Correct.
The De revolutionibus itself is not consistent with the single surviving early version of the system, described by Copernicus in the early manuscript Commentariolus. Even Copernicus could not derive from his hypothesis a single and unique combination of interlocking circles, and his successors did not do so…Judged on purely practical grounds, Copernicus’ new planetary system was a failure; it was neither more accurate nor significantly simpler than its Ptolemaic predecessors.
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The Copernican system is not a discovery…but a last attempt to patch up an out-dated machinery by reversing the arrangement of its wheels. As a modern historian put it, the fact that the Earth moves is “almost an incidental matter in the system of Copernicus which, viewed geometrically, is just the old Ptolemaic pattern of the skies, with one or two wheels interchanged and one or two of them taken out.”
Why do you keep on about the Copernican system? It was shown to be quite inaccurate because it still insisted on perfect circles.
It took Kepler and then Newton to show that the planetary orbits were almost elliptical.
Kepler, although a Lutheran, was influenced by the occult, as was his mother, Katherina Kepler, and the latter’s endeavor may have led to her trial as a witch. Following his philosophy, Kepler’s main motivation for bringing the sun into the center of the planetary system, as had Copernicus before him, was that he considered it worthy of symbolic deification. In one passage he describes the sun as:
“Who alone appears, by virtue of his dignity and power, suited…and worthy to become the home of God himself, not to say the first mover.” Similar to Copernicus, Kepler was also influenced by Greek thought, and in particular the Pythagorean concept of the harmony of the spheres. Using the idea of harmonic ratios, Kepler developed his third law of motion wherein the cube of a planet’s orbital period is proportional to the square of its distance from the sun. Kepler believed that even God was subject to these “harmonic” laws and had no other choice than to make the solar system by them. At one point Kepler attributes divinity to geometry, stating:
“Geometry, coeternal with the divine mind before the origin of things, God himself (for what is there in God that is not God himself) has supplied God with the examples for the creation of the world.” --- Kepler’s Witch,
James A. Connor, 2004, pp. 275-307. The Sleepwalkers, pp. 389-393.
The woman relative who raised Katherina was executed for practicing witchcraft (
John Lear, Kepler’s Dream, 1965, p. 31).
As noted earlier, in the course of his work Copernicus stumbled upon a geocentric system that did not use Ptolemaic epicycles, but he rejected that system because it did not incorporate the crystal spheres of the Greeks. But Copernicus’trash became Tycho Brahe’s treasure. Brahe, through his discovery in 1577 of a comet, proved there were no crystal spheres in outer space, since a comet circling the sun would have crashed into the spheres. There was no more excuse to reject the geocentric alternative. Copernicus’ objection had now been answered and Tycho returned to the immobile earth with a revolving sun. Geometrically, all was sound. Everything that Copernicus’ system could do, Brahe’s could do, except the sun and the earth were switched.
One historical note of interest is that
on his deathbed Brahe asked Kepler to use his forty-years of planet-charting to support the geocentric system. Kepler fulfilled Brahe’s wishes but did so in his usual style – showing the three systems side-by-side (the Ptolemaic, Tychonic and Copernican). As
Barbour notes:
“Kepler immediately takes the opportunity to point out that, viewed in purely geometrical terms, the three forms are completely equivalent,” but Kepler believe she has
“physical and dynamical” evidence of “the severe difficulties that the two rivals to Copernicus face.” As noted earlier, the only differences are that Kepler, for his model only, employs precise elliptical orbits (and, in particular, he halves Tycho’s eccentricity of the sun-earth circumference); and uses the “area law”
so that the consequent improvements of planetary motion and speed favor him alone. If Kepler had done the same to Tycho’s or even a modified Ptolemaic model, the equivalence would not only be “geometric” but also “physical and dynamical.” Unfortunately, Barbour never mentions this fact in his review. Instead, he quotes
Kepler as saying:
“Thus, the house that we erected on the basis of the Tychonic observations we have now demolished with other observations of the same man.” In actuality, Kepler didn’t demolish anything except his chance to be honest with the application of the scientific data.Regardless of Kepler’s motivations,
Tycho Brahe’s system is its mirror image. Whatever improvements Kepler gave to his system were automatically true for Brahe’s, even if Kepler failed to apply them. In Brahe’s, the sun is in orbit around the Earth, while all the planets orbit the sun. In this way, all the distances,geometry and velocities of the heliocentric system are identical with the geocentric.
