Galileo Galilei

(1564-1642)

Galileo was a great observational astronomer (as was his predecessor Tycho Brahe). In addition he founded the modern science of mechanics (dynamics) and provided the vital link between Kepler's laws of planetary motion and Newton's description of the Universe.

His first published work (The Star Messenger) occurred late in his life; Galileo communicated most of the results of his researches by correspondence. He wrote to Kepler, saying he was a believer in the Copernican model of the universe but was not prepared to admit this publicly. This caution was to avoid ridicule from his fellow academics, rather than from fear of religious persecution; the Catholic Church allowed discussion of the heliocentric model, if framed in scientific language and not linked to theology.

In 1604, Galileo observed a nova (coinciding with a Jupiter/Saturn/Mars conjunction, which occurs every 800 years). He showed from its lack of parallax that it was very distant, contrary to the ideas of Aristotle that the heavens were perfect and unchanging.

The first telescopes were made in Holland in early 1600's. Galileo heard about them but (he claims) without constructional details. From a "deep study of the theory of refraction", he perfected the telescope over a period of several years. His first attempt consisted of two lenses inside lead tube, giving magnification of just a few times. Eventually he increased the magnification to 1000.

Telescopes could detect and identify a ship 2 hours sailing away, so was soon put to use to look out for invading ships and to enable Venetian stockbrokers to set the price of commodities in response to their supply.

Galileo was probably the first person to use the telescope to systematically study the sky. He found detail in the sky never seen before and wherever he looked, he found evidence to support the Copernican system.

He first looked at the moon, traditionally believed to be a perfect sphere. Galileo discovered mountains and valleys, recognizing them from the shadows cast on the lunar surface by light from the sun. This interpretation suggested that things in the heavens are not completely different from those on earth, as had been commonly assumed. From the length L of shadows, Galileo estimated height h of the mountains.

Galileo looked at the sun and found it had spots! (Not perfect, as the Aristotle had claimed). He used the spots to show that sun rotates about its axis every 27 days, and determined direction of axis of rotation. Unfortunately, his studies on the sun damaged his eyes; by the time of his death, he was blind.

Galileo also aimed his telescopes at the stars. Found they were not magnified into disks, unlike the moon and planets: they still appeared as points, suggesting that they must be very distant. Overwhelmed by the number of stars he could see: found hundreds in between major stars visible by the naked eye. The Milky Way was seen to consist of countless stars. He probably speculated (like others) that they were distributed in space, not on a celestial sphere.

1610: moved to Florence as "Philosopher and First Mathematician to the Grand Duke of Tuscany". The same year, looking at Jupiter, Galileo noticed 3 nearby faint objects, resembling stars. Over the next few nights, he observed that they moved relative to Jupiter in quite a different way to the stars; stayed near planet but also moved relative to it. A week later, he noticed a 4th object. Showed that the objects ('Galilean satellites') all revolve around the Jupiter and determined their period of rotation. He originally called them planets, but later satellites as suggested by Kepler. This proved that not all celestial objects circle the earth.

In both the geocentric and heliocentic models, Jupiter is moving through space. Galileo could not explain why Jupiter can move in its orbit without losing its satellites, any more than could explain why the moon remains attached to the earth. But he argued that if Jupiter can move and retain its four moons, the earth should be able to move without losing its moon. This argument by analogy made the earth seem less special. It also pointed to the need to understand the motion of objects, now called the science of dynamics.

Observing Venus, Galileo found different phases, similar to our moon, and variations in apparent diameter. This is explained on the Copernican model if Venus is nearer to the sun than is the earth.

Galileo published his discoveries in a 'periodical' called the "Message from the Stars"

1623: Galileo's friend Maffeo Barberino was elected as Pope Urban VIII. Galileo had six audiences with the new pope (in the Vatican gardens) and was presented with gifts. Galileo felt encouraged to write Dialogues on the Two Chief World Systems (finished 1630). This is a debate between three characters: Salviati (a Florentine friend, but represents G's Copernican views), Sagredo (another friend, as an intelligent layman) and Simplicio (a less-intelligent "scholar", an adherent to Ptolemism). This form of debate was used by Greek philosophers; Galileo probably thought he was being ingenious. Indeed, the Holy Office (church censors) granted permission for publication, but with conditions:

(1) Galileo state in a preface that the treatment was "from a purely theoretical standpoint"

(2) that the book conclude with a statement that God is all-powerful; to Him all things are therefore possible; consequently no physical phenomena can be adduced as necessary proof that the earth rotates on its axis and revolves around the sun.

