The law of inertia, the heliocentric system and the development of science

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running_head:
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LAW OF INERTIA,
HELIOCENTRIC
SYSTEM
AND DEVELOPMENT OF SCIENCE
M. Y. AZBEL
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The nature of the development of science is dramatic. But over a great historical distance, even large masks on the canvas of science merge, contradictions become invisible, and the development of science seems consistent, strictly logical and always directed in one direction. At a short distance, science is truly understandable only to professionals, but today’s decrees seem unconditionally true. Therefore, in order to see the nature of the development of science, the flourishing and this also happened - the extinction of its individual fields *), to see the drama of it, its characters, its convictions, one must sweat into that science that has already become history and is understandable to the end - it has turned from the arena of beats into a school truism. Then, perhaps, you will be able to imagine the present day of science in a new and more correct way.

It is very convenient to trace in this regard the path that led to the discovery of the law of inertia. In a school presentation, this law looks very simple and primitive, and it is not clear why the genius of Galileo, Descartes and Newton was needed to discover it.

Meanwhile, the law of inertia is one of the greatest and, in accordance with this, one of the deepest laws of physics.

One of the greatest, or it is universal, being valid for both electrons and galaxies. He was not shaken by any of the natural revolutions of the 20th century: neither the theory of relativity, nor quantum mechanics.

The reason for such stability of the law of inertia is its depth. It is therefore valid for all objects without exception, because it is associated not with a specific property of objects, but with a fundamental property of space and time: with

*) For example, science about the concepts of cutting or about the exact (in radix) solution of algebraic equations.

homogeneity and fabrication of space (that is, with the equivalence of any places and directed in empty space) and homogeneity of time (that is, the equivalence of any moments in time).

In fact, if a material point moving by inertia, that is, not interacting with the rest of the world, changed, for example, the direction of its movement, only one thing could be known: the non-equivalence of the direction in space - the direction in which the material point turned would be somehow different from all the others.

A question for supporters of the evaluative nature of the law of inertia: how will a material body move without interacting with anything? Well, let’s say, how would the movement of our Earth occur if the attraction of the Sun suddenly disappeared? Would its rotation around its axis be maintained or not? *)

In answering this question, it is worth bearing in mind that a number of answers to the more complex question of the free movement of a wolf have been given as a result of the work of such great mathematicians as Lagrange and Euler.

Isn’t it true that even after one question asked, the law of inertia begins to seem not only naively obvious? To put this into print, it is worth asking us when and under what conditions (a physicist would ask: in what reporting systems) the law of inertia operates. Well, for example, imagine a billiard ball lying on the frictionless floor of a tram. No forces act on the ball, and yet the observed driver will notice that from time to time (when?) the ball begins, subject to the law of inertia, to move unevenly across the floor. What’s the matter here?

Please note that such constructions are by no means exercises in scholasticism. An example of this is the concepts

*) Answers to all data questions posed in the article are at the end of the magazine.

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absolute and relative peace. Everyone knows that there is no absolute peace, but the relative peace of the interconnected gas surprisingly conditions the task of flying at near-light speeds due to the collision of happy gases.

But let’s return to the law of inertia. It’s not just not obvious. He is the first crazy law in the history of science. The afterlifer has never seen uniform motion on Earth without the action of an external force. Absolutely all experiments, without a single exception, convince us: without forces there is no movement. It is no coincidence that before Galileo it was believed that speed is proportional to the acting force. And this is the correct law for the usual speeds of that time. But it’s just very unrestrained! What does the coefficient of proportionality in it depend on? Generations of scientists can work (and are working!) to study this coefficient, especially since with increasing speed the law itself is conditioned, the very dependence between the speed of movement and the applied force. And it is not surprising: after all, the force lies, strictly speaking, outside the boundaries of mechanics (when friction occurs, the body is released).

But how can one manage to remove this always approaching force? How to abandon absolute value and the natural path of ever new, ever more subtle and complex experiments?

The answer of history is unexpected and received. The law of inertia, like all the basic laws of mechanics - Newton’s laws, was born not on Earth, but in heaven. And who knows when it would be open if our sky, like the sky of Venus, was always covered with clouds? Moreover, the law of inertia was discovered as a result of an error! Galileo, who discovered the law, believed that by inertia a body can only move in a circle!

To understand how this happened, we will have to follow the history, which lasted 25 centuries, of the formation of the heliocentric system, which was opposed by such geneticists as Aristotle and Archimedes. Let’s try to present in modern language - and therefore, inevitably changing somewhat - the arguments of the disputants.

The Earth was first deprived of immobility back in the fifth century BC. This was done by Philolaus, one of Pythagoras’ students. He believed that the Earth, together with the Sun and planets, revolves around a certain central fire.

