Planets

The planets are spherical bodies which rotate around the hub of the Earth. The planets follow a similar daily route across the sky as the Sun, along a path called the ecliptic. Five planets — Mercury, Venus, Mars, Jupiter, and Saturn are visible to the naked eye and were known to the ancients as "wandering stars;" entities which appear to move differently from the fixed path of the stars. The word "planet" comes from the Greek word planetes, meaning "wanderer."

Topics

• Discovery of Neptune
• Precession of Mercury's Orbit
• Kings Dethroned
• Astronomical Prediction Based on Patterns
• Three Body Problem

Dance of the Planets

The Sun moves in Northward and Southwards paths across the sky over the course of the year when changing seasons and the planets follow along that path, with an apparent relationship to the Sun. Mercury and Venus appear to be rotating around the Sun, while the other planets have a less direct effect. The below animation shows the Sun's progress across the sky over the course of a year as a panorama, its Northward and Southward motions, and the 'dance of the planets' as they follow the sun.

(Source)

The Copernican Revolution of the 16th century held that this relationship with the Sun was evidence that all of the planets of the Solar System moved around the Sun. At the time the idea of a Round Earth was already widely prevalent, based on the teachings of the Ancient Greeks. It was deduced that since the Earth is a round body in a Sun-centered celestial system, that the earth must also be a body in motion similar to the planets seen in the sky.

Quotes

  “ Accordingly, since nothing prevents the earth from moving, I suggest that we should now consider also whether several motions suit it, so that it can be regarded as one of the planets. For, it is not the center of all the revolutions. ”
                  —Nicolaus Copernicus

  “ I demonstrate by means of philosophy that the earth is round, and is inhabited on all sides; that it is insignificantly small, and is borne through the stars. ”
                  —Johannes Kepler

  “ In the middle of all sits Sun enthroned. In this most beautiful temple could we place this luminary in any better position from which he can illuminate the whole at once? He is rightly called the Lamp, the Mind, the Ruler of the Universe: Hermes Trismegistus names him the Visible God, Sophocles’ Electra calls him the All-seeing. So the Sun sits as upon a royal throne ruling his children the planets which circle round him. The Earth has the Moon at her service. As Aristotle says, in his On Animals, the Moon has the closest relationship with the Earth. Meanwhile the Earth conceives by the Sun, and becomes pregnant with an annual rebirth. ”
                  —Nicolaus Copernicus , De Revolutionibus, Of the Order of the Heavenly Bodies 10.

Prediction in Astronomy

Prediction in astronomy is performed through patterns. By analysis of historic tables it is possible to construct functions which can predict where a planet will be in the future. This is how prediction in astronomy has been performed since times of antiquity, and how it is performed today. See: Astronomical Prediction Based on Patterns

Ptolmaic System

Prior to the heliocentric system of Copernicus, the prevailing astronomical model featured an earth-centered system, with main attribution to mathematician and astronomer Claudius Ptolemy. The Earth was at the center of this system while the planets moved around it on epicycles. However, the movements of the planets was a mathematical construct rather than a geometric one, the epicycles being a mathematical construct to predict patterns of movement. Its authors felt that prediction was more important than a geometric depiction of the system. In Beyond Reason: Essays on the Philosophy of Paul Feyerabend its author describes Ptolemy's construct:

  “ Ptolemy continually seeks to chart and predict “the appearances” - the points of light on the celestial globe. The Almagest abandons any attempt to explain the machinery behind these appearances. Apollonius, Hipparchus, and Claudius Ptolemy decide in favor of inventing abstract mathematic devices. They view the provision of an explanation of celestial motions as beyond human powers ....⁴⁹

The great astronomers of the ancient world ... - Eudoxus, Apollonius, Hipparchos, Claudius Ptolemy — could predict where planets and stars would appear at future dates. But each explicitly rules out the possibility of explaining the physics behind the apparent motions of the cosmos Indeed, the history of planetary theory could be viewed as conceptual struggle between two opposed forces, the urge to explain and the urge to predict .... Ptolemy sacrif‌iced a philosophically coherent and unif‌ied picture of the heavens in favor of an accurate instrument of forecast ...

