Dialogue Concerning the Two Chief World Systems - Ptolemaic & Copernican
Galileo Galilei, 1632

Reference Text : Stillman Drake, University of California Press, Berkeley and Los Angeles, 1967

The text deals with an imaginary discussion among three men,

Salviati - An intellectual who seems to speak for Galileo
Sagredo - A wealthy nobleman who is seeking truth.
Simplicio - An Aristotelian philosopher who puts up ineffectual arguments for Salviati to knock down.

They will discuss the evidence for and against the Copernican and the Ptolemaic views of the World over a period of four days.
 Day 1      Day 2        Day 3         Day 4

Day 1
Basically a discussion of celestial matter and terrestrial matter.

Sagredo . " ... yesterday's( the first day) discourse may  be summarized as a preliminary examination of the following two opinions as to which is the more probable and reasonable. The first holds the substance of the heavenly bodies to be ingenerable, incorruptible, inalterable, invariant, and in a word free from all mutations except those of situation, and accordingly to be a quintessence most different from our generable corruptible, alterable bodies. The other opinion , removing this disparity from the world's parts, considers the earth to enjoy the same perfection as other integrable bodies of the universe; ..."

Sagredo. " ... sublunar bodies are by nature generable and corruptible, etc. and are therefore very different in essence from celestial bodies... This argument is deduced from simple motions."

Simplicio. " ...from Aristotle we take it that the heavens are of an impenetrable hardness and the stars are the denser parts of the heavens..."
( note - There does not seem to be in Aristotle an argument for hardness of celestial matter. This seems to be a view held by the Peripatetics in Galileo's time.)

Simplicio. " ... I consider the moon's sphere to be as smooth and polished as a mirror, whereas that of this earth ... is very rough and rugged."

Galileo (in the person of Salviati ) makes a brilliant argument countering this belief. If the moon, or any celestial body were highly smooth and polished it would be invisible in reflected light ! The fact that the moon's entire surface is visible can only be explained by it having a roughly textured surface. As an example of this he places a mirror on a white wall. The wall is equally bright from all angles of view, whereas the mirror is bright only when the viewer's angle matches that of the sun's rays. Moreover, Galileo had already observed the cratered surface of the moon in the telescope.

Salviati. " Does not Aristotle say that because of the great distance, celestial matters can not be treated very definitely?"

Salviati.  Argues that sunspots are indeed on the surface of the sun. They appear and disappear so the sun can not be taken to be made of unalterable substance.

Simplicio. Even though the evidence exists for a similarity between the earth and the moon he can not grant such a similarity because
"... the immense separation between earth and heavenly bodies seems to me to  imply a great dissimilarity."

Day 2

This day is taken up mainly by a discussion of motion. Salviati argues that there are no experiments on the earth which would preclude the daily rotation  of the earth. Previous arguments from Ptolemy to the present day failed to account for the fact that the bodies falling on the earth , or birds or clouds in the sky, share the horizontal component of the earth's surface velocity and this component is not sensed by the observers. A popular argument against the rotation of the earth was that a ball dropped from a tower would strike the earth some distance away from the tower because as the ball fell towards the earth the tower would be moving away from it. Galileo's counter argument is very important since it brings in the notion of compounding the motion of the tower with the motion of the falling ball.

Day 3

This day is basically devoted to the annual motion of the earth around the sun. However, it begins with a discussion of the location of the supernova of 1572. Simplicio brings forth a book by a Peripatetic philosopher(Christoph Scheiner) in which is argued from the observational data of the astronomers that the supernova was between the earth and the moon. Galileo (i.e. Salviati) makes a detailed calculation using similar or the same data and shows how the author had failed to proved his point and in fact make the Aristotelian position on the inalterability of the heavens even more desperate. The discussion is highlighted by an understanding of error analysis by Salviati, including the effects of systematic errors. Sagredo summarizes the discussion by concluding that Salviati has completely demolished the philosopher's proofs of the sub lunar location of the super nova.

