Everything that has been said so far about the development of science is only a prehistory. modern science. A. Einstein and L. Infeld write: “Attempts to read the great story about the secrets of nature are as old as human thinking itself. However, only a few more than three centuries ago, scientists began to understand the language of this story. From that time, that is, from the time of Galileo and Newton, reading progressed rapidly. And further: “The most fundamental problem, which remained unresolved for a thousand years due to complexity, is the problem of movement” ( Cit. but: Einstein A., Pnfeld L. The evolution of physics. M., 1965, p. eight.).

First guiding idea modern science, modern natural science belongs to Galileo and concerns the problem of motion.

Before Galileo, the generally accepted point of view in science was that the speed of a body's movement is greater, the greater the force pushing it, and if the action of this force stops, the body will stop. This position was clearly formulated by Aristotle, and at first glance it corresponds to experience.

Galileo showed that this view is erroneous. Consider the example of a wheelbarrow being pushed by a person along a horizontal path. If the person stops pushing the wheelbarrow, it will roll for some distance and stop. It would seem that Aristotle is right. Let's not, however, rush to conclusions. Well, what if we make the path along which the wheelbarrow rolls more even and reduce the friction between the axles and bushings of the wheels of the wheelbarrow, for example, due to better lubrication. Obviously, free movement wheelbarrow after the removal of the pushing force will last longer, the wheelbarrow will roll a greater distance.

Let us suppose that we have succeeded in making the path perfectly even and, of course, absolutely horizontal, and we have completely abolished friction in the wheels of the wheelbarrow, and even eliminated the friction between the surrounding air and the walls of the wheelbarrow. In fact, it is impossible to do all this, but one can assume. What would happen then? Let's answer this question with the words of Galileo: “... the speed, once reported to a moving body, will be strictly preserved, since the external causes of acceleration or deceleration are eliminated, a condition that is found only on a horizontal plane, because in the case of movement along inclined plane down there is already a cause of acceleration, while when moving up an inclined plane there is a deceleration; it follows from this that the movement on the horizontal plane is eternal, for if the speed is constant, the movement cannot be reduced or weakened, much less destroyed" ( Cit. Quoted from: Einstein L., Infeld L. Ibid., p. 12.)

Therefore, instead of the Aristotelian point of view: the body moves only when there is an external influence on it- Galileo introduced a new, completely different principle: if no external influence is made on the body, then it is either at rest or moves in a straight line with a constant speed. Here is how A. Einstein and L. Infeld assessed this discovery of Galileo: “The discovery made by Galileo and his application of scientific reasoning methods was one of the most important achievements in the history of human thought, and it marks the real beginning of physics. This discovery teaches us that intuitions based on direct observation cannot always be trusted, as they sometimes lead on the wrong track. Einstein A., Infeld L. Ibid., p. ten.) .

Before continuing the story of what Galileo did in science, we want to acquaint the reader with the biography and some character traits of this brilliant man.

Galileo Galilei was born on February 15, 1564 (the same year as W. Shakespeare) in Pisa. His father, Vincenzo, was a musician. The family was aristocratic, but not rich. In 1574 the family moved from Pisa to Florence. Here Galileo was accepted into the monastic order as a novice, studied in a monastery; the main thing that he learned during this time and that was very useful for him later was the works of Greek and Latin writers. At the insistence of his father, Galileo left the monastery (because of an allegedly serious eye disease), and in 1581, again under the influence of his father, he entered the University of Pisa to study medicine.

However, Galileo showed no great interest in medicine. But he became interested in mathematics, mechanics, physics and astronomy. In this, the father's friend Ostilio Ricci played the main role; on his advice, Galileo read the works of Euclid and Aristotle. But, the closer Galileo became acquainted with the works of Aristotle, primarily mechanics and physics, the more doubts and objections they aroused in him.

Galileo's scientific interests were finally determined. He devoted himself entirely to mathematics, geometry, mechanics and physics, left the University of Pisa and moved to Florence.

The name of Galileo became known among Italian mathematicians after he wrote works in which he gave a method for determining the composition of metal alloys based on the use of hydrostatic balances and gave methods for calculating the center of gravity of bodies of various shapes (this was a continuation of the works of Archimedes).

From 1589, Galileo held the chair of mathematics at the University of Pisa, and from 1592, at the University of Padua. According to biographers, during his stay at the University of Pisa, Galileo was forced to conduct his teaching work by the then generally accepted method, i.e. "according to Aristotle". As for his scientific activity, the situation was different. In Pisa, Galileo wrote the essay “On Motion”, which was preserved in the manuscript, in which, in particular, the issue of the rotation of the Earth around its own axis was considered: without naming the name of Copernicus, which he then undoubtedly knew, Galileo defended his position.

Galileo lived in Padua for about 18 years (1592 - 1610). His teaching work at the University of Padua continued to be based on established and strictly maintained positions at the time. Galileo was forced, for example, to talk in lectures about the Ptolemaic system and to prove the alleged inconsistency of the views of Copernicus. Let us not forget that it was during the Padua period of Galileo's life that Giordano Bruno was executed. During these 18 years, Galileo published, in addition to the Starry Herald, only one scientific article - a description of the so-called proportional compass ( The proportional compass is a simple, ingenious tool that allows you to change the scale of the dimensions being taken. This is achieved by the fact that the axis of rotation of the legs of the compass relative to each other is movable (set in accordance with the desired change in scale and fixed), and the measurement of the size and its application in a changed scale are carried out by the opposite ends of the legs of the compass. If the axis of rotation of the legs of the compass is exactly in the middle position, i.e. the length of all four parts of the legs of the compass is the same, there will be no change in scale. If you move the center of rotation, for example, so that two parts of the legs of the compass are 3 times longer than the other two, then the scale ratio will be 1:3.) (Fig. 1), the use of which facilitates geometric constructions and the solution of many problems.

The years spent by Galileo in Padua turned out to be the most creative for him. It was at this time that Galileo came to his laws of falling and finally became convinced of the correctness of the Copernican theory, that is, he dealt with the very problems that his main works were later devoted to.

Of great importance in the life of Galileo were last years his life in Padua. During this time he built his first optical telescope, which gave 3x magnification, and then a telescope with 32x magnification, made observations of the night sky. The results of these observations (which are discussed below) were of great importance.

The authority of Galileo grew greatly as a result of his astronomical research. He accepted the offer of the Grand Duke of Tuscany, moved to Florence and took the post of court philosopher and court mathematician, as well as professor of mathematics at the University of Pisa (a position that did not oblige him to lecture). This gave Galileo the opportunity to complete his teaching work and devote all his time to scientific research.

In 1615, Galileo was summoned to Rome by the Inquisition to explain his work, which had a clear pro-Copernican and anti-Aristotelian character. 3 1616 index congregation ( Congregations - religious organizations, consisting of both spiritual and secular persons, led by monastic orders; pursued the political line of the Catholic Church. The Index Congregation is one of them, it was in charge of censorship and compiled the "List of Prohibited Books" - in Latin "Index librorum prohibitorum", hence the name.) decided to ban the book of Copernicus "On Appeals celestial spheres”and classifying his teachings as heretical. Although Galileo was not mentioned in this decision, it directly concerned him - he was forced to abandon print and public support for the teachings of Copernicus.

Nevertheless, Galileo continued his scientific research. He wrote two main works: "Dialogue on the two systems of the world - Ptolemaic and Copernican" (briefly "Dialogue") and "Conversations and mathematical proofs concerning two new branches of science related to mechanics and local motion" (briefly "Conversations "). Both works, "Dialogue" and "Conversations", are written in the form of a conversation between three persons - Salviati, Sagredo and Simplicio. All of them are not fictitious persons: Salviati and Sagredo are friends of Galileo, his followers, Simplicio is one of the commentators of Aristotle, a peripatetic, a scholastic.

Galileo himself characterizes these people with the following words: “For many years now I have repeatedly visited the amazing city of Venice, where I had conversations with Signor Giovan Francesco Sagredo, a man of high birth and a very sharp mind. At the same time, there was also Signor Philippe Salviati, who had arrived from Florence, whose least adornment was the purity of the blood and a brilliant condition - a noble mind who did not know a higher pleasure than research and reflection. With these two persons I have often had occasion to discuss the questions mentioned above ( Galileo has in mind mainly the questions of the systems of the world of Ptolemy and Copernicus.) in the presence of a certain peripatetic philosopher, who, as it seems, was not so hindered in the knowledge of the truth as the glory he acquired in the interpretation of Aristotle ”( Galileo Galilei. Fav. tr. M.: Nauka, vol. 1, p. 103.) .

