A Virtual Planetarium
Winter Solstice Virtual Abrams Planetarium 360 Video
Winter Solstice Virtual Abrams Planetarium 360 Video source: John French
"A browser-based virtual planetarium of stars and planets, customizable to any location and time."
A link to a tool. Much ado is made of what is called "retrograde" motion. This idea is not as it seems. Planets cannot be actually observed to move backwards overnight. The motions of the planets are not as mysterious as claimed and this will be the subject of the next article in the series.
Carl Sagan Explains Ptolemy's Geocentric Model
Please keep in mind the advances in astronomy are not as advertised and Copernicus, Kepler and Newton and the rest were mystically minded men. The criticism of Earth centered model is that the epicycles were too complicated and yet this same kind of motion is used today to explain how moons orbit the planets that orbit suns. The fact is the heliocentric model is the one with all the problems and complexities that would result in the modern patchwork of ad hoc cosmology most think real. Yet all the NASA and other international spake fakery and Hollywood special effected reasoning can't alter the facts that the heliocentric based model is faith based and not based in fact as I shall demonstrate. There are many flaws to be found and now we shall look at so-called retrograde motion and we shall see the fallacy. (check into this one: The other criticism of Ptolemaic model is that planets would have to slow down and speed up as they orbit the Earth. Copernicus invented circularly reasoned orbits of perfection. Kepler came along and with Tycho Brahe observation discovered that the planets did not circle the Sun, and so invented the idea of the orbital ellipse.
By the way Newton, Kepler and the rest were superstitious men who are best described as alchemists and astrologists. Astronomy, by the way is the earlier term. I shall post links to some articles that discuss Newton's mysticism at the end of this article.
COSMOS (1980) Ep 3 source: Nina S.
Ptolemy's Epicycles vs Kepler's Ellipses & Two Points (Sun and imagined in order to make ellipse)
"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."
"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."
The Solar Analemma
SkyMarvels™ SUN'S SIGNATURE: the Solar Analemma (celestia celestia4all) source: celestia4allCreator
What Model Was Always Used For Planetariums?
"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."
"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."
source: The Ptolemaic Model