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Lecture 6: EXERCISES B:

1.When did Galileo make his first important telescopic discoveries?

 

2.About how old was he?

 

3.What was he doing professionally at the time?

 

4.Briefly describe his early education and previous scientific experience.

 

5.Should Galileo be given any credit at all for the invention of the telescope?

 

6.What exactly did Galileo see through his telescope that caused him to conclude that the moon had mountains?

7.What exactly did he see that caused him to conclude that Jupiter had moons revolving around it?

 

8.Galileo attacked the Aristotelian world-view on many fronts. If the moon had mountains, which Aristotelian teaching would this refute?

 

9.Which Aristotelian doctrine did Jupiter's moons disprove?

 

10. At first, Galileo argued that the earth could be moving. Later he argued that it did move. How could one use the moon's mountains to make it plausible that it was possible that the earth moved?

 

11.How could Jupiter's moons be used to make it plausible that it was possible that the earth moved?

 

12. Since the telescope distorted images around the edges and gave them colored fringes, some people concluded that it was not a reliable instrument for science. How could one show that it could be relied on in science?

13. Although the moon looked bigger through the telescope, the stars looked smaller. What did Galileo's opponents conclude from this?

 

14.How did Galileo explain this surprising phenomenon?

is. Did Galileo have any independent evidence for this explanation or was it ad hoc?

 

16. Galileo pointed out that when a ship begins its journey, sometimes one has the sensation that the shore is moving away from the ship. How is this fact relevant to the question of the earth's motion?

 

17. What good reason could the Aristotelians give for saying that in fact it is the ship that is moving, not the shore?

 

18. The Aristotelians argued that if the earth rotated, birds flying to the east would get left behind. Assuming the earth's circumference is 25,000 miles, how fast would the birds have to fly just to keep even, according to the Aristotelians?

 

19.Galileo replied that the birds would have no more problems than would a fly in the cabin of a fast moving ship. If you were an Aristotelian, how would you answer this point?

 

20. According to the Aristotelians, if the earth is moving, then the paths of cannonballs should be affected. Suppose a certain cannon projects balls with a total flight time of 2 seconds. If it were aimed straight north, where would the ball land, according to the Aristotelians? Is this predicted effect big enough to be experimentally detectable?

 

21.How would Galileo answer this point?

 

22. One can test whether a released object such as a cannonball or bird continues to share the motion of the "parent" body. Galileo claimed to have done the following experiment: a ball was released from the top of the mast of a moving ship. According to Galileo, where should the ball land?

23. According to Aristotle, where should the ball land? (Assume the time of fall is one second and that the ship is moving at 30 mph.) Is the effect big enough so that sailors throwing down ropes from the crows nest, etc., would have noticed it?

 

24.Sophisticated Aristotelians would have invoked the impetus theory to explain this particular experimental result. How would such an explanation go?

 

25. A heavy ball rolled on a smooth floor goes a long way but eventually comes to a stop. How would the impetus theory explain this?

 

26.How would Galileo account for this?

 

27. According to the impetus theory, would birds and cannon balls behave differently than they do if the earth moved?

 

28.So far we have discussed Galileo's arguments that it was possible that the earth moved. Now let us turn to his attempts to show that it actually did. The first argument was based on his discovery of the phases of Venus.
Explain why this discovery went against the Ptolemaic system.

 

29.Could the Copernican system account for this phenomenon?

30.How about the Tychonic system?

 

31. Galileo became interested in sunspots because they appeared to move across the face of the sun. How might this phenomenon be relevant to the question of whether the earth moved around the sun?

 

32.Galileo thought that the tides provided the best argument for the earth is diurnal motion. According to Galileo, what caused the tides?

 

33.On Galileo's account, how often should the tides ebb and flow? How did he explain the discrepancy between his account and observations?

34. Was Galileo's account of the tides consistent with his account of the motion of the ball dropped 'from the ship's mast?

35-36. The clearest experimental arguments for Copernicus' theory came from 19th century discoveries - stellar parallax and Foucault's pendulum. Briefly describe each of these and show how they support the Copernican system. Does
each provide evidence for diurnal rotation, annual revolution, or both?

 

REVIEW QUESTIONS

1.Order of Events.

In evaluating the arguments for and against a scientific theory, we have to be very sensitive to what was (and was not) known at the time. Give an approximate date for each of the following developments.

 

(a)The prediction that Venus should have phases.