The contents of these two remarkable books of Galileo are discussed below. One of them, "Dialogue", was even published in 1632 on Italian in Florence. However, the publication of the "Dialogue" was the beginning of a difficult test for Galileo. Despite his age and the support of influential friends, he had to go to Rome and appear before the court of the Inquisition. After lengthy interrogations, Galileo was forced to renounce the teachings of Copernicus, and on June 22, 1633, to bring public repentance. A ban was imposed on the Dialogue, and Galileo himself, almost until his death on January 8, 1642 (in 1637 he became blind), was forced to lead a secluded life in a villa in Lrchetri, not far from Florence.

A Latin translation of the "Dialogue" was published in a number of countries (mainly Protestant), and in 1638 "Conversations" were published in Holland. Galileo's books were received with great interest.

Speaking about the personality of Galileo, about his human features, it is necessary to note intolerance towards scholasticism and thoughtless worship of scientific authorities. Let us show this by the example of three passages from Galileo's Dialogue. Through the mouth of the Sagredo, Galilei says: “Once I was in the house of a very respected doctor in Venice, where they sometimes gathered - some to learn, and others out of curiosity - to look at the dissection of a corpse, carried out by the hand of this not only scientist, but skillful and experienced anatomist. It was on that very day that he happened to be investigating the origin and origin of the nerves, on which question there is a certain disagreement among the Galenic physicians ( Galei is a Roman physician and naturalist.) and peripatetic physicians. The anatomist showed how the nerves come out of the brain, pass in the form of a powerful trunk through the back of the head, then stretch along the spine, branch out throughout the body and reach the heart in the form of only one very thin thread. Then he turned to a certain nobleman, whom he knew as a Peripatetic philosopher, and in whose presence he revealed and showed all this with exceptional care, and asked him if he was now satisfied and convinced that the nerves come from the brain, and not from the heart. And this philosopher, thinking for a while, answered: “You showed me all this so clearly and tangibly that if Aristotle’s text did not say the opposite, and it directly says that nerves originate in the heart, then it would be necessary to recognize this as true. !"" ( Galileo Galilei. Fav. tr., v. 1, p. 206.).

To people who blindly believe in the authority of Aristotle, Galileo also speaks in the words of Salviati: “Many times I was surprised how it could happen that these people, striving to support literally every word of Aristotle, do not notice the harm that they cause to the reputation of Aristotle, and how they, instead of increasing his authority, undermine his credibility. For when I see them strenuously trying to support those propositions which, in my opinion, are quite obvious, how they are trying to convince me that this is how a true philosopher should act and that Aristotle himself would have done just that, then my confidence is greatly reduced that he reasoned correctly in other areas, which are more remote for me" ( Galileo Galilei. Fav. tr., v. 1, p. 209.).

And finally, we will cite one more excerpt from Galileo's "Dialogue" concerning the attitude towards scientific authorities. The discussion is between the peripatetic philosopher Simplicio, who has already exhausted his evidence in defense of the position of Aristotle, and the supporter of Galileo Salviati:

« Simplicio. But if we leave Aristotle, then who will serve as our guide in philosophy? Name some author.

Salviati. A guide is needed in unknown and wild countries, but in an open and smooth place only a blind person needs a guide. A blind man will do well if he stays at home. The one who has eyes in his forehead and a mind should use them as guides. However, I do not say that one should not listen to Aristotle, on the contrary, I praise those who peer at him and study him diligently. I blame only the tendency to surrender to the power of Aristotle so much as to blindly subscribe to his every word and, not hoping to find other grounds, to consider his words an inviolable law. This is an abuse, and it entails the great evil that others no longer try to understand the power of Aristotle's proofs. Galileo Galilei. Fav. tr., v. 1, p. 210.).

Galileo believed, and this was the most important source of his success, that the starting point for the knowledge of nature is observation, experience. On this occasion, Einstein and Infeld write ( Einstein L., Infeld L. Evolution of physics, p. 48.): “The laws of nature, establishing the connection of successive events, were unknown to the Greeks. The science linking theory and experiment actually began with the work of Galileo.”

The great merit of Galileo in astronomy, in substantiating and approving heliocentric system Copernicus. With the help of the telescopes he built, which are mentioned above, Galileo discovered that the Sun rotates around its axis, and there are spots on its surface; the largest planet in the solar system, Jupiter, has moon-like satellites (Galileo discovered 4 of the largest satellites out of 13 currently known); the surface of the moon is mountainous, and the moon itself has libration, i.e., visible periodic oscillations of a pendulum nature around the center; phases of Venus, which, however, people with sharp eyesight can see with the naked eye; an unusual view of the planet Saturn, created (now known) by its rings, representing the totality solids. Galileo discovered a huge number of stars invisible to the naked eye and with the help of insufficiently powerful instruments (spotting scopes); saw what seemed to be a nebula Milky Way is made up of individual stars.

These observations, which are of great importance and aroused unprecedented interest, were described by Galileo in his essay The Starry Herald. It is interesting to note that Kepler, one of the greatest mathematicians and astronomers of the 16th-17th centuries, got acquainted with the Starry Herald that arrived in Prague. Kepler cordoned off Galileo's observations very highly; this can be seen from his essay "Discourse on the Starry Herald".

The proof of the validity of the heliocentric system of Copernicus was very important at the time of Galileo. great importance. The fact is that the concept of Copernicus was attacked. On the one hand, these were ecclesiastical, mainly Catholic, circles, the dogmas of which did not coexist in any way with the views of Copernicus. On the other hand, these were doubts about the fidelity of the heliocentric system of the world, expressed by a number of scientists. Doubts boiled down mainly to the fact that in the case of the rotation of the Earth around its axis or movement in orbit around the Sun on the surface of the Earth, according to these scientists, a very strong (hurricane) wind should have arisen, directed in the opposite direction, objects thrown up , would have to stay behind and fall to the surface of the Earth far from the place where they were thrown. In fact, none of this happens.

Galileo in the Dialogue formulates these doubts and objections in the words of Salviati as follows:

« Salviati. As the strongest argument, everyone cites the experience with heavy bodies: falling from top to bottom, the bodies go in a straight line perpendicular to the surface of the Earth; this is considered an irrefutable argument in favor of the immobility of the Earth. After all, if it had a daily circulation, then the tower, from the top of which a stone was allowed to fall, would be transported by the circulation of the Earth, while the stone falls, for many hundreds of cubits ( The cubit is a pre-existing measure of length, approximately the length of the ulna (455 - 475 mm).) to the east, and at such a distance from the foot of the tower the stone would have hit the Earth" ( Galileo Galilei. Fav. tr., v. 1, p. 224.).

And further: “Ptolemy and his followers give another experience, similar to the experiment with abandoned bodies; they point to things that, being separated from the earth, are held high in the air, such as clouds and flying birds; and since they cannot be said to be carried along by the earth, since they are not in contact with it, it seems impossible that they could maintain its speed, and it would seem to us that they are all moving very rapidly towards the west; if we, carried by the Earth, were to pass our parallel in twenty-four hours - and this is at least sixteen thousand miles - how could the birds keep up with such a movement? Meanwhile, in fact, we see that they fly in any direction, without the slightest tangible difference, either to the east or to the west ”( Galileo Galilei. Fav. etc., vol. 1, p. 230) .

Indeed, what an interesting science of mechanics, what a complex subject of motion and what difficult tasks had to be solved 400 years ago by the most talented and educated people! Let us note, however, for the sake of truth, that modern scientists stand face to face with no less difficult problems(this will be discussed below).

