Kepler and the Key to the Copernican system
How pseudo-scientists insist Kepler's elliptical trajectories are real
In 1609, Johannes Kepler published Astronomia Nova, which provided the mathematical and theoretical cornerstone of the Copernican theory advanced 60 years before by a cabal of astrologers and cartographers centred around Wittenberg University. The universities of Wittenberg, Ingolstadt, Tübingen, and Leipzig contained a core group of alchemists who regularly exchanged information on various topics during the 16th century. Astrology and cartography were key elements of concern to them. Perhaps surprisingly, so was the lack of pre-eminence of the Sun in the heavenly skies. Without any empirical evidence to support their ideas this tight-knit group of astrologers pushed to dislodge the Earth from its throne at the centre of our local system and replace it with the Sun. Michael Mästlin and others played key roles, but the stars of the production were Georg Joachim Rheticus and Johannes Kepler. Rheticus wrote his second work under the name of an obscure canon from Ermland called Nicolaus Copernicus. I will elaborate upon the reason for this in a future article.
Kepler graduated from the University of Tübingen. Tübingen had longstanding ties to the University of Wittenberg. One of the leading alchemists at Tübingen was Johannes Stöffler, whose students included Sebastian Müller and Philip Melanchthon, Luther's famous sidekick. Melanchthon's name was synonymous with the University of Wittenberg. He became known as the 'Teacher of Germany' as he was deeply involved in forming the indoctrination systems in that country during his lifetime. From 1511 onwards, Stöffler was appointed professor at Tübingen University by Duke Ulrich of Württemberg to the recently created Chair of Mathematics and Astronomy. Stöffler was also a good friend of Johannes Reuchlin, who produced 'On the Art of Kabbalah' in 1517 and was close to his grand-nephew Philip Melanchthon. Reuchlin had traveled widely and knew the alchemists surrounding Marcello Ficino and Giovanni Pico della Mirandola. Reuchlin became renowned in part also for his famous battle of words with Thomas Pfefferkorn in what would come to be known as the Reuchlin-Pfefferkorn Controversy.
Kepler was well aware of the significance of these men. His teacher, Michael Maestlin, had graduated from Wittenberg and later became a professor at Tübingen. Maestlin linked Rheticus and the Wittenberg circle of influence directly to Kepler. At Tübingen, Philip Apian taught Mästlin. Philip Apian was the son of Peter Apian, a renowned mathematics professor at the University of Ingolstadt. In or around 1539, Rheticus had traveled south from Wittenberg to visit several fellow astrologers for advice on how he should go about composing his two most famous works, Narratio Prima and 'On the Revolution of the Celestial Spheres.' Peter Apian published his most famous work 'Astronomicum Caesareum' in 1530 and one year later would be appointed the court mathematician to the Holy Roman Emperor, Charles V. If you were going to write a revolutionary work on celestial mechanics deploying trigonometry and geometry to bolster your claims who else would have been more suitable a man to visit than Peter Apian? Conventional historians accept that Rheticus met with Apian on this occasion, although there is no record of what they discussed.
Having graduated and worked at Tübingen University for many years, Mästlin was appointed a full mathematics professor in 1584. By this stage, Mästlin was well connected with the royal court of the Duke of Württemberg and the court of the Duke of Bavaria. It was with the mysterious figure of Hans Georg Herwart von Hohenburg, a close confidante of the Duke of Bavaria, that Mästlin and Kepler maintained close professional relationships where they discussed matters relating to astrology and chronology. Historians have primarily discarded Hohenburg, but he played a key role in getting Kepler a position as an assistant with Tycho Brahe at the royal court of Rudolph II in 1600. He was also the author of a rather bizarre but little-known book called 'Thesaurus Hieroglyphicorum' published in 1610. It features many images of Egyptian obelisks. The obelisk was a trademark of Rheticus, and he often depicted pictures of obelisks prominently in his work.
Once established as an assistant to Brahe, Kepler did nothing to assist his cause, and it looked at one point that the working relationship between the two had broken down irretrievably. Nevertheless, Brahe had some fondness for Kepler and believed that Kepler would accept Brahe's Tychonic system of the universe. Brahe appears to have been highly naive and unaware of the larger game. Nor did he seem to understand how dangerous the Tychonic system was to those who sought to destroy it.
After the murder of Tycho Brahe in late 1601, Johannes Kepler finally realised his dream. For years, he had been obsessed with accessing Brahe's entire collection of planetary data and proving that the Sun was at the centre of the solar system, guiding the planets in their orbits. After struggling for many years to understand the motions of Mars, Kepler finally published his Astronomia Nova (New Astronomy) in 1609. Kepler gained worldwide and lasting fame with its publication, and it has become a key work in the canon of modern astronomical celestial mechanics. Decades later, Newton relied on the veracity of Kepler's laws of planetary motion when he introduced and applied his force of gravity to explain the elliptical trajectories of the planets. No one doubted Kepler's integrity nor his dedication to the principle that observational empirical data must be used as the key to unlocking the underlying natural laws that govern the motions of the planets. Since the publication of New Astronomy, few people have dared to question either the rules he created or the methodology he used to devise them. They have been written in biblical stone and can never be edited, updated, or, dare it be said, erased.