(b)The discovery that Venus does have phases.

(c)The invention of the telescope.

(d)The experimental determination of the angle of stellar parallax.

(e)The observation that comets move through the places where the crystal spheres were thought to be.

(f)Publication of Galileo's technical systematic account of the motions of projectiles and falling bodies.

(g)Galileo's trial by the Inquisition.

 

2.Galileo's Attack on Aristotelian Physics and Cosmology' 'and Ptolemaic Astronomy.

What evidence or arguments did Galileo provide against each of the following doctrines? Be precise but brief.

 

(a)Heavenly bodies are perfect and immutable.

(b)On earth heavier bodies fall faster than lighter ones.

(c)If a body is moving horizontally, something must be continually pushing it.

(d)The Ptolemaic system.

 

3.Comparison of the Tychonic and Copernican Systems.

Although Galileo did not often discuss it, the major rival to the Copernican system at his time was the Tychonic system (not the Ptolemaic).

 

(a)Give a list of various reasons why Galileo's opponents preferred Tycho's system to that of Copernicus.

 

(b)Give a list of a variety of reasons why Galileo preferred the Copernican theory.

 

4.Observation and the 'Reliability of the Telescope.

Everyone agreed that science should be based on observation, but which observations can be trusted?

 

(a)List a variety of reasons why some of Galileo's opponents distrusted the telescope.

 

(b)How did Galileo answer each of these objections? (Could he answer all of them?)

 

(c)Did Galileo ever criticize his opponents' observation claims? If so, give examples. If not, explain why not.

SAMPLE EXAM

1.In 1543, Copernicus published a theory of the solar system and other heavenly bodies according to which the earth moved. Galileo became a defender of this theory in the early 1600's.

In a few sentences, describe the major reason or argument which each of the following groups of Galileo's contemporaries gave against the Copernican theory:

 

(a)Observational astronomers

 

(b)Physicists interested in describing the motions of bodies

(c)Theologians

 

2.Part of Galileo's defense of his own position was an attack on alternative views. Outline a variety of reasons or arguments which Galileo could give for rejecting each of the following theories.

 

(a) The theory that heavenly bodies are perfect and unchanging

 

(b) The Ptolemaic system

(c) The Tychonic system

 

3.(a) Why did Galileo consider his theory of tides to be so important?

 

(b)Describe in detail two different criticisms of Galileo's theory of tides.

 

4. (a)According to Galileo's theory, what factors cause a hockey puck moving across a very large ice rink to eventually stop?

 

(b)According to the impetus theory, what factors determine how far it moves before stopping?

 

(c)What experiment could one do in order to refute or undermine the impetus theory and to confirm Galileo's theory?

 

5.People at the time also raised methodological objections to Galileo's work. Briefly describe their criticisms of:

 

(a) The use of the telescope in observational astronomy

(b) The use of ideal laws or idealizations in science

(c) How did Galileo reply to each of these objections?

GOOD ANSWERS TO SAMPLE EXAM

(Taken from blue books)

(a)There was no observable stellar parallax. Opposing observational astronomers took this to mean that the earth can't move, since if th earth did move it meant that either the stars are way off in the distance, which they didn't consider to be true, or that there should be
observable stellar parallax.

 

(b)Physicists describing bodies in motion - they were caught up in the impetus theory and could not understand what force kept the earth moving, (if it did not lose impetus), and why things such as birds or balls dropped from high distances did not lose their impetus and become"left behind" in relation to the earth's movement. They concluded
thatsince birds, etc., are not left behind the earth must not be moving - they did not have a theory of inertia.

 

(c)Joshua 10:12 and 10:13 tells of how Joshua stopped the sun in the sky for a day. This implies that normally the sun moves around the earth which is Ptolemaic. Since fundamentalist religion assumes a
literal interpretation of the Bible, a fundamentalist theologian would reject the argument that the earth was moving on this ground. The Church held that since Copernicus could not supply proof of the earth's motion, the argument for the motion of the sun and the geo-centricity
of the earth was just as valid and more credible by direct sense experience. The Copernican theory was a mathematical hypothesis,according to the Catholic Church, and remained a priori and unproved.

 

2.(a) In argument against the theory that heavenly bodies are perfect and unchanging Galileo could make use of the mountains on the moon, the fact that when viewed in its crescent shape (the moon) there we're ridges and uneven edges, or the 4 stars of Jupiter. Galileo could argue that the positions of the heavens change, as evidenced by the 4 stars of Jupiter, or the phases of Venus. Galileo could make note of the changes even in the number of stars, what was to be done about falling stars, he could argue.

