Plato's Homework Problem

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Plato gave his students a major problem to work on. Their task was to find a geometric explanation for the apparent motion of the planets, especially the strange retrograde motion. One key observation: as a planet undergoes retrograde motion (drifts westward with respect to the stars), it becomes brighter. Plato and his students were, of course, also guided by the Pythagorean Paradigm. This meant that regardless of the scheme they came up with, the Earth should be at the unmoving center of the planet motions. One student named Aristarchus violated that rule and developed a model with the Sun at the center. His model was not accepted because of the obvious observations against a moving Earth.

Some of the observations that convinced the Greeks that the Earth was not moving are

  1. The Earth is not part of the heavens. Today the Earth is known to be just one planet of eight (plus 5 dwarf planets at the time of writing) that orbit an average star in the outskirts of a large galaxy, but this idea gained acceptance only recently when telescopes extended our vision.
  2. The celestial objects are bright points of light while the Earth is an immense, nonluminous sphere of mud and rock. Modern astronomers now know that the stars are objects like our Sun but very far away and the planets are just reflecting sunlight.
  3. The Greeks saw little change in the heavens---the stars are the same night after night. In contrast to this, they saw the Earth as the home of birth, change, and destruction. They believed that the celestial bodies have an immutable regularity that is never achieved on the corruptible Earth. Today astronomers know that stars are born and eventually die (some quite spectacularly!)---the length of their lifetimes are much more than a human lifetime so they appear unchanging. Also, modern astronomers know that the stars do change positions with respect to each other over, but without a telescope, it takes hundreds of years to notice the slow changes.
  4. Finally, our senses show that the Earth appears to be stationary! Air, clouds, birds, and other things unattached to the ground are not left behind as they would be if the Earth was moving. There should be a strong wind if the Earth were spinning as suggested by some radicals. There is no strong wind. If the Earth were moving, then anyone jumping from a high point would hit the Earth far behind from the point where the leap began. Furthermore, they knew that things can be flung off an object that is spinning rapidly. The observation that rocks, trees, and people are not hurled off the Earth proved to them that the Earth was not moving. Today we have the understanding of inertia and forces that explains why this does not happen even though the Earth is spinning and orbiting the Sun. That understanding, though, developed about 2000 years after Plato.

Plato taught that since an infinite number of theories can be constructed to account for the observations, we can never empirically answer what the universe is really like. He said that we should adopt an instrumentalist view: scientific theories are just tools or calculation devices and are not to be interpreted as real. Any generalizations we make may be shown to be false in the future and, also, some of our false generalizations can actually ``work''--an incorrect theory can explain the observations (see the scientific method page for background material on this).

Aristotle bust Aristotle (lived 384--322 B.C.E.) was a student of Plato and had probably the most significant influence on many fields of studies (science, theology, philosophy, etc.) of any single person in history. He thought that Plato had gone too far with his instrumentalist view of theories. Aristotle taught a realist view: scientific, mathematical tools are not merely tools---they characterize the way the universe actually is. At most one model is correct. The model he chose was one developed by another follower of Plato, Eudoxus. The planets and stars were on concentric crystalline spheres centered on the Earth. Each planet, the Sun, and the Moon were on their own sphere. The stars were placed on the largest sphere surrounding all of the rest.

Aristotle chose this model because most popular and observational evidence supported it and his physics and theory of motion necessitated a geocentric (Earth-centered) universe. In his theory of motion, things naturally move to the center of the Earth and the only way to deviate from that is to have a force applied to the object. So a ball thrown parallel to the ground must have a force continually pushing it along. This idea was unchallenged for almost two thousand years until Galileo showed experimentally that things will not move or change their motion unless a force is applied. Also, the crystalline spheres model agreed with the Pythagorean paradigm of uniform, circular motion (see the previous section).

A slight digression: Another conclusion drawn from Aristotle's teachings was that the Earth was unique with its own set of physical laws that were different from how things worked in the heavens. The Earth was a world and filled with change and decay while the planets, Moon, and Sun were perfect, unchanging and essentially ornaments on the sky, not worlds that could be explored. (Imagine the transformation of our viewpoint when we discovered using telescopes that those wandering points of light are worlds like the Earth and then later discovered other planets orbiting other stars!) Now, to return to the motions of the planets...

Astronomers continued working on models of how the planets moved. In order to explain the retrograde motion some models used epicycles---small circles attached to larger circles centered on the Earth. The planet was on the epicycle so it executed a smaller circular motion as it moved around the Earth. This meant that the planet's distance from us changed and if the epicyclic motion was in the same direction (e.g., counter-clockwise) as the overall motion around the Earth, the planet would be closer to the Earth as the epicycle carried the planet backward with respect to the usual eastward motion. This explained why planets are brighter as they retrogress.

Ptolemy's world map
Ptolemy's view of the world. Select the image to go to Jim Siebold's ancient maps database from which this picture came (will display in another window).

Ptolemy's geocentric universe

Ptolemy portrait Ptolemy (lived 85--165 C.E.) set out to finally solve the problem of the planets motion. He combined the best features of the geocentric models that used epicycles with the most accurate observations of the planet positions to create a model that would last for nearly 1500 years. He added some refinements to explain the details of the observations: an ``eccentric'' for each planet that was the true center of its motion (not the Earth!) and an ``equant'' about which each planet moved uniformly in relation to (not the Earth!). See the figure below for a diagram of this setup.

Epicyclic motion in a geocentric universe
Select image to show animation of retrograde motion.

These refinements were incompatible with Aristotle's model and the Pythagorean paradigm---a planet on an epicycle would crash into its crystalline sphere and the motion is not truly centered on the Earth. So Ptolemy adopted an instrumentalist view---this strange model is only an accurate calculator to predict the planet motions but the reality is Aristotle's model. This apparent contradiction between reality and a calculation device was perfectly fine in his time. Our modern belief that models must characterize the way the universe actually is is a tribute to the even longer-lasting influence of Aristotle's realism. Ptolemy was successful in having people adopt his model because he gathered the best model pieces together, used the most accurate observations and he published his work in a large 13-volume series called the ``Almagest'', ensuring that his ideas would last long after he died.

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last updated: January 8, 2013

Is this page a copy of Strobel's Astronomy Notes?

Author of original content: Nick Strobel