Like all scientific works of the sixteenth and seventeenth centuries, Kepler wrote Astronomia Nova in Latin. The first translation of Kepler's work into English was only undertaken in 1992 by the scientific historian William H. Donahue. This fact alone should raise eyebrows for a work that is fundamental to our understanding of celestial mechanics. The number of people who have read and understood this work is minimal. Before publicising Kepler's work, Donahue had written an article for the Journal for the History of Astronomy. The title of the article 'Kepler's Fabricated Figures: Covering up the Mess in the New Astronomy' can hardly have inspired confidence in those who were hoping to read about a determined scientist who never gave up on his dream to unlock the secrets of the motions of the planets. Despite the political turmoil that engulfed his life, he was a man who nevertheless succeeded in producing a work of such intellectual magnitude that it changed the world forever. Unfortunately, the facts laid out by Donohue are more prosaic.
In New Astronomy, Kepler formulated two of his three laws. His third law would come much later when he published his Harmonices Mundi (The Harmony of the World) in 1619. In New Astronomy, Kepler devoted most of his efforts to establishing the proper motion of Mars around the Sun. Like Brahe, he knew that Mars was the key to unlocking our local system. This long struggle resulted in his first two laws of planetary motion. At the beginning of the book, Kepler includes a picture that he claims shows the trajectory of Mars from 1582 to 1600, as observed from a stationary Earth lying at the centre of the universe. This image is shown in the figure below
The next figure shows a time-delayed image of the orbit of Mars taken from Earth by amateur astronomer Tunc Tezel in 2018.
It is left to the reader to judge whether these two images have similarities. Judging by the article William Donohue wrote1 about his study of Kepler's work, he was surprised to discover how confusing and sloppy it was. As he says in the very first paragraph, all Kepler had to do was to plot the points of the orbit of Mars, and they would fall on an ellipse with one focus on the Sun. Kepler did not do this. Donahue is bending over backward to try and work out exactly how Kepler arrived at his conclusion from the observed data points that Mars is moving around the Sun in an elliptical orbit.
In Donahue’s own words,
We might at this point condemn Kepler for fraud and bring the case to a close. But this would be to ignore what is perhaps the most fascinating question: Why did he do it [fake the numbers]? Was it simply a matter of wanting the argument to be cleaner and neater, or was there some deeper justification? …..In other words there is little point in attempting to make the observations generate the theory. Not only would the numbers be confused, but Kepler saw clearly that no satisfactory theory could come of such a procedure. So, rather than obliterate the traces of his earlier struggles, or present them in their messy detail, he chose a short cut. And while we might criticise him for presenting deductions from the theory instead of from observations,we can also use this as an occasion for better understanding of what Kepler thought he was doing.
Donahue claims that Kepler did not use empirical data to derive his theory of elliptical orbits, but that's okay because, since then, scientists have proven that planets move in elliptical orbits. That, at least, is the implication. No other scientific work in the world can show from empirical data that planets move in elliptical orbits, so Kepler's work is all we have. If Kepler's work is bogus, no one has proven that the planets move in elliptical orbits.
The problem with Kepler's work.
The most obvious problem is that when Newton's laws are applied to Kepler's theory of elliptical planetary orbits, the theory falls apart. Let us now restate the three laws of motion that Newton outlined in Principia:
A body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is acted upon by a force. This is known as the law of inertia.
At any instant of time, the net force on a body is equal to the body’s acceleration multiplied by its mass or, equivalently, the rate at which the body’s momentum is changing with time. This is known as the law of acceleration under an impressed force.
If two bodies exert forces on each other, these forces have the same magnitude but opposite directions. This is known as the law of reciprocal action.
According to classical physics, the trajectory of any object moving through our local system around the sun is governed by two kinematic variables: the centripetal force that pulls on the object and drags the object toward the sun and the tangential velocity bestowed on the object that the object has always possessed and always will possess. This is implied in Newton’s laws above. Beyond these two variables, there is nothing else. It isn't easy to demonstrate how a planet finds itself in a stable orbit around the sun. Nevertheless, it is assumed that at some point in the past, each planet moved within the sphere of influence of the sun and was captured in such a way that the tangential velocity and the centripetal force exerted on the object acted to pull it into an elliptical orbit. At this point, we need to distinguish between the tangential velocity, the object’s initial velocity, and its so-called orbital velocity. As pointed out by Miles Mathis2, orbital velocity is a misnomer as it is not a velocity but a complex motion produced by the tangential velocity and the centripetal acceleration. The product of these two kinetic elements causes the object to move around the sun.
