He formulated three laws of planetary motion relative to the sun. Kepler's laws. space speeds

Did you know, what is a thought experiment, gedanken experiment?
It is a non-existent practice, an otherworldly experience, the imagination of what is not really there. Thought experiments are like daydreams. They give birth to monsters. Unlike a physical experiment, which is an experimental test of hypotheses, a “thought experiment” magically replaces an experimental test with the desired, untested conclusions, manipulating logical constructions that actually violate logic itself by using unproved premises as proven ones, that is, by substitution. Thus, the main task of the applicants of "thought experiments" is to deceive the listener or reader by replacing a real physical experiment with his "doll" - fictitious reasoning on parole without the very physical check.
Filling physics with imaginary, "thought experiments" has led to an absurd, surreal, confusing picture of the world. A real researcher must distinguish such "wrappers" from real values.

According to Kepler's second law, called the "Law of Regions" in the planetary system. Kepler's third law, called the "Law of Periods", postulates that "The square of the period of any planet around the Sun is proportional to the cube of the average distance between the planets of the Sun."

Johannes Kepler was a German astronomer, physicist and mathematician who formulated the three basic laws of planetary motion. His work greatly influenced Tycho Brahe, the dedicated astronomer who gave Kepler a mission to study the orbit of Mars. Kepler's research continued for eight years until he collected the data Tycho had collected over twenty years and concluded that the orbit was an ellipse, not a circle as was thought. This conclusion has been extended to others.

Relativists and positivists argue that the "thought experiment" is a very useful tool for testing theories (also arising in our minds) for consistency. In this they deceive people, since any verification can only be carried out by a source independent of the object of verification. The applicant of the hypothesis himself cannot be a test of his own statement, since the reason for this statement itself is the absence of contradictions visible to the applicant in the statement.

It was thanks to these discoveries that the planetary model of Copernicus was adopted, thus he came to the conclusion that the Sun is the center solar system, and not the Earth, as previously thought. Kepler formulated three laws that became known as Kepler's laws. Here is how they are presented.

Kepler's first law. The planets describe elliptical orbits with the Sun at one of their foci, as shown in the figure. The eccentricity of the figure's ellipse has been exaggerated to make it easier to understand, because the orbit of the planets is nearly circular. Kepler's second law. The straight line connecting the Sun to the planet describes equal areas with equal time intervals.

We see this in the example of SRT and GR, which have turned into a kind of religion that governs science and public opinion. No amount of facts that contradict them can overcome Einstein's formula: "If the fact does not correspond to the theory, change the fact" (In another version, "Does the fact not correspond to the theory? - So much the worse for the fact").

This law can be described by the expression. This ratio determines that the planets move at different speeds, depending on their distance from the Sun. In addition, it allows you to define two points. Aphelion: The farthest point of the Sun, where the planet moves more slowly.

The square of the period of rotation of a planet around the Sun is directly proportional to the cube of the ray described by the trajectory between this planet and the Sun. Mathematically, a can be rewritten as an equation. Kepler, during a period engulfed by religious conflicts between Catholics and Protestants, laid the foundations for modern interpretations of celestial phenomena for physical reasons. He argued throughout his life in favor of the heliocentrism of Nicholas, as opposed to the geocentrism of Aristotle-Ptolemy. Based on these assumptions, this work intends to briefly describe the intellectual trajectory of Johannes Kepler and the foundations of the modern.

The maximum that a "thought experiment" can claim is only the internal consistency of the hypothesis within the framework of the applicant's own, often by no means true, logic. Compliance with practice does not check this. A real test can only take place in a real physical experiment.

An experiment is an experiment, because it is not a refinement of thought, but a test of thought. Thought that is consistent within itself cannot test itself. This has been proven by Kurt Gödel.

Something that has always intrigued mankind since the earliest civilizations has been the movement celestial bodies. The observation of the stars in the sky has led to the formation of a variety of traditions and beliefs. The idea of the Earth as the fixed center of the cosmos is long gone, from Western classical antiquity to the Renaissance.

In the history of science, few characters have been as intriguing as Johannes Kepler. His personal life was marked by a series of misfortunes, such as his mother being persecuted by the courts of the Holy Office. If today Astronomy propagates the idea that the planets develop an elliptical orbit and follow physical laws in their space travel, we must consider as essential the Laws of Planetary Motions formulated by Kepler.