Ptolemy stressed that he could never hope to explain the wanderings of the planets. His inspiration was only to f‌ind a geometrical calculus through which he might forecast when next a given planet would halt in its eastward motion, “back-up” a few degrees, and then continue forward again. Understanding beyond this exceeded Ptolemy’s objectives. The Almagest was but a computational machine; it had some success in saying when celestial events might occur, but did not even undertake to ask why they occurred.⁵⁰

~

Ptolemy was content to “save appearances” and did not speculate about the underlying fabric of the heavens. He did not even care whether the mathematical constructions he used for astronomical purposes were consistent with one another .... Whenever two constructions yields equivalent mathematical results, there was, in Ptolemy’s view, no astronomical difference between them. We are at liberty to account for the one anomaly in terms of “eccentrics” and the other in terms of “epicycles” - whichever way round we please. So far as Ptolemy is concerned, the question of the physical reality or unreality of these motions is beside the point ...

From the physicist’s point of view, the equant was a very unsatisfactory device. Mathematically it might do a job, but there was something intrinsically mireasonable about it. Ptolemy thought physics irrelevant to astronomy, and conf‌ined himself to mathematics.⁵²⁴⁹

On the one hand was the subject of descriptive and physical cosmology, predominantly Aristotelian .... On the other hand was the highly complex mathematical theory concerned with the phenomenological determination and prediction of the irregularities of planetary motions .... We shall call this mathematical theory “Ptolemaic Theory”, ... There are many widespread misconceptions about this Ptolemaic Theory ... First, there never was such a thing ... as a Ptolemaic System. The complex mathematical theory is arranged so as to deal with each planet separately and individually. There is no single mathematical connection between these several models, only a general similarity in the methods used for each.⁵³ ”

Copernican System

The Copernican System, introduced in 1543, attempted to move the Ptolemaic System forward with by proposing a Sun-centered Solar System. However, this model still featured epicycles, arranged in a way so that the Sun was the center.

What Is This Thing Called Science?
By Alan Chalmers

  “ In View of the strength of the case against Copernicus, it might well be asked just what there was to be said in favour of the Copernican theory in 1543. The answer is, ‘not very much’. The main attraction of the Copernican theory lay in the neat way it explained a number of features of planetary motion, which could be explained in the rival Ptolemaic theory only in an unattractive, artificial way. The features are the retrograde motion of the planets and the fact that, unlike the other planets, Mercury and Venus always remain in the proximity of the sun. A planet at regular intervals regresses, that is, stops its westward motion among the stars (as viewed from earth) and for a short time retraces its path eastward before continuing its journey westward once again. In the Ptolemaic system, retrograde motion was explained by the somewhat ad hoc maneuver of adding epicycles especially designed for the purpose. In the Copernican system, no such artificial move is necessary. Retrograde motion is a natural consequence of the fact that the earth and the planets together orbit the sun against the background of the f‌ixed stars. Similar remarks apply to the problem of the constant proximity of the sun, Mercury and Venus. This is a natural consequence of the Copernican system once it is established that the orbits of Mercury and Venus are inside that of the earth. In the Ptolemaic system, the orbits of the sun, Mercury and Venus have to be artificially linked together to achieve the required result.

Thus there were some mathematical features of the Copernican theory that were in its favour. Apart from these, the two rival systems were more or less on a par as far as simplicity and accord with observations of planetary positions are concerned. Circular sun-centred orbits cannot be reconciled with observation, so that Copernicus, like Ptolemy, needed to add epicycles, and the total number of epicycles needed to produce orbits in accord with known observations was about the same for the two systems. In 1543 the arguments from mathematical simplicity that worked in favour of Copernicus could not be regarded as an adequate counter to the mechanical and astronomical arguments that worked against him. Nevertheless, a number of mathematically capable natural philosophers were to be attracted to the Copernican system, and their efforts to defend it became increasingly successful over the next hundred years or so. ”

Copernicus and Epicyles

Some assert that Copernicus ended up with even more epicycles than Ptolmy. From p.42 of Galileo Was Wrong its authors provide the following:

  “ One of the more obvious faults of De revolutionibus was that for all its complaints against ancient epicycles, Copernicus actually produced more epicycles than Ptolemy! Ptolemy’s system has forty epicycles, whereas Copernicus ends up with forty-eight. Yet in the earlier work, the Commentariolus, Copernicus stated that his heliocentric system needed, onlv thirty—four epicycles, and even this numeration was off by four.⁸⁶ What happened, of course, was that since the Commentariolus was merely a preliminary thesis, Copernicus soon discovered that when the time came to work out the f‌iner details of his system a couple of decades later, he was forced to add fourteen more epicycles just to make his version of celestial mechanics come close to the accuracy of Ptolemy’s.⁸⁷ As one source puts it: “...recent computer analyses...have shown the Copernican Prutenic Tables — so named because they were dedicated to the duke of Prussia — to have been scarcely more accurate.”⁸⁸

