Galileo’s acceleration experiment

The modern view of the controversy

• It was on this page that Galileo first noted an observation of the moons of Jupiter. This observation upset the notion that all celestial bodies must revolve around the Earth. Galileo published a full description in Sidereus Nuncius in March 1610

• Sagredo, Simplicio, and Salviati

• Salviati: I greatly doubt that Aristotle ever tested by experiment whether it be true that two stones, one weighing ten times as much as the other, if allowed to fall, at the same instant, from a height of, say, 100 cubits, would so differ in speed that when the heavier had reached the ground, the other would not have fallen more than 10 cubits.

• Simplicio: His language would seem to indicate that he had tried the experiment, because he says: We see the heavier; now the word see shows he had made the experiment.

• Sagredo: But I, Simplicio, who have made the test, can assure you that a cannon ball weighing one or two hundred pounds, or even more, will not reach the ground by as much as a span ahead of a musket ball weighing only half a pound, provided both are dropped from a height of 200 cubits.

Experiment vs. Philosophy

• This marks the beginning of the modern era in science---the attitude that assertions about the physical world by authorities, no matter how wise or revered, stand or fall by experimental test.

• Galileo wrote in Italian, not Latin, so that anyone could understand.

• He made his argument via a dialogue.

Design the experiment

• Objective: show that the rate of gravitational acceleration is independent of mass

• Materials:

• Pool ball

• Tennis ball

• Salviati: But tell me, gentlemen, is it not true that if a block be allowed to fall upon a stake from a height of four cubits and drive it into the earth, say, four finger-breadths, that coming from a height of two cubits it will drive the stake a much less distance; and finally if the block be lifted only one finger-breadth how much more will it accomplish than if merely laid on top of the stake without percussion? Certainly very little. If it be lifted only the thickness of a leaf, the effect will be altogether imperceptible. And since the effect of the blow depends upon the velocity of this striking body, can any one doubt the motion is very slow .. whenever the effect is imperceptible?

Design the Experiment

• Objective: Demonstrate the relation (direct, indirect, no relation) between mass and inertia, and between velocity and intertia.

• Materials:

Various sports balls

Triple beam balance

Rulers

Office supplies

Stopwatches

• One day in 1641, while I was living with him at his villa in Arcetri, I remember that the idea occurred to him that the pendulum could be adapted to clocks with weights or springs, serving in place of the usual tempo, he hoping that the very even and natural motions of the pendulum would correct all the defects in the art of clocks. But because his being deprived of sight prevented his making drawings and models to the desired effect, and his son Vincenzio coming one day from Florence to Arcetri, Galileo told him his idea and several discussions followed. Finally they decided on the scheme shown in the accompanying drawing, to be put in practice to learn the fact of those difficulties in machines which are usually not foreseen in simple theorizing

Design the Experiment

• Objective: Find the relation (direct, inverse, no relation) between the amplitude of a pendulum’s swing, and its period. Find the relation between mass and period.

• Materials:

Triple beam balance

Fishing line and sinkers

Stopwatches

Office Supplies

• [SALV.] Shut yourself up with some friend in the largest room below decks of some large ship and there procure gnats, a fish in a bowl, and a dripping bottle. Then, the ship lying still, observe how those small winged animals fly with like velocity towards all parts of the room; how the fish swim indifferently towards all sides; and how the distilling drops all fall into the bottle placed underneath. Make the ship move with what velocity you please, so long as the motion is uniform and not fluctuating this way and that.  You will not be able to discern the least alteration in all the forenamed effects, nor can you gather by any of them whether the ship moves or stands still.  ...

• [SAGR.] Though it did not occur to me to try any of this out when I was at sea, I am sure you are right.  I remember being in my cabin wondering a hundred times whether the ship was moving or not, and sometimes I imagined it to be moving one way when in fact it was moving the other way.  I am therefore satisfied that no experiment that can be done in a closed cabin can determine the speed or direction of motion of a ship in steady motion. 

Design the Experiment!

• Objective: Demonstrate that a ball, thrown from a body moving at constant velocity, continues moving with that body.

• Materials

Various sports balls

The Acceleration Hypothesis

• SALV:A falling body accelerates uniformly: it picks up equal amounts of speed in equal time intervals, so that, if it falls from rest, it is moving twice as fast after two seconds as it was moving after one second, and moving three times as fast after three seconds as it was after one second.

Design the Experiment

• Objective: Demonstrate the relation (direct, indirect, no relation) between the height of a fall and the time it requires.

• Materials:

Tennis balls

Stopwatch

Galileo’s Discoveries

• The telescope• Moons• Sun-centered solar system• Pendulum (clock)• Concept of momentum• Uniform gravitational acceleration• Inertial (Galilean) frames• Time-squared law of uniform acceleration

With the loss of many of his defenders in Rome because of Dialogue Concerning the Two Chief World Systems, Galileo was ordered to stand trial on suspicion of heresy in 1633. The sentence of the Inquisition was in three essential parts:

• Galileo was found "vehemently suspect of heresy," namely of having held the opinions that the Sun lies motionless at the centre of the universe, that the Earth is not at its centre and moves, and that one may hold and defend an opinion as probable after it has been declared contrary to Holy Scripture. He was required to "abjure, curse and detest" those opinions

• He was ordered imprisoned; the sentence was later commuted to house arrest.

• His offending Dialogue was banned; and in an action not announced at the trial, publication of any of his works was forbidden, including any he might write in the future

“Eppur si muove”

“And yet it moves”