Galileo: the Telescope &
the Laws of Dynamics

Galileo Galilei (1564-1642) was a pivotal figure in the development of modern astronomy, both because of his contributions directly to astronomy, and because of his work in physics and its relation to astronomy. He provided the crucial observations that proved the Copernican hypothesis, and also laid the foundations for a correct understanding of how objects moved on the surface of the earth (dynamics) and of gravity.

Newton, who was born the same year that Galileo died, would build on Galileo's ideas to demonstrate that the laws of motion in the heavens and the laws of motion on the earth were one and the same. Thus, Galileo began and Newton completed a synthesis of astronomy and physics in which the former was recognized as but a particular example of the latter, and that would banish the notions of Aristotle almost completely from both.

One could, with considerable justification, view Galileo as the father both of modern astronomy and of modern physics.

The Telescope

Galileo did not invent the telescope. The Dutch, notably Christine Huygens, were the first to invent and experiment with lenses (to improve eye sight). But Galileo was the first to use the telescope to study the heavens systematically. His little telescope was poorer than even a cheap modern amateur telescope, but what he observed in the heavens rocked the very foundations of Aristotle's universe and the theological-philosophical worldview that it supported. It is said that what Galileo saw was so disturbing for some officials of the Church that they refused to even look through his telescope; they reasoned that the Devil was capable of making anything appear in the telescope, so it was best not to look through it. That is, the telescope was an instrument of the Devil. That such was so could be no clearer than the image of the moon as it appeared through Galileo's telescope:

For the moon was not perfect, it had blemishes and scars. A year later, when other copies of the telescope were made, many others made sketches of the moon, concerning its imperfect nature:

Opps it does not appear that all of the objects in Aristotle's Universe are, in fact, perfect. The moon has defects!

Well if the moon had defects then Saturn was way whacked out:

Sunspots

Galileo observed the Sun through his telescope and saw that the Sun had dark patches on it that we now call sunspots (he eventually went blind, perhaps from damage suffered by looking at the Sun with his telescope). Furthermore, he observed motion of the sunspots indicating that the Sun was rotating on an axis. These "blemishes" on the Sun were contrary to the doctrine of an unchanging perfect substance in the heavens, and the rotation of the Sun made it less strange that the Earth might rotate on an axis too, as required in the Copernican model. Both represented new facts that were unknown to Aristotle and Ptolemy.

The Moons of Jupiter

 Galileo observed 4 points of light that changed their positions with time around the planet Jupiter on a nightly basis. He concluded that these were objects in orbit around Jupiter. Indeed, they were the 4 brightest moons of Jupiter, which are now commonly called the Galilean moons (Galileo himself called them the Medicea Siderea---the ``Medician Stars''). Here is a simulation of the system which approximates Galileo's field of view and the poor optics of his telescope (which is why the images are not sharp).

In this simulation you can observe the "real" system of Jupiter and its moons over the course of a 14 hour night. The simulation will pause 1/2 way through so that you can notice the change in positions on a 7 hour timescale. The simulation then transitions to a 10 hour day light period where Galileo is shown to have random daytime thoughts about physics. The next night is then available and the positions of the moons have advanced 10 hours forward and Galileo can then make another set of observations of the configuration of the moons as he builds up his log book:

Galileo's observations were done over the course of 15 nights in January of 1610; two of which were cloudy:

Clearly, the nightly changes in the positions of the moons relative to Jupiter was obvious for Galileo (and anyone else that observed the system).

These observations again showed that there were new things in the heavens that Aristotle and Ptolemy had known nothing about. Furthermore, they demonstrated that a planet could have moons circling it that would not be left behind as the planet moved around its orbit. One of the arguments against the Copernican system (and the original heliocentric idea of Aristarchus) had been that if the moon were in orbit around the Earth and the Earth in orbit around the Sun, the Earth would leave the Moon behind as it moved around its orbit.

The Phases of Venus

Galileo used his telescope to show that Venus went through a complete set of phases, just like the Moon.

