Tycho Brahe a Physics Preview Publication

An Historical Perspective

The importance of Tycho Brahe and Johannes Kepler in the minds of Americans can be seen by comparing their names to Descartes, Galileo and Isaac Newton, for name recognition. Galileo and Newton score high in recognition, probably because the falling object and gravity are simple concepts to represent pictorially, and therefore, also simple to superficially explain. Descartes scores next by an association with the statement, "I think therefore I am." Kepler follows in name recognition amplitude but only at a fraction of Descartes score, which is in turn small compared to Galileo and Newton. Tycho Brahe is absolutely unknown to the general American public. Incidentally, I single out the American public because it is the only public I know about, well enough to speak.

These facts are interesting on several accounts. The first of these is in terms of the men themselves, and the importance of their work to mankind in general. This category has further delineating aspects, one of which is chronological. In terms of each man’s influence on the work of each of the other men, Tycho Brahe, Descartes, and Galileo, are independent seminal influences. Of these three, the most difficult to replace, should he not have been included in the mix, is Tycho. The raw data of the planetary motions meticulously compiled by Tycho Brahe with his naked eye and tracking tools of his own design, is the penultimate example of, and a testament to, the importance of the experimental physicist. The great 19th century experimental physicist Michael Faraday, one of the most important men that ever lived, is even paled in the shadow of Tycho Brahe. Without Tycho, Kepler and Newton, and any possible replacements, must wait, and wait, and wait. I can see a 20th century little different from a 19th century, had Tycho Brahe never lived. The ball would have relied on Galileo and Descartes.

How important then was Kepler, once Tycho is here? The strange union of these two peculiar visionary giants is probably the most fortuitous scientific social event for mankind, to have ever occurred. The closest parallel to the biblical Adam and Eve, that exists in man’s recorded history.

Once Tycho, then Kepler must be regarded as the most important man to follow. Kepler is unique in many notable ways. He stumbled along never hiding his flaws, so certain he was, in the accuracy of Tycho’s data and the ultimate importance of his work. Remove Kepler and how long do we wait for Tycho’s work to be systematically analyzed or reproduced?

The improved development of the telescope and improved pendulum would assist with data acquisition. The interpretation of the data would be aided by analytical geometry. But the timing would be off, and would not include, the struggling, human account of Kepler, and the inspiring celestial laws his struggle revealed. How long do we wait then for another giant? Another Isaac Newton?

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 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 the same until I met Kepler. Kepler's three laws fascinated me for years to come. I suspected that these laws were a gateway that had not been opened. This turned out to be true and what follows is my take on Kepler's three laws.

I differentiate now between what I call Keplerian or Newtonian space, and what I call Euclidean space. 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 allows the study of rigid form.

Keplerian space is kinematic, while Newtonian space is dynamically extended (by the inclusion of mass). By defining these spaces with this slightly more rigorous attention to detail we can map the mathematics from one frame to another. The law of areas turned out to be the consequence of a more fundamental ratio. I will show (altho' 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 [2pir/pir^2] = [2/r].

For any given line length a perfect 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. If we represent it in terms of Euclidean space, we have an ellipse. 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).

I say that the orbital conic, which is an ellipse in Euclidean space, is an economic circle in Keplerian time-space. On what do I base this conclusion? We have seen that the ratio that defines the economics of the circle is, circumference line length to area. The form of this varying ratio stays the same for all circles, ie. 2/r. This magnitude stays the same for any given circle with respect to any segment of the circumference and its radially enclosed pie shaped area. So I must show that the orbital conic meets the same criteria.

The orbital conic will have to meet this 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 time, to the radially swept out area, must also equal the same magnitude as the ratio between the entire period and the accompanying swept out area. The law of areas is a special case of this consequence, and this consequence is a manifestation of the principle of least action. The principle of least action is the thread that connects all stable systems in the universe. The law of areas is not a special case of angular momentum.

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.

Author's note 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. 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 often get hung up in one or the other to the exclusion of the rest for awhile. Thanks.

my regards, johnreed