The planets move around the Sun in elongated elliptical orbits, with the Sun at one of the two focal points of the ellipse.

The straight line segment connecting the Sun and the planet cuts off equal areas in equal intervals of time.

The squares of the orbital periods of the planets around the Sun are related as the cubes of the semi-major axes of their orbits.

This study is intended to briefly reflect on the intellectual trajectory of Johannes Kepler and the foundations of modern astronomy through the perception of the American writer James A., a former Jesuit priest, doctor of theology, literature and science. He is the author of Kepler's Sorcerer: an astronomer's discovery of cosmic order in the midst of religious wars, political intrigues, and the heresy of his mother's judgment. We also support Ronaldo Rogerio de Freitas Murao. Brazilian Ph.D. in astronomy, retired director of the National Observatory, founder of the Museum of Astronomy and Allied Sciences.

Johannes Kepler had a sense of beauty. All his adult life he tried to prove that the solar system is a kind of mystical work of art. He first tried to link her device to five regular polyhedra classical ancient Greek geometry. (A regular polyhedron is a three-dimensional figure, all the faces of which are equal to each other regular polygons.) At the time of Kepler, six planets were known, which were supposed to be placed on rotating "crystal spheres". Kepler argued that these spheres are located in such a way that between neighboring spheres fit exactly regular polyhedra. Between the two outer spheres - Saturn and Jupiter - he placed a cube inscribed in the outer sphere, in which, in turn, the inner sphere is inscribed; between the spheres of Jupiter and Mars - a tetrahedron (regular tetrahedron), etc. Six spheres of the planets, five regular polyhedra inscribed between them - it would seem, perfection itself?

Muran is the author of the book "Kepler": the discovery of the laws of planetary motion. Interest in Connor's work came about because it is one of the few foreign works on the life of Johannes that has been translated into Portuguese. But this idea, which represents our planet, in the vastness of the universe revolving around the sun, has come a long way until it establishes itself. Connor and Ronaldo Rogerio de Freitas Murao on Kepler's intellectual trajectory. In the next section, with the help of the mentioned intellectuals and physicists, historians of science and philosophers, we will seek to redefine such concepts.

Alas, having compared his model with the observed orbits of the planets, Kepler was forced to admit that the actual behavior of celestial bodies does not fit into the harmonious framework outlined by him. As the modern British biologist J. B. S. Haldane aptly remarked, “the idea of the universe as a geometrically perfect work of art turned out to be another beautiful hypothesis, destroyed by ugly facts.” The only surviving result of that youthful impulse of Kepler was a model of the solar system, made by the scientist himself and presented as a gift to his patron Duke Frederick von Württemburg. In this beautifully executed metal artifact, all the orbital spheres of the planets and the regular polyhedra inscribed in them are hollow containers that do not communicate with each other, which on holidays were supposed to be filled with various drinks to treat the guests of the duke.

In the era of Kepler, the idea in relation to the cosmos that prevailed referred to the geocentric system of Ptolemy, in which the Earth occupied the center of the world. Aristotle also followed a long tradition established by pre-Socratics: everything is heavy falling, and that which shines, like air, water and earth mixed in a glass jar, calms down with earth in the background, air above everything and water in the middle. Heavy things separate themselves from light, wet things separated from droughts, hot things from holidays, and light things from dark things.

Therefore, said Aristotle, the earth must be at the center of the universe, since, as can be seen, the earth is heavy, and the air that extends towards the sky is light. Paulo Abrantes, a physicist and scientist in the history of science, points out that in Aristotelian cosmology the universe was divided into two regions: the celestial region and the sublunar region below the moon's orbit. four elements: earth, water, air and fire. After the sphere of the Moon, the spheres of the planets, including the sun. The world is limited to a fixed sphere. We can see that the finiteness of the cosmos is a hidden feature in the Aristotelian conception, and the immutable aspect of the sphere of the fixed, that is, beyond the world limited by this region, is not subject to change.

Only after moving to Prague and becoming an assistant to the famous Danish astronomer Tycho Brahe (1546-1601), Kepler came across ideas that truly immortalized his name in the annals of science. Tycho Brahe collected data all his life astronomical observations and accumulated vast amounts of information about the motion of the planets. After his death, they passed to Kepler. These records, by the way, were of great commercial value at that time, since they could be used to compile updated astrological horoscopes (today, scientists prefer to remain silent about this section of early astronomy).