At first glance, it may seem that the doubts and objections expressed regarding the heliocentric system of the world are solid, that Ptolemy and his followers are right. But this, of course, is not the case. Let's give the floor to Galileo (Salviati):

« Salviati. Retire with one of your friends in a spacious room under the deck of some ship, stock up on flies, butterflies and other similar small flying insects; let you have there also a large vessel with water and small fish swimming in it; hang, further, a pail at the top, from which water will fall drop by drop into another vessel with a narrow neck, substituted below. While the ship is stationary, observe diligently how small flying animals move with the same speed in all directions of the room; fish, as you will see, will swim indifferently in all directions; all the falling drops will fall into the set vessel, and you, throwing an object, will not have to throw it with more force in one direction than in the other, if the distances are the same; and if you jump with both feet at once, you will jump the same distance in either direction. Observe all this diligently, although there is no doubt in your mind that as long as the ship is stationary, this is how it should be. Now force the ship to move at any speed, and then (if only the movement is uniform and without rolling in one direction or another) in all the above phenomena you will not find the slightest change and you will not be able to determine from any of them whether the ship is moving or standing still. still. By jumping, you will move the same distance across the floor as before, and you will not make big jumps towards the stern than towards the bow, on the grounds that the ship is moving quickly, although during the time you are in the air, the floor under you will move in the direction opposite to your jump, and, throwing something to a comrade, you will not have to throw it with more force when he is at the bow and you are at the stern than when your relative position is reversed ; the drops, as before, will fall into the lower vessel, and none will fall closer to the stern, although while the drop is in the air, the ship will travel many spans ( A span is an ancient measure of length, approximately equal to the distance between the ends of the divorced thumb and forefinger of an adult's hand.) ; fish in the water will swim with less effort towards the front than towards the back of the vessel; with the same agility they will rush to the food placed in any part of the vessel; finally, butterflies and flies will still fly in all directions, and it will never happen that they gather at the wall facing the stern, as if tired, following the rapid movement of the ship, from which they were completely isolated, holding on for a long time. time in the air; and if a little smoke is formed from a drop of burning incense, then it will be seen how it rises and keeps like a cloud, moving indifferently, no more in one direction than in the other. And the reason for the consistency of all these phenomena is that the movement of the ship is common to all objects on it, as well as to air; that is why I said that you must be below deck, because if you were on it, that is, in the open air, not following the course of the ship, you should see more or less noticeable differences in some of the aforementioned phenomena: the smoke would undoubtedly begin to lag behind with the air, flies and butterflies, due to air resistance, would likewise not be able to follow the movement of the ship in those cases when they would separate from it at a fairly noticeable distance; if they keep close, then, since the ship itself is an irregular structure and takes with it the parts of the air closest to it, they will not special effort will follow the ship; in the same way we see, when riding postal, how annoying flies and horseflies follow the horses, flying up now to one part of their body, then to another; in falling drops, the difference will be insignificant, and in jumps or thrown bodies it will be completely imperceptible ”( Galileo Galilei. Fav. tr., v. 1, p. 286 - 287.).

As we remember, Ptolemy argued that birds and clouds should not keep up with the movement of the Earth. Now, as follows from this experiment of Galileo, which establishes the principle of relativity of motion, both birds, clouds, and the Earth itself participate in the same motion - the motion of the Earth (which in this case is similar to the motion of a ship) - and therefore move relative to each other will not.

It is impossible to give a clearer and more convincing answer to the objections of the Ptolemies than Galileo's, based on simple experience. talking modern language and using modern scientific terminology, we would say that Galileo established the independence of the course of mechanical phenomena from selected inertial reference systems. Although these things will be discussed below, we will still make some clarifications. The reference system is understood as a system of bodies (maybe even one body), relative to which (which) the movement is considered. The system is considered inertial in the case when the position established by Galileo is fulfilled in it: if no impact is made on the body (the body is not affected by any force, we would say now), it is either at rest or moves rectilinearly on a horizontal plane at a constant speed. In other words, the system is considered inertial when the body is free from interaction with other bodies. In fact, such systems do not exist (some forces always act on the body), but you can imagine them and approach them.

Rectilinear and uniform motion of a body on a horizontal plane without any influence on it external forces is called inertial motion ( Inertia from Latin word inertia - rest, inactivity; the inertia or inertia of a body is understood as the property of a body to maintain its state in the event that external forces do not act on it.) . Hence the name of inertial systems. Galileo established: although the position of a moving body (its coordinates), its speed, the nature of the trajectory ( Trajectory - a line that the center of mass of a moving body passes.) movements depend on the choice of an inertial frame of reference (for example, a stationary ship, i.e., the Earth, or a ship moving in relation to the Earth in a straight line and uniformly), the laws of mechanics, the flow of mechanical phenomena do not depend on which particular system of reference the studied mechanical traffic.

In other words, mechanical phenomena, as already mentioned, proceed in the same way in all inertial frames of reference. This position is called Galileo's principle of relativity. It should not be confused with Einstein's theory of relativity, which will be discussed below. Speaking modern scientific language, we can formulate Galileo's principle of relativity as follows: the laws of mechanics are invariant (Invariance - immutability, independence of any value (values, equations) in relation to some transformations; for example, the independence of the equations of mechanics with respect to transformations of coordinates and time in the transition from one inertial frame of reference to another.) regarding the choice of inertial frame of reference.

Galileo in "Dialogue" showed that the statements of Ptolemy's supporters about the alleged impossibility of the Earth's daily rotation around its axis and its movement in orbit around the Sun are unfounded. This was the most important argument in favor of the heliocentric system of the world of Copernicus.

It is interesting to note one more argument of Galileo in favor of the heliocentric system of the world, Astronomical observations of displacement celestial bodies, visible from the Earth, can in principle be explained both from the standpoint of the heliocentric system of the world and the daily rotation of the Earth around its axis, and from the standpoint of the geocentric system of the world, according to which all celestial bodies revolve around the motionless Earth. In the first case, taking the heliocentric system of the world as a basis, the explanation astronomical observations behind the movement of celestial bodies is relatively simple - all the planets solar system(including the Earth) revolve around the Sun in close to circular (as most supporters of the heliocentric system thought in Galileo's time) orbits. In the second case, i.e., having adopted the geocentric system of the world, the explanation of the motion of celestial bodies observed from the Earth turns out to be very artificial: the trajectories of celestial bodies would turn out to be incredibly complex, and the speeds would have to change from fantastically large to very small.

Here is what Galileo writes about the daily rotation of the Earth around its axis.

« Salviati. If we take into account the vast volume of the stellar sphere compared with the insignificance of the terrestrial globe, which is contained in it many and many millions of times, and then think about the speed of movement, which in a day and night must complete a complete revolution, then I cannot convince myself that there may be someone who considers it more correct and probable that such a revolution is made by the stellar sphere, while the globe remains motionless.

Sagredo. If absolutely all the phenomena of nature that can be dependent on such movements give rise to the same consequences in one case as in the other, without any difference, then I would immediately recognize the one who considers it more correct to make the whole Universe move, only to keep the Earth immovable, even more unreasonable than the man who, having climbed to the top of the dome of your villa to look at the city and its environs, demanded that the whole area revolve around him and he did not have to work turning his head ”( Galileo Galilei. Fav. tr., v. 1, p. 213.).

It has already been said above about the discoveries of Galileo in the field of mechanics, thanks to which he (together with Newton) is rightly considered the founder of modern science. In addition to what has already been mentioned, it is necessary to name some other important achievements of Galileo.

Of great importance are studies of the free fall of bodies and their motion along an inclined plane. Galileo established that the speed of free fall of bodies does not depend on their mass, as Aristotle thought, and the path traveled by falling bodies is proportional to the square of the fall time. It was a great discovery. It made it possible in the future to establish the numerical equality of the gravitational and inertial masses of bodies, which will be discussed later.

Galileo created the theory of parabolic motion and determined that the trajectory of a thrown body, that is, a body moving under the action of an initial push and gravity, is a parabola.

Much was done by Galileo in the field of the theory of strength and strength of materials. Very interesting are the considerations expressed by Galileo about mechanical similarity and that in the case when the weight of the body is significant, there is no similarity in relation to the strength of the bodies.

Here is what Galileo writes on this issue: “If we take a wooden log of a certain thickness, embedded, say, in a wall at a right angle so that it is parallel to the horizon, and suppose that its length reaches the extreme limit at which it can still hold , i.e., that with an increase in its length by another hair, it breaks from its own weight, then this log will be the only one of its kind in the world. If its length, let us suppose, exceeds its thickness by a hundred times, then we will not be able to find a single log from the same tree, which, with a length exceeding its thickness by a hundred times, would be able to withstand exactly the same amount as taken for example: all logs bigger size they will break, but the smaller ones will be able, in addition to their own gravity, to withstand some more load. What I have said about the ability to support one's own weight applies to other structures ( Cit. Cited from: Sedov L.I. Galilei and the foundations of mechanics. Moscow: Spider, 1961, p. 36-37).

In this regard, Galileo expressed very interesting considerations about the advantages in terms of "strength" and mobility of small animals compared to large ones and about the existence of a limit on their size. The exact solution of these questions was found only after about three hundred years.