This observation was among the most important in human history, for it provided the first conclusive observational proof that was consistent with the Copernican system but not the Ptolemaic system. The crucial point is the empirical fact that Venus is never very far from the Sun, in terms of angular displacement, in our sky Thus, as the following diagrams indicate, in the Ptolemaic system Venus should always be in crescent phase as viewed from the Earth because as it moves around its epicycle it can never be far from the direction of the sun (which lies beyond it), but in the Copernican system Venus should exhibit a complete set of phases over time as viewed from the Earth because it is illuminated from the center of its orbit.

Phases of Venus in the Ptolemaic and Copernican systems

It is important to note that this was the first empirical evidence (coming almost a century after Copernicus) that allowed a definitive test of the two models. Until that point, both the Ptolemaic and Copernican models described the available data. The primary attraction of the Copernican system was that it described the data in a simpler fashion, but here finally was conclusive evidence that not only was the Ptolemaic universe more complicated, it also was incorrect.

Myriad Observations Showing Phenomena Unknown to Aristotle

In addition to the observations noted above, Galileo made many other observations that undermined the authority on which the Ptolemaic universe was built. Some of these included
  1. Showing that the planets were disks, not points of light, as seen through the telescope.

  2. Showing that the great "cloud" called the Milky Way (which we now know to be the disk of our spiral galaxy) was composed of enormous numbers of stars that had not been seen before.

  3. Observing that the planet Saturn had "ears". We now know that Galileo was observing the rings of Saturn, but his telescope was not good enough to show them as more than extensions on either side of the planet.

  4. Showing that the Moon was not smooth, as had been assumed, but was covered by mountains and craters.
As each new wonder was observed, increasing doubt was cast on the prevailing notion that there was nothing new to be observed in the heavens because they were made from a perfect, unchanging substance. It also raised the credibility issue: could the authority of Aristotle and Ptolemy be trusted concerning the nature of the Universe if there were so many things in the Universe about which they had been completely unaware?

Galileo and the Leaning Tower

Galileo made extensive contributions to our understanding of the laws governing the motion of objects. The famous Leaning Tower of Pisa experiment may be apocryphal. It is likely that Galileo himself did not drop two objects of very different weight from the tower to prove that (contrary to popular expectations) they would hit the ground at the same time. However, it is certain that Galileo understood the principle involved, and probably did similar experiments. The realization that, as we would say in modern terms, the acceleration due to gravity is independent of the weight of an object was important to the formulation of a theory of gravitation by Newton.

Galileo also did experiments on projectile motion to clearly show just how wrong the Arisotelian concepts were:

Galileo and the Concept of Inertia

Perhaps Galileo's greatest contribution to physics was his formulation of the concept of inertia: an object in a state of motion possesses an ``inertia'' that causes it to remain in that state of motion unless an external force acts on it.

Most objects in a state of motion do NOT remain in that state of motion. For example, a block of wood pushed at constant speed across a table quickly comes to rest when we stop pushing. Thus, Aristotle held that objects at rest remained at rest unless a force acted on them, but that objects in motion did not remain in motion unless a force acted constantly on them. Galileo, by virtue of a series of experiments (many with objects sliding down inclined planes), realized that the analysis of Aristotle was incorrect because it failed to account properly for a hidden force: the frictional force between the surface and the object.

Thus, as we push the block of wood across the table, there are two opposing forces that act: the force associated with the push, and a force that is associated with the friction and that acts in the opposite direction. Galileo realized that as the frictional forces were decreased (for example, by placing oil on the table) the object would move further and further before stopping. From this he abstracted a basic form of the law of inertia: if the frictional forces could be reduced to exactly zero (not possible in a realistic experiment, but it can be approximated to high precision) an object pushed at constant speed across a frictionless surface of infinite extent will continue at that speed forever after we stop pushing, unless a new force acts on it at a later time.

