What was ptolemys model of the universe

This was required to explain the retrograde motion of a planet. His work is described in the "Almagest" - the Arabic title of the work, meaning roughly "Great Work. Working all of this out was a triumph of detailed mathematics.

By precise adjustments of this nature, he was able to find a system that reproduced the planetary positions relatively accurately. Although we tend to present his model as simple sketches, his real work was a huge body of accurate calculations that allowed him to adjust the model to provide an accurate fit to the observations of the positions of the planets.

In common with another great astronomer, Kepler, Ptolemy also wrote on astrology. It had convincing strong points: It fit all of the available data. It predicted the earth was standing still, in agreement with observation even though we now know that this observation was wrong.

It predicted approximately where the planets were found even centuries after Ptolemy died. Thus, although Aristotle's spherical cosmology had a very long life, mathematicians who wished to make geometrical models to account for the actual motions of heavenly bodies began using different constructions within a century of Aristotle's death.

These constructions violated Aristotle's physical and cosmological principles somewhat, but they were ultimately successful in accounting for the motions of heavenly bodies. It is in the work of Claudius Ptolemy, who lived in the second century CE, that we see the culmination of these efforts.

In his great astronomical work, Almagest, [2] Ptolemy presented a complete system of mathematical constructions that accounted successfully for the observed motion of each heavenly body. Ptolemy used three basic constructions, the eccentric, the epicycle, and the equant.

An eccentric construction is one in which the Earth is placed outside the center of the geometrical construction. Here, the Earth, E, is displaced slightly from the center, C, of the path of the planet. Although this construction violated the rule that the Earth was the center of the cosmos and all planetary motions, the displacement was minimal and was considered a slight bending of the rule rather than a violation.

The eccentric in the figure below is fixed; it could also be made movable. In this case the center of the large circle was a point that rotated around the Earth in a small circle centered on the Earth.

In some constructions this little circle was not centered in the Earth. The second construction, the epicycle, is geometrically equivalent to the simple movable eccentric.

In this case, the planet moved on a little circle the center of which rotated on the circumference of the large circle centered on the on theEarth.

When the directions and speeds of rotation of the epicycle and large circle were chosen appropriately, the planet, as seen from the Earth, would stop, reverse its course, and then move forward again. Thus the annual retrograde motion of the planets caused, in heliocentric terms by the addition of the Earth's annual motion to the motion of the planet could roughly be accounted for.

But these two constructions did not quite bring the resulting planetary motions within close agreement with the observed motions. Ptolemy therefore added yet a third construction, the equant. In this case, the center of construction of the large circle was separated from the center of motion of a point on its circumference, as shown below, where C is the geometrical center of the large circle usually called in these constructions the excentric circle but the motion of the center of the epicycle, P middle figure , is uniform about Q, the equant point righthand side figure.

Ptolemy combined all three constructions in the models of the planets, Sun, and Moon. A typical construction might thus be as in the picture below, where E is the Earth, C the geometric center of the eccentric circle, Q the equant point, F the center of the epicycle, and P the planet. As mentioned before, the eccentric was often not fixed but moved in a circle about the Earth or another point between the Earth and the equant point.

Typical Ptolemaic planetary model From Michael J. The idea was to break down the complex observed planetary motion into components with perfect circular motions. In doing so, however, Ptolemy violated the cosmological and physical rules of Aristotle. The excentric and epicycle meant that planetary motions were not exactly centered on the Earth, the center of the cosmos.

This was, however, a "fudge" that few objected to. The equant violated the stricture of perfect circular motion, and this violation bothered thinkers a good deal more. The net effect was as illustrated in the following animation. As the center of the epicycle moves around the deferent at constant angular velocity, the planet moves around the epicycle, also at constant angular velocity. The apparent position of the planet on the celestial sphere at each time is indicated by the line drawn from the earth through the planet and projected onto the celestial sphere.