Galileo was born in the city of Pisa in the family of a musician. Galileo's father wanted to make him a doctor, for which he sent him to the University of Pisa in 1581. However, Galileo's interests lay in another area, and he, having abandoned his studies, moved to Florence. Here Galileo took up the study of mathematics and mechanics and wrote several works on mechanics. In 1589, Galileo received a chair at the University of Pisa, and in 1592 at the University of Padua, where he worked until 1610. During all this time, Galileo was engaged in scientific research in the field of physical and mathematical sciences, as well as the technical problems of his time.

Galileo Galilei

Galileo quite early became an opponent of the mechanics and astronomy of Aristotle. Viviani, a student of Galileo, testifies that Galileo, while still in Pisa, refuted the teaching of Aristotle that heavy bodies fall faster than light ones. According to his testimony, Galileo allegedly even carried out experiments, throwing various bodies from an inclined tower in Pisa to experimentally confirm the fallacy of Aristotle's opinion 1 . Galileo's letter to Kepler, written in 1597, testifies to Aristotle's early critical attitude to astronomy. In this letter, he writes:

“I consider myself lucky to have found such a great ally in the search for truth. Indeed, it is painful to see that there are so few people who strive for the truth and are ready to abandon the perverse way of philosophizing. But this is not the place to complain about the sad state of our time, I just want to wish you good luck in your wonderful research. I do this all the more willingly because for many years I have been an adherent of the teachings of Copernicus. It explained to me the cause of many phenomena that are completely incomprehensible from the point of view of generally accepted views. To refute the latter, I have collected many arguments, but I do not dare to publish them. Of course, I would decide on this if there were more people like you. But since this is not the case, I keep myself cautious. 2 .

The arguments in defense of the doctrine of Copernicus, which Galileo speaks of in his letter, were probably his new discoveries in the field of mechanics (later he will cite them in defense of this doctrine).

After 13 years, Galileo had new arguments confirming the teachings of Copernicus. They were already based on the astronomical discoveries of Galileo. In 1608 or 1609

Galileo learned about the invention of the Dutch masters of the telescope and in 1609 he designed such a telescope himself. Galileo's telescope tube had a convex objective lens and a concave eyepiece lens.

It gave more than a thirty-fold increase (Fig. 11). Observing the sky with this telescope, Galileo made a number of important observations. He discovered that the surface of the Moon - a celestial body - does not fundamentally differ in appearance from earth's surface. Like the Earth, the Moon has mountain peaks and depressions. Galileo further established that the planets, in contrast to fixed stars are similar to the Moon and are visible through the tube in the form of round luminous disks. Venus, just like the Moon, changes its appearance over time from a round disk to a narrow crescent. Galileo also discovered the moons of Jupiter. He noticed that four small stars (satellites) revolve around Jupiter, just as the Moon revolves around the Earth. Galileo also established that the number of fixed stars is much greater than what can be seen with the naked eye.

Relying on his discoveries, Galileo cautiously but persistently embarked on the path of spreading and substantiating the teachings of Copernicus as a theory of the actual structure of the Universe. He immediately met with resistance from theologians, who either denied the discoveries of Galileo, or referred to the authority scripture . However, Galileo skillfully fought, tried not to touch on purely theological issues. In 1516, the disturbed church officially condemned the teachings of Copernicus, his book was included in the list of banned ones, and Galileo was warned that from now on he did not dare to adhere to this teaching and propagate it. Galileo was forced to be silent for a while. However, the factual material he collected from the field of mechanics and astronomy, which is a confirmation of the Copernican system, forced Galileo, despite the prohibition of the church, to look for ways to defend Copernicus at all costs. Galileo knew that at the same time he could count on his authority as a scientist, which by that time was great, as well as on the favor of some circles of the higher clergy. However, it was impossible to speak directly in defense of the "Copernican heresy" without being immediately seized by the Inquisition. After evaluating the whole situation, Galileo decided to write a book that would essentially substantiate the Copernican system, but in such a way that the author of the book could not formally be accused of defending it. This book was published in 1632 under the title "Dialogue Concerning the Two Chief Systems of the World: Ptolemaic and Copernican." It was written in the form of a conversation or discussion between an adherent of the teachings of Copernicus - Senor Salviati and a defender of the Ptolemaic system - Simplicio. A third person also participated in the dispute - Sagredo, who essentially stood on the side of Salviati. To protect himself from being accused of heresy, Galileo in the preface indicated that the doctrine of the movement of the Earth was forbidden by the church and that in the book this doctrine was only discussed, not approved. However, neither the preface nor the form of the essay could deceive anyone. The defender of the Ptolemaic system - Simplicio looked very pale and was constantly beaten by the arguments and jokes of his opponents. The reader clearly imagined which side the author was on and what goal he was actually pursuing. Shortly after the publication of this book, a lawsuit was initiated against Galileo. At the beginning of 1633, Galileo was summoned to Rome, where he was charged with having disobeyed a decree prohibiting adherence and promotion of the teachings of Copernicus. Galileo rejected this accusation, pointing out that he nowhere asserts the truth of this doctrine, but speaks of it only presumably as a hypothesis. However, he had to admit that, having been carried away, he set out too convincingly the conditional arguments for the position that he wanted to refute. The Inquisition was satisfied with this explanation, but demanded a public renunciation of the teachings of Copernicus, which Galileo had to do. After the process, Galileo, being under the supervision of the Inquisition, continued to study scientific activity and wrote a new one treatise"Conversations and mathematical proofs about two new sciences", devoted to questions of mechanics, acoustics and some others. The manuscript of this work was printed in Holland in 1638. In 1642, Galileo died. At his death, two representatives of the Inquisition were present.

From the outside, the process of Galileo looked like a victory for the church, but in reality it was her defeat. As a result of the activities of Galileo and his struggle, the heliocentric doctrine became widely known and captured the minds of the cultured people of Europe. True, the book of Galileo, like the book of Copernicus, for a long time (until 1822) was on the list of banned books. However, already in the second half of the XVII century. this prohibition was ignored.

In the Dialogue, two types of arguments are given in defense of the Copernican theory. Firstly, Galileo relies on his astronomical discoveries, which confirmed that the Earth is the same body as other planets, and it is impossible to talk about its exclusivity. Secondly, arguments based on his discoveries in the field of mechanics. They refuted Aristotle's theory of motion and removed the objections to the motion of the Earth, which were expressed by Ptolemy. Already Copernicus rejects these objections, arguing that the movement of bodies together with the Earth must be considered natural movement. Galileo goes even further, arguing that any movement on a horizontal surface on the Earth, if friction forces are excluded, is, using the terminology of Aristotle, natural, that is, movement that does not require the action of a force. It goes on forever, maintaining its speed. At the same time, Galileo does not simply assert this position, but refers to experience. Dialogue participants discuss this experience. We consider the motion of a body along a perfectly smooth (that is, friction-free) inclined plane. If a body moves up an inclined plane, then its speed decreases, if it moves down, it increases. The question is, how does a body move along a horizontal plane? The answer suggests itself: the body moves at a constant speed. Galileo would later formulate this conclusion in a more general form:

“When a body moves along a horizontal plane without encountering any resistance to movement, then, as we know from all that has been stated above, its movement is uniform and would continue constantly if the plane extended in space without end” 3 .

In this form, Galileo formulates the law of inertia. This is not yet the general formulation of the law of inertia, which was given later. But here, of course, done fundamentally new step. In this formulation, uniform motion is understood as a rectilinear motion with a constant speed, and this law is already fundamentally different from the formulations of the "impetus" theories. On the other hand, it should be noted that although Galileo formulated the law of inertia for horizontal motion, he understood it more broadly. This can be judged from the way Galileo discusses the question of why objects do not fly apart from the rotating Earth, as is the case for a rapidly rotating wheel. Galileo definitely says that a body thrown off the wheel rim then tends to move in a straight line tangentially with a constant speed, regardless of whether it flies off in a horizontal or some other direction, and only gravity prevents this.

At the same time, the question arises why the bodies located on the Earth, during its rotation, do not scatter from its surface? Galileo does not resolve this issue, he believed, speaking in modern terms, that centrifugal acceleration is negligible compared to the acceleration of gravity.

Thus, we see that, on the one hand, Galileo understood the law of inertia more widely than he formulated it, and on the other hand, he probably understood that the motion of the Earth cannot be considered strictly inertial.

