear by assertion, but assertion alone is of no value. I'll continue to hammer it out until I'm satisfied that it is brief, to the point, and rationally valid. The counter magnitude includes you, and appears to have been accessed now, comparatively less than the rest of the web site (probably fortunate for me). But the web site is not that old and some of these accesses have been by me as I work on it. So, if you are one of the few that foraged his/her way through this section, please accept my apologies for its inclusion and if you are not completely exhausted or totally bored, click on continue above to go to another, shorter section on gravity that will ultimately be combined with this section. My main reason for including this section is to show the crude process by which it develops. I think that Newton was inspired by the flaws he saw in Kepler's work. Flaws that Kepler readily shared with what he knew would eventually be his reader. The Principia is of course on a parr with Euclid and Appolonius and Archimedes, and modeled in that classic tradition. The Principia is arguably one of the greatest works to have ever been written. The arduos process of its creation is not visible. I can safely say that absent the word processor, I may have never completed a single section of my ranging and scattered manuscripts, although I began the process with a typewriter, tape recorder and several secretaries. It is all the more a tribute to Newton that his work was done by hand and pen. I will always recall my first experience with Newton's Method as the first time I became aware of the extreme intellectual power of its developer. The repetitive process of division on unweildy long numbers often left me in the middle of trying to locate my position in the process. And I had a calculator that performed the computational part of the work. It amazed me that Newton not only did this work by hand, but that it could be developed at all in so succinct a mathematical form. So when I speak of Kepler as my idol, it is like speaking of my father with whom I could identify closely. Isaac Newton however, is probably the most important man to have ever lived and any flaw I find in his system, is presented as an after thought, or slight modification to eliminate a restricted view. His work will continue to be the local base operational method of choice, even as our conceptual understanding of the processes increase.


Kepler's Law of Areas	Stone, String and Finger