The Aristotelian idea, as interpreted and propagated by Ptolemy, had characteristics that could be accepted by scholars and laymen alike. And it is precisely this observational question that is one of the foundations supporting the geocentric system, since the Aristotelian-Ptolemaic universe considered many phenomena observed in the sky. Connor, the idea that the entire universe revolved around her seemed logical and natural to Ptolemy's followers. Assigning movement to the ground did not seem like a reasonable idea to those who understood its weight and lightness of air.

While processing the results of Tycho Brahe's observations, Kepler encountered a problem that, even with modern computers, might seem intractable to some, and Kepler had no choice but to carry out all the calculations manually. Of course, like most astronomers of his time, Kepler was already familiar with the Copernican heliocentric system ( cm. The Copernican principle) and knew that the Earth revolves around the Sun, as evidenced by the above model of the solar system. But how exactly does the Earth and other planets rotate? Let's imagine the problem as follows: you are on a planet, which, firstly, rotates around its axis, and secondly, rotates around the Sun in an orbit unknown to you. Looking into the sky, we see other planets that also move in orbits unknown to us. Our task is to determine, from the data of observations made on our globe rotating around its axis around the Sun, the geometry of the orbits and the speed of movement of other planets. This is what, in the end, Kepler managed to do, after which, based on the results obtained, he deduced his three laws!

Another point that strengthened the geocentric idea is related to theology, since this idea, by placing the Earth at the center of the universe, strengthened the canon of Christendom, which placed man, the image and likeness of God, living in the privileged place of divine creation, Aristotle-Ptolemy's Cosmology in various aspects considered the biblical cosmos of Genesis.

Moreover, for Christians, the place where one was born, was born, was born, died, and ascended to the Father was special. However, although Christianity attributed this meaning to the earth, Connor points out that this was not an Aristotelian thought in relation to it. Aristotle never thought of the Earth as a special place or the apple tree of his eyes. The earth took the lowest position in the cosmos, where everything that was chaotic and everything that was corrupt in the end sat. The world under the moon was a private universe where living beings were born and then died, and sooner or later all life returned to rot.

First law describes the geometry of the trajectories of planetary orbits. Perhaps you remember from school course geometry that the ellipse is a set of points in the plane, the sum of the distances from which to two fixed points - tricks is equal to a constant. If this is too complicated for you, there is another definition: imagine a section of the lateral surface of a cone with a plane at an angle to its base, not passing through the base - this is also an ellipse. Kepler's first law just states that the orbits of the planets are ellipses, in one of the focuses of which the Sun is located. Eccentricities(degree of elongation) of orbits and their removal from the Sun in perihelion(the closest point to the Sun) and apogelia(the most distant point) all planets are different, but all elliptical orbits have one thing in common - the Sun is located in one of the two foci of the ellipse. After analyzing Tycho Brahe's observational data, Kepler concluded that planetary orbits are a set of nested ellipses. Before him, it simply did not occur to any of the astronomers.

However, although the Aristotelian cosmology differed significantly from the Christian idea, the geocentric theory was protected by tradition and official authorities. Geocentrism was based on everyday experience, however, the Ptolemaic system was not the only voice that tried to explain the world in Kepler's time, and dissenting voices of the geocentric system complained to demonstrate their failures.

Then there was the infinite cosmos of Nicholas of Cusa, with God in the eternal omnipresent center. Third, there was the "heliostatic" Copernican universe, in which the planets, including the Earth, revolved around the Sun, which was fixed in place. Finally, there was a model resurrected by Tycho Brahe, first discussed by Heraclides Ponticus, a student, in which the Sun revolved around the Earth and the planets revolved around the Sun.

The historical significance of Kepler's first law cannot be overestimated. Before him, astronomers believed that the planets moved exclusively in circular orbits, and if this did not fit into the scope of observations, the main circular motion was supplemented by small circles that the planets described around the points of the main circular orbit. It was, I would say, first of all a philosophical position, a kind of indisputable fact, not subject to doubt and verification. Philosophers argued that the celestial structure, unlike the earthly one, is perfect in its harmony, and since the circle and the sphere are the most perfect of geometric figures, it means that the planets move in a circle (and this delusion I still have to dispel among my students over and over again today). The main thing is that, having gained access to Tycho Brahe's vast observational data, Johannes Kepler was able to step over this philosophical prejudice, seeing that it does not correspond to the facts - just as Copernicus dared to remove the Earth from the center of the universe, faced with arguments that contradict persistent geocentric ideas, which also consisted in the "wrong behavior" of the planets in their orbits.