The next part of this day's discussion addresses the annual motion of the earth in its orbit.  Salviati explains that Venus and Mars really do change their visual size when viewed through a telescope. The lack of naked eye visual change is explained as a physiological feature of the eye wherein refracting light appears to give the planet or star a halo of "hair".

The explanation of retrograde motion in the Copernican system is far more elegant than that in the Ptolemaic system.
When the earth is at a, a sighting to the planet is made along line aa'. In a given time the earth moves to b and the outer planet to b'. The sighting along bb' crosses that of aa' giving the visual impression that the planet has slipped backwards compared to the background of the fixed stars. These complex visual sightings can be easily explained if it is assumed we are making our observations from a moving platform, rather than from a fixed one.
Salviati next gives a very subtle argument in favor of the earth's orbital motion based on the visual behavior of the sunspots (Scheiner and sunspots. From extensive and careful studies of the sunspots Galileo had concluded that they were on the sun's surface. Moreover, these spots moved in a regular way across the Sun's surface such that one could deduce that the sun itself revolve about an axis with a period of about one month. By tracking the sunspot motion one could infer the surface rotation of the sun. At certain times of year the tracks followed by the spots would be curved lines proceeding from bottom to top. At other times of year the tracks would be curved lines proceeding from top to bottom. At two times of the year the tracks would be straight lines with the motion going either from bottom to top or from top to bottom.

paths curved downward

sunspot moving up

sunspot paths curved up

sunspot moving downwards
This effect can be explained most easily by assuming that the sun rotates around an axis that is at an angle to the plane of the earth's orbit (the ecliptic). By requiring that this axis remain fixed in its direction ( conservation of angular momentum) the sunspot motion can be explained by our looking at the rotating sun from different positions in the orbit. The case where the sunspots move in straight lines from left to right upwards corresponds to the sun's axis of rotation being perpendicular to our line of sight. These sun spots disappear to the right and are high. Six months later our line of sight is again perpendicular to the sun's axis of rotation. The spots appear high on the left and move downwards to the right. The case where the paths appear curved downwards corresponds to our view being of the northern hemisphere of the sun ( The axis points toward us.) Six months later we are viewing the southern hemisphere and the sun spot tracks are moving on upward arched tracks.

If we tried to force the observation onto the sun's motion, with the earth held fixed then the sun would have to engage in four motions:

This last point would be counter to physical principles. Precession of the sun's axis of rotation would require an enormous torque.

This third day also deals with the lack of apparent relative motion of the stars. Some parallax was expected, but the amount was not known. The only way one could account for a lack of parallax was to assume the stars were very far away. Simplicio, uttering a common criticism of the Copernican system, found it absurd to have such a vast space between Saturn and the stellar sphere.

Day 4

Salviati attempts to show that the tides are caused by a combination of the earth's orbital motion and daily rotation. He uses as an example a vessel of water which is accelerated. The water redistributes itself in response to the acceleration. The cause of the acceleration, according to Salviati is the difference in absolute velocity experienced by the waters of the earth according to the diagram:

In this picture, v is the orbital speed of the earth. Salviati claims that the difference in speeds of the waters at points a and b constitute an acceleration, and hence the tidal flow to and fro is a consequence of the earth's motion. He explicitly rejects any direct influence of the moon or sun on the tides. Galileo's theory of tides is incorrect. It is understandable that he did not know of gravity in a quantitative sense. This was yet to be revealed some 56 years later in Isaac Newton's work. Galileo's rejection of the lunar influence on the tides was based on his aversion to occult or mystical explanations in the physical world. Perhaps more curious is that the argument he presents on the 4th day contradicts what he proved on the second day, namely that the velocity v of the earth's orbital motion should have no effect on the motion of the waters because this velocity is common to all parts of the earth. The modern explanation of the tides depends on Newtonian mechanics and the effect of the moon and the sun on the waters of the earth.
Maffeo Barberini, Urban VIII