Simultaneously with the law of inertia, Galileo uses another basic provision of classical mechanics, the so-called law of independence of the action of forces, again as applied to the motion of bodies in the Earth's gravity field. The body tends, according to Galileo, to maintain its horizontal velocity not only when it is supported by a horizontal plane, but also when it falls freely, i.e. if the body falls, then the horizontal component of the velocity is not affected by the force of gravity acting vertically. On the other hand, the change in the vertical component of the velocity under the action of gravity does not depend on whether the body is in horizontal motion or not.

Based established laws Galileo explains why we do not notice the movement of the Earth while on it. So, for example, a freely falling stone falls vertically, since at the moment of throwing it has the same speed as the surface of the Earth at the point of throwing. This speed he maintains when falling. Galileo cites for confirmation the experience of throwing a stone from the mast of a moving ship. He analyzes other experiments with throwing bodies on the Earth and shows that with their help it is impossible to refute the hypothesis of the Earth's motion. Summarizing his explanations, Galileo formulates the classical principle of relativity. He emphasizes that the movement of inertia can be noticed only without participating in this movement, since it does not affect things that are in such movement. Explaining this situation, Galileo gives the following example:

“Seclude yourself with one of your friends,” he writes, “in a spacious room under the deck of a ship, stock up on flies, butterflies and other similar small flying insects; let you have there also a large vessel with water and small fish swimming in it; hang further, above, a bucket, from which water will fall drop by drop into another vessel with a narrow neck, substituted below. While the ship is stationary, observe diligently how small flying animals move with the same speed in all directions of the room; fish, as you will see, will swim indifferently in all directions; all falling drops will fall into the substituted vessel, and you, throwing an object, will not have to throw it with more force in one direction than in the other, if the distances are the same, and if you jump with both feet at once, then jump the same distance in any direction. Observe all this diligently, although there is no doubt in your mind that as long as the ship is stationary, this is how it should be. Now make the ship move at any speed, and then (if only the movement is uniform and without rolling in one direction or another) in all the phenomena mentioned you will not find the slightest change and you will not be able to determine from any of them whether the ship is moving or standing still. still" 4 .

Galileo's discoveries in the field of mechanics were directly related to his substantiation of the teachings of Copernicus, but, of course, they also had independent significance (that is, for the development of mechanics in general). Strictly speaking, the development of mechanics as the doctrine of mechanical motion begins with the works of Galileo. Other studies on Galileo's mechanics will be discussed below.

Galileo, a prominent representative of the scientific revolution, deserves credit not only for the struggle to substantiate the heliocentric system of the world, and not only as the founder of mechanics. He outlined a new experimental method for the study of nature, which became the main method of experimental natural science. The source of knowledge, according to Galileo, is experience and only experience. He condemns scholasticism, divorced from reality and based solely on authorities. The merit of Galileo lies not only in the fact that he considers experience to be the source of knowledge. Experience as a source of knowledge was proclaimed even before Galileo, and science was actually built on experience before him. Aristotle, as Galileo rightly emphasizes, recognized that experience is the source of knowledge. For developing science, it was important how knowledge should be built from experience, i.e., to find the right scientific method experience: Galileo did just that. Before Galileo, experience was only, so to speak, the starting point of knowledge. Research method in in general terms consisted mainly of two links: direct observations (very often random) and the construction of a general theory based on these observations. The third link, which consisted in verifying the conclusions of the constructed theory, was either completely absent, or was in its infancy, was not developed in any way. Therefore, science in antiquity had a contemplative character. It remained the same within the framework of medieval scholasticism, and this determined, on the one hand, its crudely empirical, and, on the other hand, speculative character. Such was Aristotle's teaching about the sky and its dynamics. It was based on the simplest direct] observations, not analyzed in any detail. The daily practice of antiquity and the Middle Ages showed, for example, that in order to pull the same cart at a greater speed, more effort must be applied, or that often heavier bodies fall faster than light ones. These and similar observations seemed to Aristotle enough to construct a system of all dynamics, which had a fantastic character. Neither Aristotle nor his students thought of trying not only to reconcile the theory of motion with the observed facts, but to derive consequences from this theory and, on specially designed experiments, to verify its correctness or incorrectness.

Galileo acts differently: in investigating motion, he breaks away from the immediate results of individual experiments. The laws and regulations on which it relies are scientific abstractions and do not follow from single observable facts. Thus, the law of inertia could not be directly tested by Galileo. on experience. It was impossible to directly observe the movement of the body without friction. And the law that a body falls with uniform acceleration could not, strictly speaking, be verified at that time by experience either. However, scientific abstraction penetrates more deeply into the essence of phenomena than a simple statement of facts, which is an expression of the general that is hidden in these facts, goes beyond the phenomena in the study of which it first arises. Scientific abstraction is expressed in the form of a hypothesis. A hypothesis allows you to foresee new facts and phenomena based on the conclusions from it. Therefore, the scientific hypothesis becomes the guiding idea in further scientific research. At the same time, testing the conclusions from its consequences and predictions turns the hypothesis into a scientific law.

The experimental method of Galileo is especially clearly seen in the example of his study of the laws of falling bodies. Galileo starts with the assumption that bodies fall with constant acceleration. This is still a hypothesis; although it is based on direct observations and some considerations, it is still a guess. Galileo draws consequences from these assumptions. He proves that if a body falls with uniform acceleration, that is, if v~t, then the distance traveled is proportional to t 2 . The technique of the experiment did not allow direct verification of this conclusion (at that time there were not even ordinary pendulum clocks). Therefore, Galileo decides to test this law for the case of bodies moving along an inclined plane. He takes a long board with a groove lined with parchment. Under one end of the board, it strengthens the stand so that the board forms an inclined plane. By making the ball slide down the chute, it measures the time it takes for the ball to travel - a certain distance along the chute. Galileo measured the time of the ball's movement by the amount of water flowing out of the vessel through a small hole. Having made measurements, Galileo found that a body moves uniformly accelerated along an inclined plane, and this is true for inclined planes with different angles of inclination. Hence, Galileo concludes that this position is also true for free fall, since the vertical downward movement of the body can be considered as the limiting case of its movement along an inclined plane, when the angle of inclination tends to 90 °. Thus, the experiment confirms the main hypothesis, and now we can assume that the law of fall has been established. This study quite clearly contains a new link: substantiation of the stated hypothesis, conclusion from it with the help of a specially designed experimental study.

So the method scientific research Galileo can be characterized as follows: from observations and experiments, an assumption is established - a hypothesis, which, although it is a generalization of experiments, includes something new that is not directly contained in each specific experiment. A hypothesis makes it possible to deduce certain consequences in a strictly mathematical and logical way, to predict some new facts that can be verified experimentally. Checking the consequences and confirms the hypothesis - turns it into a physical law. In basic terms, this method becomes the main method, following which natural science develops.

In his writings, Galileo also outlined the main features of a new idea of ​​the nature of matter, movement and laws of the material world - mechanical materialism. Galileo was an opponent of Aristotle's doctrine of matter and form, and in his writings he revived the ideas of the ancient atomists. Material things, according to Galileo, consist of countless tiny particles, between which there are voids. Changes in nature occur as a result of the movement and redistribution of these particles, which are not destroyed and are not created again. Reviving the atomistic hypothesis, Galileo outlines the main features of the quantitative mechanical understanding of nature. He denies the innumerable hidden qualities introduced by the scholastics (aspirations, dislikes, etc.) and laughs at their methodology. Matter, according to Galileo, has only simple geometric and mechanical properties.

“Never,” writes Galileo, “I will not demand from external bodies anything other than size, figures, quantity, and more or less rapid movements in order to explain the emergence of sensations of taste, smell and sound; and I think that if we eliminated ears, tongues, noses, then only figures, numbers and movements would remain, but not smells, tastes and sounds, which, in our opinion, outside a living being are nothing but empty names. 5 .

Thus, in the person of Galileo, science launched an offensive on the entire front against the worldview of medieval theologians, priests, monks and scholastics, as a result of which he was dealt a crushing blow. At the same time, Galileo laid the foundations for a new experimental method for studying nature, was one of the founders of natural science and a new worldview - mechanical materialism, which became the main worldview of physicists and natural scientists in general. Finally, Galileo laid the foundations of dynamics; with his research, in fact, this area of ​​physical sciences begins to develop.