Galileo and the Church

Galileo's challenge of the Church's authority through his assault on the Aristotelian conception of the Universe eventually got him into deep trouble with the Inquisition. Late in his life he was forced to recant publicly his Copernican views and spent his last years essentially under house arrest. His story certainly constitutes one of the sadder examples of the conflict between the scientific method and "science" based on unquestioned authority. Unfortunately, there still are many forces in modern society that would shackle the scientific method of open enquiry in ideological chains of one kind or another.

Summarizing Aristotle's View

Aristotle held that there are two kinds of motion for inanimate matter, natural and unnatural. Unnatural (or "violent") motion is when something is being pushed, and in this case the speed of motion is proportional to the force of the push. (This was probably deduced from watching ox-carts and boats.) Natural motion is when something is seeking its natural place in the universe, such as a stone falling, or fire rising. (We are only talking here about substances composed of earth, water, air and fire, the "natural circular motion" of the planets, composed of aither, is considered separately).

For the natural motion of heavy objects falling to earth, Aristotle asserted that the speed of fall was proportional to the weight, and inversely proportional to the density of the medium the body was falling through. He did also mention that there was some acceleration, as the body approached more closely its own element, its weight increased and it speeded up. However, these remarks in Aristotle are very brief and vague, and certainly not quantitative.

Actually, these views of Aristotle did not go unchallenged even in ancient Athens. Thirty years or so after Aristotle's death, Strato pointed out that a stone dropped from a greater height had a greater impact on the ground, suggesting that the stone picked up more speed as it fell from the greater height.

Galileo disputes all of Aristotle's ideas in a satirical manner:

Two New Sciences

Galileo set out his ideas about falling bodies, and about projectiles in general, in a book called "Two New Sciences". The two were the science of motion, which became the foundation-stone of physics, and the science of materials and construction, an important contribution to engineering.

The ideas are presented in lively fashion as a dialogue involving three characters, Salviati, Sagredo and Simplicio. The official Church point of view, that is, Aristotelianism, is put forward by the character called Simplicio, and usually demolished by the others. Galileo's defense when accused of heresy in a similar book was that he was just setting out all points of view, but this is somewhat disingenuous---Simplicio is almost invariably portrayed as simpleminded.

Salviati states:

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.

This then 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's Virtual Experiments (Go Here and Learn)

Galileo was an exacting experimentalist, fully aware of the value of precise measurements and repeatable experimental detail:

Translated Quote from one of Galileo's Journals:

A piece of wooden moulding or scantling, about 12 cubits long, half a cubit wide, and three finger-breadths thick, was taken; on its edge was cut a channel a little more than one finger in breadth; having made this groove very straight, smooth, and polished, and having lined it with parchment, also as smooth and polished as possible, we rolled along it a hard, smooth, and very round bronze ball. Having placed this board in a sloping position, by raising one end some one or two cubits above the other, we rolled the ball, as I was just saying, along the channel, noting, in a manner presently to be described, the time required to make the descent. We repeated this experiment more than once in order to measure the time with an accuracy such that the deviation between two observations never exceeded one-tenth of a pulse-beat. Having performed this operation and having assured ourselves of its reliability, we now rolled the ball only one-quarter the length of the channel; and having measured the time of its descent, we found it precisely one-half of the former. Next we tried other distances, compared the time for the whole length with that for the half, or with that for two-thirds, or three-fourths, or indeed for any fraction; in such experiments, repeated a full hundred times, we always found that the spaces traversed were to each other as the squares of the times, and this was true for all inclinations of the plane, i.e., of the channel, along which we rolled the ball. We also observed that the times of descent, for various inclinations of the plane, bore to one another precisely that ratio which, as we shall see later, the Author had predicted and demonstrated for them.

For the measurement of time, we employed a large vessel of water placed in an elevated position; to the bottom of this vessel was soldered a pipe of small diameter giving a thin jet of water which we collected in a small glass during the time of each descent, whether for the whole length of the channel or for part of its length; the water thus collected was weighed, after each descent, on a very accurate balance; the differences and ratios of these weights gave us the differences and ratios of the times, and this with such accuracy that although the operation was repeated many, many times, there was no appreciable discrepancy in the results.