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NSC111: Physics/Earth/Space
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III. Models of the solar system

In ancient times, it was pretty obvious that the Moon went around the Earth. This was obvious partly because it was and is true.

The ancients also noticed the Sun moving around the Earth -- a perfectly reasonable explanation of its apparent motion, and the simplest one available. When other moving heavenly bodies were discovered, it seemed obvious that they, too, went around the Earth; this is the geocentric model of the universe.

Aristotle deduced the correct shape of the Earth by about 350 BC (though the Earth was held to be round by earlier scholars), and the size of the Earth was correctly estimated by Eratosthenes of Cyrene in about 235 BC.

Don't let anyone tell you that Columbus' opponents (15th century AD) thought the world was flat! Indeed, Columbus was wrong and his critics were right: Columbus seriously underestimated the size of the Earth, and therefore the distance from Spain to East Asia. If the Americas hadn't been there, Columbus would have been just another discredited crackpot. His supplies would never have brought him all the way to the Spice Islands; they barely got him to Bermuda.

There was a good physical explanation for a geocentric model and for a spherical Earth. By 350 BC or so, the most widely accepted scientific ideas held that the world below the Moon was made of four elements (earth, air, water, fire), which naturally "gravitated" toward the center; this model, along with much of the rest of current knowledge, was systematized by Aristotle. It was pretty obvious that if you let go of anything except air or fire, it fell. Furthermore, fire rose through air, so air must naturally tend to be lower than fire. This meant that the Earth was made of, in ascending order, a sphere of earth, a sphere of water, a sphere of air, and a sphere of fire which was sometimes held responsible for the "char marks" on the moon. On the other hand, the heavenly bodies did not fall. Therefore they must be made of something different (the fifth element or "quintessence").

Ptolemaic system In the second century AD, Claudius Ptolemy (an atheist as we now understand the term) systematized this into what is now known as the Ptolemaic system (see figure). The earth was seen as the center, because that's what both observation and theory indicated. Heliocentric (sun-centered) systems had been proposed but did not seem to be supported by the evidence.

Aristarchus of Samos (310-230 BC) is one of the best known of the ancient Greek speculative cosmologists. He proposed that the Sun was the center of the universe -- probably for religious reasons as the Sun may have represented God to him -- and even tried to estimate the distance from the Earth to the Sun, using trigonometry and the known Earth-Moon distance.

Tradition has it that an earlier heliocentric proposal was made by a Pythagorean, Philolaus, in the 5th century BC. This proposal was definitely religious in origin. Philolaus believed the Sun to be the "hearth of the universe."

("Aristarchus and the Motion of the Earth," Webster's Interactive Encyclopedia, 1999)

But--even though it was a great aid to calculation--there was a fly in the Ptolemaic ointment. In order to track the observed motions of the planets with reasonable accuracy, Ptolemy had to do something unfortunate with his system. He introduced the equant.

Ptolomy's system of deferent, equant and epicycle Equants are points off-the-center of a circle. In Ptolemy's system each planet's circular orbit (deferent) around the Earth had the Earth sitting somewhere a bit off of the true center of the deferent. The equant was an equal distance on the opposite side of the center of the deferent, with the planet's epicycle moving through equal angles around the equant at equal speeds, and the planet itself moving uniformly around the epicycle. The equant--rather than the epicycle, which as a perfect circle was perfectly fine--violated the aesthetic sensibilities of everybody, including Ptolemy himself. He included equants merely to reproduce what was observed.

Worse yet, each separate planet required a different combination of deferent, epicycle and equant to reproduce its observed motions. The obviously ad hoc nature of this was also aesthetically unpleasing.

But a Polish canon named Nicolaus Copernicus realized that putting the Sun in the center of the system would allow a much more aesthetically pleasing result, in which the planetary orbits were concentric circles, their centers were not offset from the Sun's position, and the distances of the planets from the Sun were directly related to their apparent speed of motion across the sky. This was an aesthetic triumph, and, when published, was immediately convincing to a number of astronomers including Galileo Galilei.