1 On the question of the validity of this testimony, Viviani is currently expressing different opinions. Some historians deny the authenticity of these experiments, while others believe that Viviani's testimony should be trusted.
2 Daneman F. History of natural sciences. T. II. M.-L., ONTI, 1933, p. 29.
3 Galileo Galileo. Selected works. T. II. M., "Nauka", 1964, p. 304.
4 Galileo Galileo, Selected Works. T. I. M., "Nauka", 1964, p. 286.
5 Anthology of world philosophy. T. II. M., "Thought", 1970, p. 224-225.

Galileo Galilei and his role in the development of classical science

The work on the justification of heliocentrism was started by Galileo Galilei, whose works predetermined the whole face of classical, and in many respects modern science. It was he who laid the foundations for a new type of worldview, as well as a new science - mathematical experimental natural science. In order to penetrate deeper into mathematical laws and comprehend the true nature of nature, Galileo improved and invented many technical devices and tools - a lens, a telescope, a microscope, a magnet, an air thermometer, a barometer, etc. Their use gave natural science a new dimension unknown to the Greeks. Former thoughts about the universe have given way pilot study in order to comprehend the universal mathematical laws operating in it.

G. Galileo (1564-1642)

It is very important that Galileo combined his systematic orientation to experience with the desire for its mathematical understanding. And he put it so highly that he considered it possible to completely replace traditional logic as a useless tool of thinking with mathematics, which alone is capable of teaching a person the art of proof.

The mathematical analytical method of Galileo led him to a mechanistic interpretation of being, allowed him to formulate the concept of physical law in its modern sense. We can assume that, starting with the work of this scientist, science has completely broken with a purely qualitative interpretation of nature. Galileo's discoveries in the field of mechanics and astronomy were of particular importance for the establishment of a new type of science. It was they who laid a solid foundation in the justification of heliocentrism.

Heliocentrism is a picture of the world, representing the center of the Universe, the Sun, around which all the planets, including the Earth, revolve.

One of the most serious problems hindering the establishment of a new worldview was the long-standing belief, which was formed in antiquity and was maintained throughout the Middle Ages, that there is a fundamental difference between terrestrial and celestial phenomena and bodies. Since the time of Aristotle, it has been believed that the heavens are the location of ideal bodies, consisting of ether and rotating in ideal circular orbits around the Earth. Earthly bodies arise and function according to completely different laws. Therefore, before creating comprehensive theories and discovering the laws of nature, scientists of the New Age had to refute the division into earthly and heavenly. The first step in this direction was taken by Galileo.

After in 1608 . the telescope was invented, Galileo improved it and turned it into a telescope with a 30x magnification. With his help, he made a number of outstanding astronomical discoveries. Among them are mountains on the Moon, spots on the Sun, phases of Venus, four largest satellites of Jupiter. He was the first to see that the Milky Way is a cluster of a huge number of stars. All these facts proved that celestial bodies are not ethereal creatures, but quite material objects and phenomena. After all, there cannot be mountains on an ideal body, like on the Moon, or spots, like on the Sun.

With the help of his discoveries in mechanics, Galileo destroyed the dogmatic constructions of Aristotelian physics that had dominated for almost two thousand years. Galileo opposed the thinker, whose authority was considered indisputable, and for the first time tested many of his statements empirically, thereby laying the foundations for a new branch of physics - dynamics - the science of the motion of bodies under the action of applied forces. Before that, the only more or less developed branch of physics was statics.

Statics is the science of the balance of bodies under the action of applied forces, founded by Archimedes.

Galileo also studied free fall bodies and, on the basis of his observations, found out that it does not depend at all on the weight or composition of the body. After that, he formulated the concepts of speed, acceleration, showed that the result of the action of a force on a body is not speed, but acceleration.

Galileo also analyzed the throwing movement, on the basis of which he came to the idea of ​​inertia, which has not yet been formulated precisely, but played a huge role in the further development of natural science. Unlike Aristotle, who believed that all bodies tend to reach the place allotted to them by nature, after which the movement stops, Galileo believed that a moving body tends to remain in constant uniform rectilinear motion or at rest, unless some external force stops it. or does not deviate from the direction of its movement. The idea of ​​inertia made it possible to refute one of the objections of the opponents of heliocentrism, who argued that objects located on the surface of the Earth, in the event of its movement, would inevitably be thrown off it, and that any projectile launched upward at a right angle would necessarily land at some distance from the starting point of the throw. The concept of inertia explained that the moving Earth automatically transmitted its movement to all bodies on it.

Another objection of the opponents of heliocentrism was that we do not feel the movement of the Earth. The answer to it was also given by Galileo in the classical principle of relativity he formulated. According to this principle, it is impossible to establish by any mechanical experiments carried out inside the system whether the system is at rest or moves uniformly and rectilinearly. Also, the classical principle of relativity states that there is no difference between rest and uniform rectilinear motion, they are described by the same laws. Equality of movement and rest, i.e. inertial systems - resting or moving relative to each other uniformly and rectilinearly, Galileo proved by reasoning and numerous examples. For example, a traveler in a ship's cabin with with good reason believes that the book lying on his desk is at rest. But a man on the shore sees that the ship is sailing, and he has every reason to assert that the book is moving, and, moreover, at the same speed as the ship. Is this how the book actually moves or is it at rest? This question obviously cannot be answered with a simple "yes" or "no". An argument between a traveler and a man on the shore would be a waste of time if each of them defended only his own point of view and denied the point of view of a partner. They are both right, and in order to agree on positions, they only need to recognize that at the same time the book is at rest relative to the ship and is moving relative to the shore with the ship.

The laws of mechanics, together with his astronomical discoveries, provided that physical basis for the Copernican hypothesis, which its creator himself did not yet have. From a hypothesis, the heliocentric doctrine was now beginning to acquire the status of a theory.

But the question of the relationship between terrestrial and celestial movements, the motion of the Earth itself was not explained. The real movement of the planets also did not correspond much to their description in the heliocentric hypothesis of Copernicus (circular motion), as well as in Ptolemy's geocentrism.

The Great Mistakes of the Great Galileo

Let's move from ancient times to the pre-Newtonian era, where the great Galileo "ruled" over mechanics. The development of dynamics as a science is associated with the name of the great Italian scientist of the Renaissance Galileo Galilei(1564-1642). The greatest merit of Galileo as a mechanical scientist was that he was the first to lay the foundations of scientific dynamics, which dealt a crushing blow to the dynamics of Aristotle. Galileo called dynamics "the science of motion relative to place." His work "Conversations and Mathematical Proofs Concerning Two New Sciences" consists of three parts: the first part is devoted to uniform motion, the second to uniformly accelerated, and the third to the forced motion of thrown bodies.

In ancient mechanics, the term "speed" was not. More or less fast movements were considered, as well as "equal speed" ones, but there was no quantitative characteristic of these movements in the form of speed. Galileo for the first time approached the solution of the problem of uniform and accelerated motion of massive bodies and considered the motion of bodies by inertia.

Galileo is credited with discovering the law of inertia. They do this even in textbooks - school and not only. Galileo expressed this law as follows: “The movement of a body that is not affected by forces (of course, external ones) or their resultant is equal to zero is a uniform movement in a circle.” So, according to Galileo, celestial bodies moved, "left to themselves." In fact, the movement by inertia, as is known, can only be uniform and rectilinear. As for the celestial bodies, they are “knocked down” from this movement by an external force - the force gravity.

Considering Galileo's view of inertia, we are convinced of its illegality: the error in reasoning arose from the fact that Galileo did not know about the law of universal gravitation, discovered later by Newton.

Proving the principle of relativity, Galileo argued that if the ship moves uniformly and without pitching (Fig. 23), then no mechanical experiment can detect this movement. He suggested mentally placing vessels with water flowing out of them, with fish swimming in them, flying flies and butterflies in the hold, and argued that whether the ship is standing or moving evenly, their actions do not change. At the same time, one should not forget that the movement of the ship is not rectilinear, but circular (though, along a circle of large radius, which is one or another section of the Earth).

Rice. 23. Galileo's ship (it can be seen that it is sailing in a circle)

Now we know that in a system moving along a curve, which is also a circle, it is impossible to observe the law of inertia: this system is not inertial. Indeed, in Galileo's principle, the value of the velocity of relative motion does not play a role, as well as the velocity of motion of one inertial frame relative to another.

But if the ship is given the first cosmic speed(8 km / s), then all objects in its hold, like the ship itself, will become weightless. A mechanical experiment carried out with sufficient accuracy will show that for real speeds of movement, the movements of bodies in the hold of a moving ship and a stationary ship will differ from each other. Moreover, the movement of bodies will change if the ship moves at the same speed, but in different courses - for example, along the meridian and along the equator. Not only the bodies moving in the hold will stray from the intended trajectory, but the ship itself in the Northern Hemisphere will drift to the right along the course, and in the Southern Hemisphere - to the left. Interestingly, these deviations, caused by the rotation of the Earth as a non-inertial system, do not even depend on the direction of motion.

