The Copernican Model (a.k.a Sun Centered)
"The geocentric system was still held for many years afterwards, as at the time the Copernican system did not offer better predictions than the geocentric system,"
"The change from circular orbits to elliptical planetary paths dramatically improved the accuracy of celestial observations and predictions. Because the heliocentric model by Copernicus was no more accurate than Ptolemy's system, new observations were needed to persuade those who still held on to the geocentric model."
"In 1543, the geocentric system met its first serious challenge with the publication of Copernicus' De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres), which posited that the Earth and the other planets instead revolved around the Sun. The geocentric system was still held for many years afterwards, as at the time the Copernican system did not offer better predictions than the geocentric system, and it posed problems for both natural philosophyand scripture. The Copernican system was no more accurate than Ptolemy's system, because it still used circular orbits. This was not altered until Johannes Kepler postulated that they were elliptical (Kepler's first law of planetary motion)."
source: Geocentric model - Wikipedia
"When Copernicus transformed Earth-based observations to heliocentric coordinates he was confronted with an entirely new problem."
Copernicus vs Ptolemy
Copernicus created the demonstrably more complicated system as it would need to be fallaciously ad hoc patched by Kepler and Newton. The heliocentric model is not based on demonstrable natural reality but on prejudice and faith based solar supposition. The Geocentric model is the one based on actual observation.
""The idea that Copernicus used only 34 circles in his system comes from his own statement in a preliminary unpublished sketch called the Commentariolus. By the time he published De revolutionibus orbium coelestium, he had added more circles. Counting the total number is difficult, but estimates are that he created a system just as complicated, or even more so."
"Claudius Ptolemy refined the deferent-and-epicycle concept and introduced the equant as a mechanism for accounting for velocity variations in the motions of the planets. The empirical methodology he developed proved to be extraordinarily accurate for its day and was still in use at the time of Copernicus and Kepler. Owen Gingerich describes a planetary conjunction that occurred in 1504 that was apparently observed by Copernicus. In notes bound with his copy of the Alfonsine Tables, Copernicus commented that "Mars surpasses the numbers by more than two degrees. Saturn is surpassed by the numbers by one and a half degrees." Using modern computer programs, Gingerich discovered that, at the time of the conjunction, Saturn indeed lagged behind the tables by a degree and a half and Mars led the predictions by nearly two degrees. Moreover, he found that Ptolemy's predictions for Jupiter at the same time were quite accurate. Copernicus and his contemporaries were therefore using Ptolemy's methods and finding them trustworthy well over a thousand years after Ptolemy's original work was published.
When Copernicus transformed Earth-based observations to heliocentric coordinates he was confronted with an entirely new problem. The Sun-centered positions displayed a cyclical motion with respect to time but without retrograde loops in the case of the outer planets. In principle, the heliocentric motion was simpler but with new subtleties due to the yet-to-be-discovered elliptical shape of the orbits. Another complication was caused by a problem that Copernicus never solved: correctly accounting for the motion of the Earth in the coordinate transformation. In keeping with past practice, Copernicus used the deferent/epicycle model in his theory but his epicycles were small and were called "epicyclets".
In the Ptolemaic system the models for each of the planets were different and so it was with Copernicus' initial models. As he worked through the mathematics, however, Copernicus discovered that his models could be combined in a unified system. Furthermore, if they were scaled so that the Earth's orbit was the same in all of them, the ordering of the planets we recognize today easily followed from the math. Mercury orbited closest to the Sun and the rest of the planets fell into place in order outward, arranged in distance by their periods of revolution. Although Copernicus' models reduced the magnitude of the epicycles considerably, whether they were simpler than Ptolemy's is moot. Copernicus eliminated Ptolemy's somewhat-maligned equant but at a cost of additional epicycles. Various 16th-century books based on Ptolemy and Copernicus use about equal numbers of epicycles.
The idea that Copernicus used only 34 circles in his system comes from his own statement in a preliminary unpublished sketch called the Commentariolus. By the time he published De revolutionibus orbium coelestium, he had added more circles. Counting the total number is difficult, but estimates are that he created a system just as complicated, or even more so.
Koestler, in his history of man's vision of the universe, equates the number of epicycles used by Copernicus at 48. The popular total of about 80 circles for the Ptolemaic system seems to have appeared in 1898. It may have been inspired by the non-Ptolemaic system of Girolamo Fracastoro, who used either 77 or 79 orbs in his system inspired by Eudoxus of Cnidus. Copernicus in his works exaggerated the number of epicycles used in the Ptolemic system; although original counts ranged to 80 circles, by Copernicus's time the Ptolemic system had been updated by Peurbach towards the similar number of 40; hence Copernicus effectively replaced the problem of retrograde with further epicycles."