Even after Kepler’s modifications, anomalies regarding the motions of the heavenly bodies remained, and stubbornly so. Although geometrically speaking the orbits are not perfect circles, they are not perfect ellipses either, but precess at different rates and contain various eccentricities. Quoting
Hoyle again:
The planetary orbits are not strictly ellipses, as we have so far taken them to be, because one planet disturbs the order of another through the gravitational force that it exerts….In all cases the orbits are nearly circles….It is curious that although the actual orbits do not differ in shape much from circles the errors of a circular model can nevertheless be quite large. Indeed, errors as large as this were quite unacceptable to Greek astronomers of the stature of Hipparchus and Ptolemy. It was this, rather than prejudice, which caused them to reject the simple heliocentric theory of Aristarchus….The Hipparchus theory grapples with the facts whereas the circular picture of Aristarchus fails to do so….The theory of Ptolemy, a few minor imperfections apart, worked correctly to the first order in explaining the planetary eccentricities.Copernicus with his heliocentric theory had to do at least as well as this, which meant that he had to produce something much better than the simple heliocentric picture of Aristarchus…. Kepler achieved improvements, but not complete success, and always at the expense of increasing complexity. Kepler and his successors might well have gone on in this style for generations without arriving at a satisfactory final solution, for a reason we now understand clearly. There is no simple mathematical expression for the way in which the direction of a planet – its heliocentric longitude – changes with time. Even today we must express the longitude as an infinite series of terms when we use time as the free variable. What Ptolemy, Copernicus, and Kepler, in his early long calculations, were trying to do was to discover by trial and error the terms of this series. Since the terms become more complicated as one goes to higher orders in the eccentricity, the task became successively harder and harder…Professor of celestial mechanics at Columbia University,
Charles Lane Poor, says much the same:
From the time of Newton, it has been known that Kepler’s laws are mere approximations, computer’s fictions, handy mathematical devices for finding the approximate place of a planet in the heavens. They apply with greater accuracy to some planets than to others. Jupiter and Saturn show the greatest deviations from strictly elliptical motion. The latter body is often nearly a degree away from the place it would have been had its motion about the sun been strictly in accord with Kepler’s laws. This is such a large discrepancy that it can be detected by the unaided eye. The moon is approximately half a degree in diameter, so that the discrepancy in the motion of Saturn is about twice the apparent diameter of the moon. In a single year, during the course of one revolution about the sun, the Earth may depart from the theoretical ellipse by an amount sufficient to appreciably change the apparent place of the sun in the heavens.Take a figure like Galileo, a contemporary of Kepler and one of the few other convinced Copernicans.
Does he embrace this work and integrate it with his own?
Not at all.
He largely ignores Kepler. It is as though he is embarrassed by the extreme neo-Platonism
and harmony-mongering of his ‘ally’. In addition he does not seem to have understood,
or have wanted to understand Kepler’s astronomy of non-circular motions.
What did professional astronomers do? Well those who took Kepler at all seriously
tried to de-nature his results--as had been done early on with Copernicus. Most of these
workers were not Copernican anyway. If they were impressed by anything it was the
elliptical shape of the orbits. This was worth knowing, because for the first time one
could imagine the actual orbit in space.
So, and this will not surprise you, they
continued to use deferents and epicycles to model and predict the motions, but they
adjusted the machinery so that the path traced out would be an ellipse. So much for
Kepler’s new idea of a causal, celestial physics!
So the great vision is torn to pieces, not taken up whole by anyone. The only person to
bring it back together again to any degree is
Newton in the later 17th century, not in
Kepler’s version, but in his own particular way, so that his version is not identical to
Kepler’s.