Galileo's book aroused anger in some branches of Catholic church. Upon reading the book, Urban VIII found that the passage which he had insisted on was put in the mouth of Simplicio, who he may have taken to be a caricature of himself. He probably felt that his censors had let him down.

Galileo was summoned to Rome to appear before the Inquisition. Had he been forbidden to hold and defend Copernican views (as his signed document stated), or had he been warned against teaching Copernican ideas ?

On 22 June 1633, Galileo was forced to renounce any views which conflicted with the Ptolemaic system. As a penance, he had to recite Psalms each week for 3 years and for the rest of his life was held under 'house arrest' in his villa near Florence. The results of the trial had a chilling effect on other intellectuals of the day.

1638: Galileo wrote Dialogues Concerning Two New Sciences, in which the same three characters debate, but this time about earthly things.

Died 1642 after becoming blind. Refused burial in consecrated ground. .

1992: the Vatican declared, after a 13-year investigation, that Galileo had been "imprudently opposed" and was "right in adopting the Copernican astronomical theory" .


Besides his interest in astronomy, Galileo was concerned throughout his life with mechanics.

Terrestrial mechanics allows the possibility of experiments, controlled observations.

For example, consider a simple experiment: the free fall of an object. One can answer the question "why does the object fall ?" in several ways:

  • Because gravitational force pulls it down (according to Newton, or its efficient cause according to Aristotle)
  • Because it was released (an equally valid reason of a different kind)
  • Because it is heavier than air (the material cause, according to Aristotle)
  • Because its natural place is the centre of the earth (Aristotle's final cause)

    To understand what Galileo achieved, it is necessary to examine the pre-existing ideas of motion.

    Aristotle's Description of Motion

    In this description, which dominated thought up to and through the Middle Ages, the four "elements" each have their natural places: Water and earth are endowed with "gravity", fire and air with "levity".

    These are intrinsic properties of the elements and do not require further explanation.

    In the heavens, however, things are observed to be different: the stars and planets move in circles. Aristotle inferred that the heavenly bodies are not made up of the 4 basic elements, but require a fifth element called the ether.

    A stone falls vertically because its natural place is the centre of the earth. This is an example of natural motion.

    A moving oxcart is an example of violent (forced or constrained) motion; the earth beneath prevents its natural motion.

    Aristotle described four "causes" of motion. So in answer to the question "why does an ox-cart move?" he identified:

  • a material cause (the cart is made of wood and can move without falling apart)
  • a formal cause (the shape or form of the cart, including its wheels, enables it to roll)
  • an efficient cause (the ox, effective in making the cart move)
  • a final cause (purpose of the motion e.g. to transport grain)

    Aristotle tried to understand nature in terms of the potentialities of objects. (e.g. an acorn has the potentiality to become an oak tree, perhaps a more significant property than any other). Change occurs when potentialities become actuality, e.g. when objects find their "natural" place. This reasoning reveals an emphasis on purpose (teleology), not necessarily divine but revealing a pattern of nature.

    Compare this account with Galileo's Dialogues on Two New Sciences, for example the debate on whether a heavy or light stone hits ground first. Galileo's discussion is much closer to the experimental basis of modern science.

    Importance of the Dialogues

    :

  • They are the first record of carefully planned and accurately executed experiments as a means of acquiring new facts. Following Tycho, Galileo established the experimental method to complement the mathematical and philosophical methods of the Greeks. Galileo was certainly not the first to disagree with Aristotle's description of motion, but was the first to offer experimental evidence against it.

  • Galileo was the first to identify momentum as a fundamental quantity in mechanics, and to show that velocity is a factor contributing to momentum (the other factor he called weight; the concept of mass had not yet been invented).

  • Galileo discovered that the rate of gain of momentum of a falling body is constant, equivalent to acceleration = constant. Leads the equations :

    v = v0 + g t, d = v0 t + (g/2) t^2 , v^2 = v0^2 + 2 g d

    (Remember, acceleration is a vector; in 1-dimensional problems, this means it can have + or - sign).

    Galileo used inclined planes to "dilute" gravity, to slow down the motion and make it more easily measured. He used his pulse and water clocks for timing.