In his other work - "Dialogue on the two main systems of the world ..." - Galileo argues that the world is a body in the highest degree perfect, and in relation to its parts the highest and most perfect order should prevail. From this, Galileo concludes that celestial bodies by their nature cannot move rectilinearly, since if they moved rectilinearly, they would irrevocably move away from their starting point and the original place for them would not be natural, and the parts of the Universe would not be located in "in perfect order". Consequently, it is unacceptable for celestial bodies to change places, that is, to move in a straight line. If the law of universal gravitation suddenly disappeared, this would happen! It is he who keeps the celestial bodies in steady motion, preventing their chaotic scattering (Fig. 24). In addition, rectilinear motion is infinite, because a straight line is infinite, and therefore indefinite. Galileo believed that it was impossible, by the very nature of nature, for anything to move in a straight line towards an unattainable goal.

Rice. 24. Natural or inertial motion according to Galileo on the example of the rotation of the Moon around the Earth

But as soon as order is achieved and the celestial bodies are placed in the best way, it is impossible that they should have a natural tendency to rectilinear motion, as a result of which they would deviate from their proper place. As Galileo argued, rectilinear motion can only "deliver material for the structure," but when the latter is ready, it either remains motionless, or if it has motion, then only circular. Moreover, Galileo argued that if a body is left to slide like on ice along a horizontal plane, then, falling from it, the body will necessarily intersect its trajectory with the center of the Earth (Fig. 25, a). But since the movement by inertia always removes the thrown body from this trajectory, it cannot cross its path with the center of the Earth in any way. This is a very common mistake; even in modern school textbooks on physics (in the seventies), the author had a chance to meet such a statement and see the corresponding drawings: for example, how a nucleus that has flown out of a cannon, continuing its flight, crosses the center of the Earth.

Rice. 25. The fall of bodies moving tangentially to the surface of the Earth: a - according to Galileo; b - according to Newton

In addition, the movement along a horizontal slippery plane is such that the body, moving away from the point of intersection of the shortest radius of the Earth with this plane, begins to move away from the center of the Earth. This means that both approaching and moving away from the center of the Earth, the body cannot move uniformly, since a force will act on it all the time (except for one point in the center of the Earth).

As we see, Galileo in his view of inertia, and consequently, of mechanics in general, was mistaken very significantly. A prophetic formulation of the laws of inertia, very close to Newtonian and accepted with minor changes in modern mechanics, was given by the French philosopher and mathematician R. Descartes (1596-1650), a contemporary of Galileo. Prophetic because Descartes also did not know about the forces of gravity and formulated this law on a whim.

In his book "Principles of Philosophy", published in 1644, he formulates the laws of inertia in this way. The first law: "Every thing continues, if possible, to remain in the same state and changes it only by meeting with another." The second law: "Each material particle separately tends to continue further movement not along a curve, but exclusively along a straight line." Therefore, instead of calling Newton's first law, or the law of inertia, the Galileo-Newton law, which is sometimes done in textbooks, or saying that the law of inertia was discovered before Newton, it should be noted that Descartes formulated it quite accurately before Newton, but not Galileo.

Therefore, the movement by inertia is necessarily rectilinear, uniform; this movement can be equated to rest by changing inertial system reference to one that would also move uniformly and rectilinearly with the speed of our moving body.

Who stood on the shoulders of giants?

So, Galileo did not bring much clarity to the sacramental questions that have remained unresolved since ancient times: how do bodies behave when forces act on them, and how do they behave when forces do not act on them?

Trying to answer at least the last of the questions posed, Galileo, as you know, came to the conclusion that bodies left to themselves, that is, on which no forces act ... go in circles! Yes, this is what Aristotle thought two thousand years ago! And just as wrong. Therefore, it looks amazing when schoolchildren are presented with something that was not there. For example, this: "The Italian scientist Galileo Galilei was the first to show that ... in the absence of external influences, a body can not only rest, but also move in a straight line and uniformly." Galileo did not show this, especially the first, which we already know about. For some reason, Galileo is credited with many things that he did not do at all: he did not throw balls from the Leaning Tower of Pisa, did not invent the telescope, was not judged by the Inquisition and did not stamp his foot, saying: “And yet it spins!”. We'll talk about this later, but for now let's return to the fact that before Newton, there was no clarity in the minds of scientists about the motion of bodies, and therefore, about mechanics in general.

Only the great Englishman Isaac Newton (1643-1727) managed to bring the mechanical world into proper order. A short list of Newton's merits is carved on a stone at his grave:

Here rests

Sir Isaac Newton,

Who by the almost divine power of his mind

first explained

With the help of your mathematical method

The movements and forms of the planets,

The paths of comets, the ebbs and flows of the ocean.

He was the first to explore the diversity of light rays

And the peculiarities of colors resulting from this,

Until that time, no one even suspected.

Diligent, shrewd and faithful interpreter

Nature, antiquities and sacred writings,

He glorified the Almighty Creator in his teaching.

He proved the simplicity required by the Gospel by his Life.

Let mortals rejoice that in their midst

Such an adornment of the human race lived.

Until now, all generations of scientists have been amazed and continue to be amazed by the majestic and integral picture of the world that was created by Newton.

According to Newton, the whole world consists of "solid, weighty, impenetrable, moving particles." These "primordial particles are absolutely hard: they are immeasurably harder than the bodies they are composed of, so hard that they never wear out or shatter." All the wealth, all the qualitative diversity of the world is the result of differences in the movement of particles. The main thing in his picture of the world is movement. The internal essence of the particles remains in the background: the main thing is how these particles move.

The great genius was born in one of the provincial English cities - Woolstrop in a farmer's family. The child was so small that they say he was baptized in a beer mug. In the elementary grades of the school, he studied mediocrely (rejoice, three-year-olds, nothing has been lost for you yet!). Then he had a moral shock - he was beaten and insulted, and the best student in the class did it. It was then that young Newton woke up with an interest in learning, and he easily became the best student himself, and then entered the best university in England - Cambridge. And 4 years after graduation, he was already a professor of mathematics at the same university. In 1696 he moved to London, where he lived until his death in 1727, which occurred at the age of 85. Since 1703 he has been President of the Royal Society of London, and for scientific services he was granted the title of Lord. And so he became a member of the House of Lords, whose meetings he attended in the most regular way. But unlike other lords, who, like our "duma members", liked to talk from the podium, for many years Newton did not utter a word. And finally, great person suddenly asked to speak. Everyone froze - they expected what the genius of all times and peoples would say so smart. In deathly silence, Newton announced his first and last speech in Parliament: "Gentlemen, I ask you to close the window, otherwise I may catch a cold!"

In the last years of his life, Newton was closely engaged in theology and, under great secrecy, wrote a book, which he spoke of as his greatest work, which should decisively change people's lives. But due to the fault of Newton's beloved dog, which overturned the lamp, there was a fire in which, in addition to the house itself and all the property, a great manuscript burned down. Here's Woland's: "Manuscripts don't burn!" Still burning...

Soon after this, the great scientist died ...

So what did Newton do that was so remarkable in mechanics? And the fact that he discovered and formulated his own laws: three laws of motion and one - universal gravitation.

Briefly, the main idea of ​​Newton's laws of motion is that a change in the speed of bodies is caused only by their mutual action on each other. Come on, did people really not know such simple things before? Imagine that not, and many do not know until now.

Take Newton's first law (this is the one that is sometimes wrongly attributed to Galileo). Newton himself formulated it very intricately, as, by the way, in many school textbooks. The author believes that it is more concise and simplest to say this: "A body is at rest or moves uniformly and rectilinearly if the resultant of the external forces applied to it is equal to zero." It seems that there is nothing to complain about here. And then they write in some textbooks: "... if forces or other bodies do not act on the body ...". This is inaccurate, and here's an example to prove it.