Fig 1. v1 and v2 are identical in magnitude but a1 and a2 differ. An ellipse is therefore impossible
At perihelion, the magnitude of the tangential velocity will be equal to the magnitude of the tangential velocity at aphelion. The magnitude of the orbital motion is much greater at perihelion due to the greater centripetal velocity caused by the increased centripetal acceleration. The planet is closer to the sun, therefore the centripetal component is greater. However this is clearly an issue. At perihelion and aphelion the magnitudes of the tangential velocities remain the same but the centripetal acceleration at perihelion is greater. This means our vector product must produce a different arc at this point from the arc at aphelion but with an ellipse these arcs are identical! The arc at aphelion must be shallower than the arc at perihilion due to the reduced magnitude of the centripetal acceleration at this point. The same argument can be applied to the ‘cigar’ shaped trajectories given to the various comets that orbit the sun. Clearly these types of trajectory are also physical impossibilities and it is astonishing that so few astronomers have challenged these notions for well over three hundred years. To this day astronomers are incapable of predicting exactly when Halley’s comet will return to our skies because they have failed to understand the true celestial mechanics that determine its motion. Until simple errors such as the one shown above are addressed these failures will only continue.
Even if we ignore Newton and apply Le Sage's Theory of Gravity3, the elliptic model fails abysmally. We will end up with varying pressures at aphelion and perihelion, so the degree of curve at these points cannot be the same.
Of course Newton famously took Kepler's work and claimed that his laws could explain the motion of the 1680 comet observed by him and others. A ludicrous claim as we now know the data was manipulated by Halley and even worse, some of that data was actual based on the observation of Eros, a minor planet4. The calculation of the orbit of this comet was nevertheless taken to be proof of the validity of Newton's laws and highlighted by Newton in Principia.
Conveniently for Newton and Halley the orbital period of the comet is supposedly somewhere in the region of 10,400 yr!
Enter stage left and a new force to save the ellipse!
Remarkably, Miles Mathis demonstrates quite clearly that Kepler's elliptical orbits, as shown above, are a physical impossibility if we apply any known law of gravity. Now, the fun begins. Rather than accepting that Kepler was wrong and something is wrong with the heliocentric model, Mathis proposes a fix5. He invents an imaginary force, a repulsive electromagnetic force, more significant at the perihelion than at the aphelion. This ensures that the combined gravitational and electromagnetic forces acting at the perihelion and the aphelion magically match exactly! Here Mathis recognises the problem.
All experiments and observations have confirmed that Kepler's equations are correct and that the shape of the orbit is indeed an ellipse, as he told us. Most physicists have been content to leave it at that. If you are an engineer and you have equations and a diagram, you have all you really need. If you are a physics teacher and you have equations and a diagram, you are well prepared: you can answer almost any question that is likely to come up. But in my paper on Celestial Mechanics, I showed that the accelerations and velocities in the elliptical orbit were impossible to explain with the gravitational field. That is to say, we have the correct equations, the correct shape, but the wrong mechanics. We have left the equations and the diagram with no foundation for almost four centuries! The proposed and accepted kinematics and dynamics, studied closely, cannot support the motions in the field. Since physics is supposed to be a mechanical explanation of natural phenomena, we have a very real problem here. We have titled this part of physics "celestial mechanics", but we have left out the mechanics almost entirely. This should be a concern to all real scientists, and not just theorists or philosophers, either. If your field does not explain your equations or your diagrams, you are not lacking in metaphysics, you are lacking in physics. What we currently have is a set of equations hanging from sky hooks.
It is essential to repeat once more that no one other than Kepler claims to have demonstrated the elliptical paths of the planets to be a physical reality. Meanwhile, if you were worried your worldview was about to implode on itself, don't worry; Mathis has the solution!
Fortunately, the solution is just as simple as the problem. It has been overlooked for centuries, but that does not mean it must be esoteric. It only means that the problem was hidden for a long time. Newton hid the problem so cunningly that no one has detected it since his time.
The solution is that the orbital field is a two-force field. It is not just determined by gravity. Therefore any orbiter must be exhibiting at least three basic motions. The two above, and one other. This other is a motion due to the combined E/M fields of the orbiter and the object orbited. In this case, the Sun and the Earth. The force created by the E/M fields is a repulsive force, like that between two protons. It is therefore a negative vector compared to the gravitational field, which is an attractive field. And so the total field described by gravity and E/M is a differential of the two. In the end, you subtract the E/M acceleration from the acceleration due to gravity.
This explains the ellipse because the E/M repulsive force increases as the objects get nearer. As the gravitational acceleration gets bigger, so does the repulsive acceleration due to E/M.
We have a balancing of forces. This not only explains the varying shape of the orbit, from circle to ellipse to parabola, it explains the correctability of the orbit. It explains why we don’t often find orbiters crashing into primaries. It explains how we had a ghost in the other focus of the ellipse: the ghost was inhabited by the E/M field.
If anyone thought Mathis was a genuine physicist and not a COINTELPRO joker, then discard common sense and enjoy the rest of your life in the matrix.