"Copernicus' theory was at least as accurate as Ptolemy's but never achieved the stature and recognition of Ptolemy's theory. What was needed was Kepler's elliptical theory, not published until 1609. Copernicus' work provided explanations for phenomena like retrograde motion, but really didn't prove that the planets actually orbited the Sun.
Ptolemy's and Copernicus' theories proved the durability and adaptability of the deferent/epicycle device for representing planetary motion. The deferent/epicycle models worked as well as they did because of the extraordinary orbital stability of the solar system. Either theory could be used today had Gottfried Wilhelm Leibniz and Isaac Newton not invented calculus.
The first planetary model without any epicycles was that of Ibn Bajjah (Avempace) in 12th century Andalusian Spain, but epicycles were not eliminated in Europe until the 17th century, when Johannes Kepler's model of elliptical orbits gradually replaced Copernicus' model based on perfect circles.
Newtonian or classical mechanics eliminated the need for deferent/epicycle methods altogether and produced more accurate theories. By treating the Sun and planets as point masses and using Newton's law of universal gravitation, equations of motion were derived that could be solved by various means to compute predictions of planetary orbital velocities and positions. Simple two-body problems, for example, can be solved analytically. More-complex n-body problems require numerical methods for solution.
The power of Newtonian mechanics to solve problems in orbital mechanics is illustrated by the discovery of Neptune. Analysis of observed perturbations in the orbit of Uranus produced estimates of the suspected planet's position within a degree of where it was found. This could not have been accomplished with deferent/epicycle methods. Still, Newton in 1702 published Theory of the Moon's Motion which employed an epicycle and remained in use in China into the nineteenth century. Subsequent tables based on Newton's Theory could have approached arcminute accuracy."
"the Ptolemaic model was not seriously challenged for over 1,300 years."
"As an indication of exactly how good the Ptolemaic model is, modern planetariums are built using gears and motors that essentially reproduce the Ptolemaic model for the appearance of the sky as viewed from a stationary Earth. In the planetarium projector, motors and gears provide uniform motion of the heavenly bodies. One motor moves the planet projector around in a big circle, which in this case is the deferent, and another gear or motor takes the place of the epicycle."
"While the fact that we base planetarium projectors on the Ptolemaic model of the universe that was developed almost 2,000 years ago may seem impressive, a better test of the model is how long the model was accepted by society. In this case, the Ptolemaic model was not seriously challenged for over 1,300 years. When and why it finally needed to be replaced will be described in the next subunit."
Copernicus Didn't Like Ptolemy's Ideas, Just Because He Found Them Distasteful.
Apolgetics Hide Problems with Copernicus
"As we discussed in the previous subunit, the Earth-centered model of the universe, refined by Ptolemy, was set firmly in place in the early part of the first millennium. It was not until 1543 that it met serious competition in the Sun-centered model of Nicolas Copernicus. Copernicus was born in 1473 in Poland and studied, among other subjects, mathematics and astronomy. He is mainly remembered for formally introducing the idea that the Sun is the center of our solar system. This heliocentric concept (sun-centered concept) was a radical idea for his time. Nearly all contemporary astronomers had adopted the Greek Earth-centered model. It was so radical a concept, in fact, that Copernicus waited until the year of his death to publish his famous essay titled, “On the Revolutions of the Heavenly Spheres.”
Copernicus had two main reasons for asserting that the Sun was the center of our solar system.
1. While the Ptolemaic model was very good at predicting the positions of the planets, it wasn't precise, and over the centuries its predictions got worse and worse.
2. Copernicus didn't like the fact that the Ptolemaic model had big epicycles to explain the retrograde motions of the planets. He knew that this could be explained instead by having the Earth also moving around the Sun.
The true motion of the planets around the Sun is not uniform circular motion, so Copernicus' model still needed to have epicycles. He had 1500 years of post-Ptolemy data to work with, and needed quite a lot of epicycles to make a new set of accurate predictions for the motions of the planets. The main simplification of the Copernican model was that the retrograde loops of the planets as seen from the Earth occur naturally as a result of the Earth's motion combined with the motions of the planets.You worked on this problem in the second part of Activity Two. Here are some illustrations to consider."
Which model is really the more complicated one, the one based on what we can actually observe or the one based on prejudice?