johnreed's take on Johannes Kepler

Posted on alt.sci.physics newsgroups

When giants speak of giants one must give that description the greatest deference. The importance of Tycho Brahe and Johannes Kepler cannot be over emphasized, but even they are paled by the significance of their work. Kepler's three laws have more to tell us than our assumptive preoccupation with gravity has allowed us to see.

Today the textbooks mention Kepler almost in passing. They note his three laws and offer that law 2 is a special case of angular momentum. A couple of elementary explanations and a deserved high reference to Newton, concludes the subject.

I can say without reservation that my interest in math did not exist until I discovered Euclidean geometry. My interest in physics was nill until I was introduced to Kepler. Kepler's three laws fascinated me for years to come. I suspected that these laws were a gateway that had not been completely opened. This turned out to be true and what follows is my take on Kepler's three laws.

I differentiate between what I call Keplerian or Newtonian space, and what I call Euclidean space. My view of Euclidean space is that space that accompanies the objects in Euclidean geometry. As I recall, that space was never defined except in terms of distance between objects, area, volume and so on. Euclidean space is devoid of motion, time, or any other form of action or change. It is purely static and in the classic case, flat, and allows the study of rigid form. Euclidean space at best, reflects one single instant in time. This definition for Euclidean space differs considerably from the mainstream use of the term.

Keplerian space is kinematic and includes more than a single instant in time, while Newtonian space is dynamically extended, Keplerian space (by the inclusion of mass). By defining these spaces with this slightly more rigorous attention to detail, we can map the mathematics from one coordinate frame to another.

The law of areas turned out to be the consequence of a more fundamental ratio. I will show (altho' with the spaces defined as above, it is trivial to do so), that the law of areas is a special, extended case of the ratio between the circumference and the area of a circle, or [2pr/pr2] = [2/r].

For any given line length a perfect Euclidean circle is the most efficient means to enclose a two dimensional area. The ratio we have noted as the circumference to area, or, [2/r] is the defining ratio for the circle economics. The interesting thing about this ratio is not so much that it exists for all circles, with a different magnitude for each circle, but that for any given circle, this ratio remains the same for any segment of the circumference, and its radially enclosed, pie shaped area. Given the symmetry of the circle, this is mundane but for the direction it points.

An orbital conic does not exist in Euclidean space. An orbital conic exists in Keplerian space, which space includes time. The fact that we classically measure the duration of the included events with clocks that are seen as external to the frame, does not change the fact that the planet exists in a space that allows a state of continual motion. If the planet were conscious it would experience duration. Keplerian space includes time. I call it time-space (to avoid confusion with the 4D space-time). If we represent the orbital conic in terms of Euclidean space, we have an ellipse (a sequence of frozen instants in time-space).

I say that the orbital conic, which is an ellipse in Euclidean space, is equivalent to an economic Euclidean circle, in Keplerian time-space. On what do I base this statement? We have seen that the ratio that defines the economics of the circle, is, the [circumference line length] to the [enclosed area]. The form of this varying ratio stays the same for all circles, ie. [2/r]. The magnitude stays the same for any given circle, with respect to any segment of the circumference and its radially enclosed, pie shaped area. Unless I am mistaken, I must prove that the orbital conic meets the same economic criteria as the Euclidean circle. To do this, I will show a direct mapping of form between the two frames.

Taking into account the different coordinate system quantities, the orbital [time-area] conic, will have to meet the Euclidean [length-area] criteria in terms of its radially swept out area (space) during its period (time). For any segment of its period the ratio of the segment per unit time, to the radially swept out area during that time, must be equivalent in magnitude to the ratio between the entire period and the accompanying, swept out area. In terms of these differentiated spaces, it is trivial to show that the law of areas is a special case of this principle, and that this is a consequence of the principle of least action.

I say that the principle of least action is the common thread that connects all stable systems in the universe. By this argument I conclude that the law of areas is not a special case of angular momentum, Rather, the law of areas is a consequence of the least action requirement for stability in the field..

Errata

We have utilized the economic property of stable systems to define the universe in terms of our local experience. Newtonian space takes the locally conserved quantity we call mass to modify Keplerian space accordingly. The generalisation of mass, to the entire universe in proportion to the magnitudes of mass found to be conserved in the local frame, is a centrist conclusion that has no compelling argument other than convenience, simplicity and elegance. .

Author's note

This post is one of a series of posts that I submit to relevant newsgroups in order to eliminate any fatal flaws that might exist in my thinking. I try to keep these simple and straight forward. If no fatal flaws are found in my logic herein, or if they are found, but not pointed out to me, I will post another paper that extends a logically consistent train of thought. These posts will hereafter be titled "johnreed's take on …", (whatever the subject might be), in order to allow the newsgroup subscriber to easily filter out my work, should he/she so desire.

Please include the e-mail option if you post a reply so that I can address it in a timely manner. Like most of you I subscribe to many newsgroups and lurk in many others, and often get hung up in one or the other to the exclusion of the rest, for extended periods of time. Thanks.

my regards,

johnreed