A century later, Philolaus had a brilliant opponent - Aristotle *). He responded to Philolaus’s hypothesis as contradicting the existence of fixed stars. After all, if the Earth is moving, all the stars should appear to be moving to an observer on Earth! It took 23 centuries to refute this objection - 3 of them after the death of Copernicus!

In the 3rd century BC. Aristarchus of Samosko proposed a system identical to the future Copernican system: the Earth and all the planets rotate in circles around the motionless Sun. Archimedes and Apollonius of Perga became opponents of Aristarchus, or Aristarchus’ system contradicts astronomical observations - in the 2nd century BC. this was strictly proven by Hipparchus. Both scientists, Aristarchus and Hipparchus, were both right and wrong: the Earth and the planets revolve around the Sun, but not in circles, but in ellipses! It would seem to be true

*) The ancient Greeks also tried to answer the question of why celestial bodies violate the general rule and do not fall to Earth. The Greeks attached them to crystal spheres because a sphere could not fall onto its own center without breaking! Seam of crystal hemispheres of the Milky Way. The idea seems naive, but it is worth remembering that in the twentieth century, Nobel laureate F. Dyson proposed the idea of ​​high civilizations creating an opaque sphere around the central light to fully utilize its energy.

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Ptolemy’s world system.

one step left. But not only Copernicus, but also Galileo failed to take this step. Circles as planetary orbits seemed absolutely indisputable: they were the only perfect curves. André Bonard, in Greek Civilization, published in 1959, writes: “It is a pity that the scientists who objected to Aristarchus did not come to Kepler’s discovery. But the prejudice about the superiority of circular motion is firmly rooted.”

The words of the ancients about the obligatory nature of orbits seem ridiculous. Let us translate, however, these words into perfect language. One of the leading ideas of modern physics, as already mentioned, is the idea of ​​homogeneity and production of space. The basic laws of physics follow from this idea. But if the planet’s orbit is not circular, then the seen direction of the greatest elongation of the orbit appears in space, which turns out to be something different from all other directions! The fact that the movement of planets is determined by their prehistory was still incomprehensible.

Therefore, Ptolemy (2nd century AD) proceeds from the geocentric system and, introducing a complex picture of the circle

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Copernican world system.

gov orbits, explains all observational facts. Moreover, he gets the opportunity to imagine the movement of the planets and even eclipses of the Sun and Moon. This struck the imagination of the ancients so much that his work received the name “Almagest” - the greatest. Ptolemy became the first astronomer in history who managed to reconcile astronomical observations with his theory. Great achievement! But, perhaps, it was precisely this that overshadowed the elucidation of the true motion of the planets for many centuries: after all, everything is so good, the theory coincides so perfectly with experiment!

17 centuries pass, and history repeats itself! The canon of the Frausenburg Cathedral, Nicolaus Copernicus, seeks only to bring the Ptolemaic system in accordance with the observations of his time and replaces: the Ptolemaic system can be somewhat simplified if we assume that the Earth and the planets revolve around the Sun, but still in a complex system of circles. And again, like Aristarchus, Copernicus has an opponent - one of the greatest astronomer-observers of all times, Tycho Brahe. He responds to the Copernican system for approximately the same reason as Hipparchus

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Kepler’s model of the Universe, which he originally proposed.

systems. After many years of flawless attempts to find the harmony of the world in the system of regular polyhedra that enclose the orbits of the planets, Kepler came to the great law: the planets move around the Sun, but they move in ellipses!

This law reflected not only Kepler’s readiness to express an insane idea that rejected the views of twenty centuries. Kepler was also extraordinarily lucky. Due to the enormous distance of the planets (especially heavy ones) from each other, their orbits are close to an ellipse - one of the three curves well known at that time (ellipse, hyperbola, parabola).

Kepler was the first to establish the laws of planetary motion. How he arrived at his second law: in equal periods of time, the planets cover equal areas - remains almost incomprehensible. After all, interral calculus does not yet exist, and the calculation of areas was not only a science, but an art: each curve required its own approach. Where did the idea of ​​creating unusual areas even come from? Probably, Kepler’s early passion will also have an impact - the specific methods for calculating areas that he invented in his work “On the Stereometry of Wine Barrels” (a genius from an applied problem is created by science!), and an almost mystical belief in the existence of unified laws of nature *), and, believe it, just a love of calculations for the sake of calculations, and what is called genius **).

Kepler’s irreconcilable scientific opponent was his contemporary Galileo. He was the first to raise the question of what moves the planets, causing their orbits to bend. Galileo considered the influence of the Sun at such a distance mystical, as well as linking the tides with the Moon. How do the planets know that in the next hour they must cover the same area as in the previous hour?