    He showed that the time of fall of a heavy object is practically independent of its weight (perhaps making use of the tower of Pisa).

    Aristotle had said "the downward movement of an object is in proportion to its size". But this leads to illogical situations, as when two halves of a cannon ball are connected by a slender thread (Ferris p.92).

    In debates, the followers of Aristotle tended to choose examples of resisted motion: a stone falling through water, or a feather through air, where size does matter. Galileo focussed on the opposite extreme, which we now recognize as being the simpler situation, and one which is approximated by dense objects moving through a rarefied medium.

    Note that in most cases of constrained motion, the object will stop if we remove the force. This had brought Aristotle to the concept that a force is necessary to sustain motion, and to the idea that speed is proportional to force or effort.

    In fact, these conclusions do apply to some real situations. For example, a raindrop reaches a terminal velocity, which depends on its mass, its radius and on the viscosity of air. After acceleration to the terminal velocity , the gravitational force is just balanced by the frictional (viscosity) force, i.e. the net force and acceleration are both zero. But this is a relatively complicated situation, which depends on properties of the air as well as those of the moving object.

    In fact, Aristotle recognised that in a vacuum all bodies would fall at the same rate but used this conclusion to argue against the existence of a void (vacuum).

    In the case of flying spears or arrows, Aristotle had to argue that air pushed aside at the front rushes to the back and pushes the object forward. Otherwise, how to explain its continued motion after the force is removed ?

  • Galileo observed that momentum imparted to an object in a particular direction does not affect its momentum in a perpendicular momentum. (This is the basis of our modern use of velocity components in mechanics problems). He proved that the path of a projectile is a parabola and prepared a range-table for gunners.

    Projectile Motion

    To the Greeks, projectile motion represented a challenge. For example, a stone thrown vertically upwards would have to be in constrained motion on its upward flight and natural motion coming down.

    Galileo needed to make no such distinction. In free fall (neglecting air resistance), an object is subject to a constant acceleration (g) downwards, independent of the magnitude or direction of velocity. (Acceleration is a vector, in this case pointing downwards; it can correspond to downward velocity increasing or upwards velocity decreasing).

    Likewise, this downward acceleration is independent of any velocity in the perpendicular (horizontal) direction. So if we fire a cannon ball horizontally, the vertical component of motion will be the same as when the ball is released from rest (initial vertical component = 0).

    d = v0 t + (g/2) t^2 becomes y = (g/2) t^2 if y is measured downwards.

    In the horizontal direction, gravitational acceleration is zero, which suggests:

    x = v0 t where v0 is the initial velocity in the horizontal (x) direction.

    This is motion at a constant velocity v0. Galileo argued that this was possible by analogy with a ball rolling on a perfectly horizontal and smooth (no friction) table. Because of its inertia, the ball maintains its velocity, in disagreement with Aristotle's assumption that uniform motion requires a constant driving force.

    Combining the expressions for x and y, so as to eliminate t, gives:

    y = (1/2) (g/v0^2 ) x^2 , the equation of a parabola.

    By analogy, a stone falling vertically on a moving earth describes a parabola, as seen from a "stationary" observer in space. But observers on the earth have the same horizontal velocity as the stone; the relative velocity between stone and observer is zero in the horizontal direction. We therefore see no evidence of the horizontal motion; the behaviour of the stone is the same as if it were released on a stationary earth.

    Likewise, long jumpers will not be seen to swerve sideways as a result of the earth's motion. In fact, any kind of motion is unaffected by the velocity of the earth in its orbit or our tangential velocity resulting from the earth spinning about its own axis, to the extent that these motions approximate (over a short time period) to straight-line motion. We conclude that the motion of objects on earth is unaffected by the earth's velocity, regarding the latter is uniform in magnitude and direction.

    In reality, the direction is not quite constant; both the axial spin and motion around the sun involve uniform motion in a circle, NOT along a straight line. The effect of this nonlinear motion is to introduce a "Coriolis force" . This "fictitious" force causes the direction of swing of a simple pendulum to precess; the direction of swing, measured with respect to the earth, rotates through 360 degrees in 24 hr at either pole, or lesser amounts at lower lattitudes and thdecreasing to zero for a pendulum swinging at the equator. The Coriolis force is insignificant for typical projectiles but is important in determining the motion of the atmosphere and weather patterns.


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