(b)The biggest argument against the Ptolemaic system was the phases of Venus. By the Ptolemaic system Venus would only appear as a crescent to earth. But Venus at times appeared almost full. Also the moons of Jupiter refuted the idea of "crystal spheres" which held the stars.

 

(c)Galileo did not really argue against the Tychonic system that often. Instead he chose to argue against the Ptolemaic system, almost ignoring-the Tychonic system. The reason Galileo could give against the Tychonic system would have to rely heavily on the belief that such a system would not be a good way to put the universe together, it lacks
the simplicity Galileo deemed necessary.

 

3.(a) Galileo thought that his theory of tides was one of his best ways of proving the Copernican theory. Because in his description of the tides' movement, it was necessary that the earth moved around the sun.

 

(b)(1) One criticism was the fact that Galileo's explanation showed only one high tide per day, yet in parts of the world there were more than one high tide per day, which could not be explained by Galileo's
theory unless accidents were involved and proved to cause more than one tide.

 

(2) Another criticism was that it was not possible for the
waters to be controlled by one force and the land by another. It contradicted what Galileo had already said about the earth's motion, that is, if the earth rotates on its axis, not only would the land rotate,but so would the sea as it would share the earth's revolution. This
meant that the water could not get left behind as Galileo suggests in his theory of tides.

 

4.(a) According to Galileo's theory, a hockey puck would eventually stop because of outside forces, such as friction, and imperfections in the ice. If these forces did not exist, the puck would continue on indefinitely. Galileo's theory is based on the principle of inertia.

 

(b) A theory of impetus would say that there is only so much impetus stored in the puck and it is making it move across the ice. The puck will stop moving once the impetus runs out. Followers of impetus also recognize outside forces but they believe that the prime mover in this case would be an internal mover that is eventually used up.

 

(c)To undermine the impetus theory one could perform the experiment over and over but on different surfaces so that one would end up with a continuum of surfaces and one could perhaps generalize about the
behavior of the puck as follows:

distanceG = Galileo's predictions

(in meters)I = Impetus' predictions

 

[Diagram is omitted]

 

The impetus theory would predict a leveling off of the distance at a certain point. According to this theory, a puck can only go so far.

According to Galileo, the closer you approximate "ideal" conditions - less friction - the farther the puck will move.

The way to undermine the IMP is to carefully record the behavior of the puck at the crucial period - as the curve approaches the ordinate and see how close you can come to a vacuum. And finally, you will conclude, as Galileo did, that there is no set distance - no maximum distance - for the puck to move.

 

(a)The use of telescope: because the images
showed chromatic aberration, as well as making the stars appear smaller, and the moon closer, many believed that the telescope was not a good instrument for measuring in science.

 

(b)Their main objection was that there was no way to test the theory if Galileo made all these ideal assumptions (such as, the air not affecting moving objects through resistance, etc.). They also said that such forces that Galileo was trying to remove through his assumptions did in fact exist and that hence a theory of principle proposed under
ideal circumstances were of no practical use.

(c)The telescope he attempted to calibrate in order to increase it's reliable. He answered the argument concerning the decrease in the size
of the stars by attempting to explain irradiation - the stars give off this"glow" that makes them appear to the human eyes as if they were larger. The telescope eliminated these. lie, additionally, improved the quality of the telescope with superior lenses and noted that if one were not an amateur that the working of the telescope is less difficult.
He pointed out that even religious leaders were using telescopes and improving its integrity.

 

(d)In regard to the use of idealizations; Galileo believed that science needed to rely on ideal situations if science wanted to form simple theories capable of explaining the behavior of large classes of events.
Science he claimed, cannot be bogged down with explaining all the sources of accidents that cause discrepancies in our results of tests and experiments. Science should not seek to explain the behavior of birds, of stones, of large bricks, under windy days, under calm days, etc. Galileo, however, didnot believe in completely ignoring such factors. Instead
science should form their laws around ideal situations, but should also includefactors that can have an effect on the outcome or behavior.
An example would be listing some of the possible causes of
discrepancies in Galileo's theory of failing bodies, such as wind, density of falling object, altitude, etc. For Galileo, as it is in science today, laws are to be given for ideal situations and scientists should where possible extrapolate their findings to such conditions.