More disturbing is the fact that, to make Ptolemy’s model appear worse than it really was, Copernicus exaggerated the number of epicycles employed by his ancient rival. Although Ptolemy used only forty epicycles, Copernicus asserted that he had eighty!⁸⁹ This gives us a strong hint that Copernicus was not in this game merely to give the world a better model of cosmology; rather, he thought of it as an historic competition that allowed him to inf‌late his opponent’s errors. ”

Footnotes:

⁸⁶ Copernicus writes in the Commentariolus: “Behold! Only 34 circles are required to explain the entire structure of the universe and the dance of the planets!” (Gingerich, The Book that Nobody Read, p. 56). But Koestler remarks: “incidentally, as Zinner has pointed out, even the famous count at the end of the Commentariolus is wrong as Copernicus forgot to account for the precession, the motions of the aphelia and the lunar nodes. Taking these into account, the Commentariolus uses thirty-eight not thirty- four circles," adding that Copernicus makes no mention of the total number of epicycles in De revolutionibus: “Apart from the erroneous reference to 34 epicycles, I have nowhere see a count made of the number of circles in De revolutionibus” (The Sleepwalkers, p. 580), perhaps hiding the fact from his reader that it contained more epicycles than the De revolutionibus. Gingerich adds: “Copernicus must have realized that with his small epicyclets he actually had more circles than the Ptolemaic computational scheme used in the Alfonsine Tables or for the Stoeff‌ler ephemerides" (op. cit., p. 58). Regarding the discrepancies among the orbits of Mars, Jupiter and Saturn in 1504, Gingerich writes: “...the evidence is f‌irm that he had observed the cosmic dance at this time [1504] and was fully aware of the discrepancies in the tables. But what is most astonishing is that Copemicus never mentioned his observation, and his own tables made no improvement in tracking these conjunctions“ (ibid., p. 59).

⁸⁷ The Sleepwalkers, p. 194-195. One reason Copernicus had so many epicycles is, rather than placing the sun in the center of the universe, he placed the Earth’s entire orbit in the center (although, according to Gingerich: “this was an unresolved mystery in the book, for Copernicus hedged on the issue,” The Book that Nobody Read, p. 163). Koestler remarks that discrepancies in the biographical literature on the number of epicycles in Copernicus’ system is due to the fact that most historians have not read Copernicus’ book but have depended on other biographers for their information. Koestler’s notes show that he did a painstaking analysis of De revolutionibus that allows him to conclude Copernicus used forty-eight epicycles (pp. 579-580). Gingerieh accounts for these extra epicycles as follows: “While he [Copernicus] had eliminated all of Ptolemy’s major epicycles, merging them all into the Earth's orbit, he then introduced a series of little epicyclets to replace the equant, one per planet” (The Book that Nobody Read, pp. 54-55). For mistaken scholarly accounts that settled on Copernicus having only 34 epicycles, Kocstler cites the Chamber's Encyclopedia as stating the Copernican system reduced the epicycles “from eighty to thirty-four,” as is the case with Herbert Dingle’s address to the Royal Astronomical Society in 1943. In my research I found the same discrepancies. Ivars Peterson writes: “Copernicus needed more circles in his sun—centered model than Ptolemy did in his Earth-centered scheme [a] total of 34 circles for all the planets and the moon" (Newton '3 Clock: Chaos in the Solar System, New York: William H. Freeman and Co. 1993, p. 54). Some add even more epicycles to Copernicus, as is the case with James Burke: “To account for the apparent alterations in speed and movement of the planets, Copernicus was obliged to use as many as ninety Ptolemaic epicycles” (The Day the Universe Changed, p. 134).

⁸⁸ Joshua Gilder and Anne-Lee Gilder, Heavenly Intrigue: Johannes Kepler, [who Brahe, and the Murder Behind One oj'I-Iistozy 's Greatest Scientific Discoveries, New York: Doubleday, 2004, p. 38.

⁸⁹ Owen Gingerich adds that the myth of having to put up with an inordinate amount of Ptolemaic epicycles perpetuated itself like an out-of-control gossip chain. He writes: “The legend reached its apotheosis when the 1969 Encyclopedia Britannica announced that, by the time of King Alfonso, each planet required 40 to 60 epicycles! The article concluded, ‘After surviving more than a millennium, the Ptolemaic system failed; its geometrical clockwork had become unbelievably cumbersome and without satisfactory improvements in its effectiveness.‘ When I challenged them, the Britannica editors replied lamely that the author of the article was no longer living, and they hadn’t the faintest idea if or where any evidence for the epicycles on epicycles could be found” (The Book that Nobody Read, pp. 56-57).