A car is driving along a beautifully flat highway with the engine turned off (as they say, “freewheeling”), slowly slowing down. And roaring the engine from the effort, the bulldozer drags a whole mountain of sand in front of it, but it moves evenly and in a straight line, albeit slowly (Fig. 26). Which of these motions can be called inertial motion? Yes, of course, the second, although I would like to point out the first. The most important thing is that the body moves uniformly and in a straight line. That's all, that's enough, nothing more is needed. The car in the first example, although slowly, is decelerating. Consequently, the forces acting on it are not compensated: there is resistance, but the traction forces are not. And many bodies act on the bulldozer, each with its own force, but all forces are compensated, their resultant is zero. That is why he continues to move uniformly and rectilinearly, that is, by inertia.

Rice. 26. Coasting a car and a loaded bulldozer

Now it is clear why Colonel Zillergut's car stopped: because his movement with the engine turned off has nothing to do with inertia. This car is affected by an unbalanced system of forces, the resultant of which is directed backwards. The car then slows down until it comes to a complete stop.

Unfortunately, many of us often misunderstand the term "inertia".

The flywheel spins by inertia, by inertia I hit my forehead on the glass when the car slowed down ... All these are everyday concepts of inertia. Strict is only that which is determined by Newton's first law. Which before him, maybe not so accurately, but formulated ... no, not Galileo - Descartes!

So, Newton understood one of the innermost secrets of nature and continued to comprehend these secrets. "The Lord God is sophisticated, but not malicious!" - Einstein liked to say and even engraved these words on his fireplace. This means that with due diligence, a person comprehends the same secrets of the Creator one after another, who does not completely forbid him to do this. And such a person who solved largest number these mysteries, so far, apparently, Newton has been and remains. And when asked how he could see so far in science, he modestly answered: “If I saw further than others, it was because I stood on the shoulders of giants!”

What attracts bodies to each other?

Newton did not name the specific names and surnames of these giants, but at least one of them can be named for sure. It seems that it was ... no, they didn’t guess again, although this name is usually mentioned first among the giants, this is not Galileo. I think it was Johannes Kepler (1571-1630). A few words about the giant, which scientists called the "legislator of the sky."

The “legislator of heaven” was born in 1571 in southern Germany into a poor family, but managed to finish school and university in Tübingen. It must be said that he also died in poverty in 1630, and after him the family was left with one worn-out dress, two shirts, several copper coins and ... almost 13 thousand guilders of unpaid salaries! And they also say that earlier scientists were paid on time and a lot ... The author, at the risk of being beaten by his colleagues, claims that it is bad when scientists live richly - their head does not think about what is necessary. They do not care about the new laws of nature, but about which bank and at what interest to put their treasures. “For where your treasure is, there your heart will be also,” said the Lord. Even the poet Petrarch noticed that wealth, as well as extreme poverty, by the way, interfere with creativity. Therefore, if science continues to be kept on a starvation diet, then one thing (unfortunately, only one thing!) Will definitely be good: grabbers and businessmen will not rush there. Yes, from the history of science, it is difficult to name a scientist (a real one, and not a businessman with degree!) who would be truly rich. Excluding the kings-scientists, who, by the way, also happened.

So, Kepler had to sip a lot of grief and worries in his life. He was ill, suffering from a strange disease - multiple vision. (What is it like for an astronomer, huh? It's like a deaf musician, but there were such people, Beethoven, for example!) Again, poverty, although he worked as a court astronomer and astrologer. Yes, and his mother slipped him a surprise - take it and tell your neighbor heretical words: “There is no heaven or hell, the same thing remains from a person as from animals!” It came to “who needs it”, and she would not have passed the fire (and in Kepler’s homeland in the small town of Veil, 38 heretics were burned in just 14 years!), If not for 6 years of Kepler’s “advocacy”!

And among such worries and troubles, Kepler introduced the concepts of "inertia" and "gravity" into mechanics, and he defined the latter as the force of mutual attraction of bodies. Everything is almost correct, if only Kepler did not associate this attraction with magnetism and did not consider that “the Sun, rotating, drags the planets into rotation with constant pushes. And only inertia prevents these planets from accurately following the rotation of the Sun. It turns out that “the planets mix the inertness of their mass with the speed of movement” ... In general, the mix turned out to be fair. But Kepler's laws of planetary motion are a masterpiece, and they pushed Newton to comprehend the law of universal gravitation.

Kepler's first law is about the elliptical motion of the planets. Everyone used to think that the planets moved in circles (again those magic circles: both Copernicus and Galileo were confused!). Kepler proved that this is not true and that the planets move in ellipses with the Sun at their focus.

The second law is that, when approaching the Sun, the planets (and comets, too!) move faster, and moving away from it, slower (Fig. 27). And the third law is already strictly quantitative: the squares of the periods of revolution of any two planets are related to each other as the cubes of their average distances from the Sun.

Rice. 27. Illustration of Kepler's second law

There is already a little left to understand what forces control the movement of the planets. A contemporary of Newton and his senior colleague, or perhaps one of those giants on whose shoulders Newton stood, Robert Hooke wrote in 1674 that “... all celestial bodies without exception have an attraction directed towards their center ... and these forces of attraction act the more, the closer to them are the bodies on which they act. One wonders how close Hooke was to discovering the law of universal gravitation, but he himself did not want to do this, referring to being busy with other works.

For the first time, the idea of ​​an accurate definition of gravity arose as early as Newton the student (remember the myth of an apple falling on his head!), but the calculations did not give the desired accuracy. The fact is that for calculations, Newton used the value of the earth's radius, inaccurately determined by the Dutch scientist Snellius, and, having obtained the value of the Moon's acceleration by 15% less than the observed one, bitterly postponed this work.

Then, 18 years later, when the French astronomer Picard more accurately determined the value of the Earth's radius, Newton took up his delayed calculations again and proved the correctness of his assumption. But even after that, Newton was in no hurry to publish his discovery. He carefully tested the new law on the motion of the planets around the Sun, on the motion of the satellites of Jupiter and Saturn, as well as on the motion of comets, and decided to publish the law of universal gravitation in his famous book "Mathematical Principles of Natural Philosophy" in 1687, which also contains three his law of motion.

Here is how this law can be formulated in a simpler and clearer way: "Every body attracts another body with a force directly proportional to the masses of these bodies and inversely proportional to the square of the distance between them."

For example, two human body at a distance of 1 m between them, they are attracted with a force of about one fortieth of a milligram-force. That's less than one billionth of the power it takes to move us. Two ships weighing 25,000 tons each at a distance of 100 m are attracted with an insignificant force of 4 N, and the absurd explanations of the collision of ships due to their mutual attraction are meaningless.

No barriers or screens can save you from the force of gravity. Although many dreamed of finding such a screen: every now and then you hear that, they say, in the XXI century. scientists will find a way to get rid of gravity. They are already drafting houses without a foundation and gravity-flying machines flying without fuel.

These searches are not new - even the English science fiction writer Herbert Wells used the idea of ​​​​a "gravitational shield", allegedly made of a special material named after the author - the inventor Cavor - cavorite. If this shield is brought under some object, then it will be freed from the attraction of the Earth and will be attracted only by celestial bodies, that is, it will take off. Wells' heroes build an interplanetary ship covered in cavorite; by opening and closing the appropriate curtains, they are attracted to that part of space where they want to fly, and thus move in space.

The science fiction writer's arguments sound convincing: we know that a screen made of some kind of conductor (for example, a sheet of metal) is impenetrable to electric field; the superconductor pushes a magnetic field out of itself, etc. Moreover, the report on the measurements of the French astronomer Allen, which appeared in the press, confirmed that the Moon, shielding us from the Sun, also creates a certain “gravitational shadow”. But it turned out that this “shadow” was only a mistake of the instruments.

Thoughts were expressed that gravity, they say, acts only on celestial bodies, but not on us. So, the English physicist Henry Cavendish built a special very accurate so-called torsion balance and was one of the first in 1798 to measure gravity on Earth. In these scales, weights were suspended on a thin and strong thread on a yoke, which were attracted by two massive balls of lead weighing 50 kg (Fig. 28). The Cavendish device was enclosed in an airtight chamber, and the movement of the rocker arm was captured by optical instruments. This is how the “gravitational constant” was determined, which turned out to be 6.67 10 - 11 N⋅m2 / kg2, in other words, two balls weighing 1,000 kg each, located at a distance of 1 m from each other, are attracted with a force of 6.67 hundred thousandths of a Newton!

Rice. 28. "Torsional balance" G. Cavendish to determine gravity

This is how weak, insignificant the gravitational forces are, and at the same time it is they who “move the world”, determining the flight of planets, stars, comets and other celestial bodies. The fall of bodies on Earth, by the way, is also the work of the "hands" of gravity, so that it is not only universal, but also omnipresent!