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
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
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..."
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
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.
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.
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.
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:
Sagredo - A wealthy nobleman who is seeking truth.
Simplicio - An Aristotelian philosopher who puts up
ineffectual arguments for Salviati to knock down.
Day 1
Day 2
Day 3
Day 4
Basically a discussion of celestial matter and terrestrial
matter.
( 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.)
"... the immense separation between earth and heavenly
bodies seems to me to imply a great dissimilarity."
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.
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.
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.
paths curved downward
sunspot moving up
sunspot paths curved up
sunspot moving downwards
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:
Galileo's argument for additional motion of sun
This last point would be counter to physical principles.
Precession of the sun's axis of rotation would require an enormous torque.
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
Dialogue Concerning two New Sciences, online"
Dialogue Concerning Two New Sciences, pdf version