# What is epicycle

## Ptolemaic system

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. Apollonius of Perga realized that this cyclical variation could be represented visually by small circular orbits, or epicycles, revolving on larger circular orbits, or deferents. Saturn is surpassed by the numbers by one and a half degrees. Near opposition , the planet would appear to reverse and move through the night sky faster than the stars for a time in retrograde motion before reversing again and resuming prograde. It was mistakenly believed that more levels of epicycles circles within circles were added to the models to match more accurately the observed planetary motions. Either theory could be used today had Gottfried Wilhelm Leibniz and Isaac Newton not invented calculus. The complexity to be described by the geocentric model The most obvious approach to the problem of predicting the motions of the heavenly bodies was simply to map their positions against the star field and then to fit mathematical functions to the changing positions. In a deferent-and-epicycle model, the parts of the whole are interrelated. A traditional planetarium projector While the fact that we base planetarium projectors on the Ptolemaic model of the universe that was developed almost 2, years ago may seem impressive, a better test of the model is how long the model was accepted by society.

Each night the planet appeared to lag a little behind the stars, in what is called prograde motion. To make the planets appear to speed up and slow down, three tricks were used. Simple two-body problemsfor example, can be solved analytically.

P is the centre of the epicycle of the Sun S. 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.

## Epicycle animation

More-complex n-body problems require numerical methods for solution. It was not until Galileo Galilei observed the moons of Jupiter on 7 January , and the phases of Venus in September that the heliocentric model began to receive broad support among astronomers, who also came to accept the notion that the planets are individual worlds orbiting the Sun that is, that the Earth is a planet and is one among several. Either theory could be used today had Gottfried Wilhelm Leibniz and Isaac Newton not invented calculus. 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. The regularity in the motions of the wandering bodies suggested that their positions might be predictable. P is the centre of the epicycle of the Sun S. The stars, it was assumed, moved on a celestial sphere around the outside of the planetary spheres. The power of Newtonian mechanics to solve problems in orbital mechanics is illustrated by the discovery of Neptune. A change in a parameter to improve the fit in one place would throw off the fit somewhere else. Subsequent tables based on Newton's Theory could have approached arcminute accuracy. The multiplication of epicycles is believed to have led to a nearly unworkable system by the 16th century, and that Copernicus created his heliocentric system in order to simplify the Ptolemaic astronomy of his day, thus succeeding in drastically reducing the number of circles. 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.

Johannes Kepler was able to formulate his three laws of planetary motionwhich described the orbits of the planets in our solar system to a remarkable degree of accuracy; Kepler's three laws are still taught today in university physics and astronomy classes, and the wording of these laws has not changed since Kepler first formulated them four hundred years ago.

Furthermore, Aristotelian physics was not designed with these sorts of calculations in mind, and Aristotle 's philosophy regarding the heavens was entirely at odds with the concept of heliocentrism.

It was mistakenly believed that more levels of epicycles circles within circles were added to the models to match more accurately the observed planetary motions.

Saturn is surpassed by the numbers by one and a half degrees.

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. Ptolemy insisted that the job of the astronomer was to explain the motions of the wanderers using only uniform circular motion - the kind of motion that most gears and wheels show.

The inferior planets were always observed to be near the Sun, appearing only shortly before sunrise or shortly after sunset. Near oppositionthe planet would appear to reverse and move through the night sky faster than the stars for a time in retrograde motion before reversing again and resuming prograde.

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