*) Kepler was a deeply religious man and left wealth for astronomy, reassuring himself that “God can be glorified not only through wealth.” But God removed from the astronomy textbook written by the pious Kepler, and the book was immediately included in the list of prohibited books by the cataloguer. This is the frequent result of an honest descent into truth.

**) It is impossible not to name at least some of Kepler’s works: the third fundamental law of planetary motion, following Newoton, as the basis for deriving the law of universal gravitation (!); explanation of tides; the idea of ​​light pressure (!), creating comet tails; prediction of the satellites of Mars and astroid; establishing one of the most important provisions of differential calculus - the conditions for the maximum of a function.

Kepler’s second law: $S_1 = S_2$.

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what? *) A fundamentally new formulation of the question was required, because the grafted question itself was incorrect. And Kepler’s answer: “The planets are moved by the world soul,” of course, could not satisfy Galileo. But since there is no force acting on the planets, Galileo reasoned, then such movement is a natural property of the planets. Galileo called it inertia and very convincingly proved the erroneous statement: the reason for the rotation of the planets is inertia, motion by inertia can only be motion in a circle, all points of which are equal (!).

Galileo considered motion in a straight line to be excluded: the transition over time from one point to another was familiar because of their non-equivalence; in addition, in this case the body would never reach the final goal (in modern language - an equilibrium stable state), and nature never sets itself inaccessible goals (that is, an equilibrium state occurs sooner or later).

This reasoning led Galileo to a contradiction not only with Kepler, but also with himself: after all, he had previously proven that motion in a circle is associated with a force acting towards the center! The contradiction seemed insoluble, and Descartes made the situation even more dramatic by showing that motion by inertia is motion in a straight line.

What moves the planets?

*) It is worthwhile to compare this question with Rutherford Bohr’s question: how does an electron know what part of the light it should emit when jumping to a new orbit?

There seemed to be no way out. But in the year of Galileo’s death, Newoton was born. He returned to Kepler, to his laws, and on their basis created an exact science of the motion of bodies.

Until now, it has only been about the evolution of ideas, about disputes between the knights of thought: Philolaus and Aristotle, Aristarchus of Samos and Hipparchus, Copernicus and Tycho Brahe, Kepler and Galileo, disputes in which it became clear that the truth had not yet been born. But scientists are living people, with their passions, pride, pride and ability to make mistakes even in small things. Galileo was convinced of the impossibility of leaving the Earth and did not notice that his formulas gave the first cosmic velocity *). He explained the tides by the movement of the Earth around the Sun (I so wanted to be the first to point out the phenomenon that proved this movement!), but the period of the tides was twice as different from his calculation and coincided with Kepler’s results. Galileo declared Kepler’s coincidence an accident **), and he himself naively and helplessly appealed to the employees that somewhere in the Sargasso Sea the tide period was “correct”. But at the same time he is trying to connect the irregular tide period in the Mediterranean Sea with its depth - and creates a new field of science: the study of surface waves and waves in closed basins! Ga-

*) By the way, how can I use the formula $S = \frac{gt^2}{2}$ to obtain an expression for the first escape velocity!

**) Let us remember Bohr: “The coincidence of a stupid theory with experiment does not prove anything; there are countless such theories.”

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Lily discovered the independence of the period of oscillation of a pendulum from amplitude - and immediately, carried away, mistakenly extended this law to any amplitude; discovered the constancy of the earth’s acceleration - and immediately concluded that it is independent of the distance to the Earth! This is how the founder of almost all areas of mechanics was mistaken *).

Thus, in a thick mixture of pronunciation and error, without rights and wrongs, science developed. But at the same time, everyone we were talking about were geniuses: their works have been in use for several centuries; they have advanced humanity many decades into the future (and what, if not the number of man-years saved, determines the degree of talent?); it took more time to understand and master their ideas - a great truth is rarely born simple and understandable **).

The presented history of the development of science, of course, is extremely simplified and written in crude masks, sometimes with a popular condensation of facts. But it is clear that development does not proceed along the straight line of a telephone pole, but rather along the complex curve of the tree of science, the branches of which are inclined at different angles to the truth and are gradually straightened to rise to a new language of knowledge.

*) About the existence of geniuses. Newton, out of scientific conscientiousness, did not publish his law of universal gravitation for 20 years, trying to derive Kepler’s laws from it, and then spent many years arguing about nature with Hooke; did not publish his discovery of differential and integral calculus, trying to find a general formula for the integral, and then proved his nature in a dispute with Leibniz. For Newton lived only in science, throughout his life he was lonely and could not sacrifice his only joy in life - weak, although weak his discoveries would have been enough for many.

**) Here, for example, is the multiplication rule from a 15th century manuscript: 7×8=? 7+8-10=5, then 5x10=50, now 10-7=3, 10-8=2 are defined and these results are variable: 3x2=6. Finally, 50+6=56, so 7x8=56.