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Ptolemy

The Aristotelian system was modified by Hipparchus whose ideas were popularized and perfected by Ptolemy. In his treatise the Almagest (``The Great System'') Ptolemy provided a mathematical theory of the motions of the Sun, Moon, and planets. Ptolemy vision (based on previous work by Hipparchus) was to envision the Earth surrounded by circles, on these circles he imagined other (smaller) circles moving, and the planets, Sun, etc. moving on these smaller circles. This model remained unchallenged for 14 centuries.

The system of circles upon circles was called a system of epicycles (see Fig. 2.14). It was extremely complicated (requiring several correction factors) but it did account for all the observations of the time, including the peculiar behavior of the planets as illustrated in Fig. 2.15. The Almagest was not superseded until a century after Copernicus presented his heliocentric theory in Copernicus' De Revolutionibus of 1543.





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This model was devised in order to explain the motion of certain planets. Imagine that the stars are a fixed background in which the planets move, then you can imagine tracing a curve which joins the positions of a given planet everyday at midnight (a ``join the dots'' game); see, for example Fig 2.13. Most of the planets move in one direction, but Mars does not, its motion over several months is seen sometimes to backtrack (the same behavior would have been observed for other celestial objects had Ptolemy had the necessary precision instruments).


 
Figure 2.13: This computer simulations shows the retrograde motion of Mars (left) and the asteroid Vesta (right). Vesta's trajectory is followed over several years; it moves from right to left (west to east), and each loop occurs once per year. The shape of the retrograde loop depends on where Vesta is with respect to Earth.  
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Figure 2.14: The simplest form of an epicycle (left) and the actual form required to explain the details of the motion of the planets (right).  
\begin{figure} \centerline{ \vbox to 1.8 in {\epsfxsize=2.7 truein\epsfbox[0 -2... ...psfxsize=2.7 truein\epsfbox[100 -230 712 562]{2.greeks/epi_2.ps}} }\end{figure}


 
Figure 2.15: Example of how a system of epicycles can account for the backtracking in the motion of a planet. The solid line corresponds to the motion of Mars as it goes around the epicycle, while the epicycle itself goes around the Earth. As seen from Earth, Mars would move back and forth with respect to the background stars. 
\begin{figure} \centerline{ \vbox to 1.8 in {\epsfxsize=2.7 truein\epsfbox[0 -200 612 592]{2.greeks/epi_3.ps}} }\end{figure}


next up previous contents
Next: From the Middle Ages Up: Aristotle and Ptolemy Previous: The motion according to

Jose Wudka
9/24/1998