Epicycles were not a problem to the medievals, because epicycles were perfect circles. In fact, Copernicus' first version of the heliocentric system was a system of no less than thirty-four circles, including epicycles, to describe the motions of just seven bodies around the central Sun.

A previous version of this page included the myth that geocentric systems included lots and lots of epicycles. This is emphatically false, though widely believed; see Chapter 4 of Owen Gingerich's The Book Nobody Read: Chasing the Revolutions of Nicolaus Copernicus, Walker Publishing, 2004. For the details of Copernicus' scheme which eliminated the ugly equant, see Appendix 1 of Gingerich's book.

Copernicus' model was hotly disputed, notably by the best living astronomer, Tycho Brahe. While Tycho acknowledged that Copernicus had succeeded in removing equants, he proposed a system which kept Copernicus' best results while avoiding the serious difficulty of finding an explanation for a moving Earth: the Sun moves around the Earth, dragging the rest of the planets with it! This is exactly equivalent, on the basis of ground-based observation, to a heliocentric model. Compare Copernicus' model (below, left) to Tycho's (below, right) and see for yourself.

The primary reason Tycho insisted that the Earth could not move is because his precise measurements of stellar size placed the stars too close for the Earth to move. If the Earth moved, we would see stellar parallax. It was not known until the 18th Century that the apparent size of stars is an illusion caused by atmospheric distortion.

Copernican system Tychian system
Copernican system Tycho's system

It cannot be overemphasized that an explanation of a moving Earth was not scientifically possible, given the dominant four-elements theory and the associated, loosely observation-based idea that anything made of the four elements always fell toward the center of the universe. There was simply no way, without invoking supernatural help, to explain how it was that the Earth would not fall to the center of a heliocentric universe. And if the planets (including the Sun) were made of something else -- the quintessence -- why couldn't they naturally move in circles, just as Earthly matter naturally fell to the center?

However, roughly contemporary discoveries by Galileo Galilei -- of mountains on the Moon, of spots on the Sun, of irregular and blemish-like surface features on Mars, of the four large moons of Jupiter, and of "ears" on the planet Saturn -- began to call into question the idea that the heavenly bodies were made of something different from the gross, heavy matter of the Earth. Ultimately this led to the true speculation that the heavens were made of the same substances as the Earth, and the false one that the planets were inhabited by intelligent beings. It also led to the realization that there wasn't anything to keep the planets from falling to the center, either!

Galileo further discovered that the planet Venus shows phases just like the Moon, which (in conjunction with changes in its apparent size) could be best explained by a heliocentric model, or by Tycho's geocentric model. But all this was observation unsupported by any model of how such things could be.

Tycho's top pupil, Johannes Kepler, was convinced of the heliocentric system for religious reasons. He thought the universe should reflect God, and as God sheds grace on us from His central position in our lives, so should the Sun shed light on all equally. He ran through a number of models, discarding them as he realized they didn't fit the data, and finally had to discard perfect circles in favor of ellipses.

Kepler's Laws of Planetary Motion are crucial in the history of science, as they represent one of the best examples of the principle that when observation falsifies a theory or model, the theory or model should be radically modified or discarded -- even if there is no explanation for the new model suggested by the observations. While Kepler always hung onto the heliocentric idea, he painfully discarded model after model until he had something that fit the best observations of his day exactly.

As important as Kepler's Laws of Planetary Motion were, they hung unsupported by any explanation. They were purely empirical; Kepler was reduced to the speculation that the planets were moved in their orbits by angels. Kepler's Laws remained purely empirical until Newton was able to explain them by his Theory of Universal Gravitation.

For more about older models of the solar system, and an up-to-date account of what we now know, explore The Nine Planets. NASA maintains simple simulations of Kepler's Laws of Planetary Motion

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Copyright © 2001, 2005 by Daniel J. Berger. This work may be copied without limit if its use is to be for non-profit educational purposes. Such copies may be by any method, present or future. The author requests only that this statement accompany all such copies. All rights to publication for profit are retained by the author.