Figure 1 - Representation of geocentrism. At the end of the Middle Ages, the geocentric idea clashed with the German cardinal Nicholas of Cuza. Secondly, the philosophers Etienne Gilson and Filofey Boner, scholars of history Christian thought, Nicholas Cuza studied in Deventer, Heidelberg and Padua, and initially became interested in the science of law and natural sciences, theology. He designated a contemplative personality and preferred to recall political conflicts, reconciliation and peace in the Church. This work of Nicholas of Cuza is divided into three books, and our attention is drawn to the second book, which discusses the universe, which, paradoxically, the conciliatory personality of the author, collided with the geocentric system.

Second law describes the change in the speed of the planets around the sun. In a formal form, I have already given its formulation, but in order to better understand it physical meaning remember your childhood. Probably, you have ever spun around a pole on the playground, grabbing it with your hands. In fact, the planets revolve around the sun in a similar way. The farther away from the Sun the elliptical orbit takes the planet, the slower the movement, the closer to the Sun, the faster the planet moves. Now imagine a pair of line segments connecting the two positions of the planet in orbit with the focus of the ellipse containing the Sun. Together with the segment of the ellipse lying between them, they form a sector, the area of \u200b\u200bwhich is precisely the same "area that the line segment cuts off." That's what the second law says. The closer the planet is to the Sun, the shorter the segments. But in this case, in order for the sector to cover an equal area in equal time, the planet must travel a greater distance in orbit, which means that its speed of movement increases.

Moreover, according to him, the fixed stellar sphere could not be the limit of the universe, and his ideas gave the characteristics of the Earth as a star among other stars. It is important to note that Cuza moved the Sun to the center of the cosmos, attributing to it "mystical" characteristics, where the entire universe was in motion, and the center of the world had a "metaphysical" center, this center was the infinite power of God. The Polish Nicolaus Copernicus, who so inspired the theories that Kepler later formulated, studied mathematics and astronomy with Domenico Maria of Novara, one of the great critics of Ptolemy's geocentric system.

In the first two laws we are talking about the specifics of the orbital trajectories of a single planet. third law Kepler allows you to compare the orbits of the planets with each other. It says that the farther away from the Sun a planet is, the longer it takes full turn when moving in orbit and the longer, respectively, lasts a "year" on this planet. Today we know that this is due to two factors. First, the farther the planet is from the Sun, the longer the perimeter of its orbit. Secondly, as the distance from the Sun increases, the linear velocity of the planet also decreases.

Novara relied on the thought of the ancient Pythagoreans to raise the hypothesis of the Sun at the center of the universe and the Earth as a planet like the others. Novara's ideas had a great influence on the thought of Copernicus, who began to study the problematic aspects of Ptolemy's geocentric theory and devote himself to the hypothesis heliocentric system. He goes on to point out that Copernicus was aware that his system seemed to violate common sense, but his friends insisted that, once his comments were published, his theory "would prove worthy and acceptable".

Later, with the publication of "Revolution Orbium Colestium", "From revolutions celestial spheres”, the ideas of Copernicus appeared codified, describing all spheres, including the Earth revolving around the Sun. However, an aspect of reverence towards the "Astro-King" was retained in his work, as we can see in the following fragment. Among them all is the sun. Now, who would place in this temple a beautiful one among the most beautiful, such a lamp, in any place better than one from which it could illuminate everything at the same time?

In his laws, Kepler simply stated the facts, having studied and generalized the results of observations. If you had asked him what caused the ellipticity of the orbits or the equality of the areas of the sectors, he would not have answered you. It simply followed from his analysis. If you had asked him about the orbital motion of the planets in other star systems, he would not have been able to answer you either. He would have to start all over again - accumulate observational data, then analyze them and try to identify patterns. That is, he simply would not have reason to believe that another planetary system obeys the same laws as the solar system.

One of the greatest triumphs of classical Newtonian mechanics is precisely that it provides a fundamental justification for Kepler's laws and asserts their universality. It turns out that Kepler's laws can be derived from Newton's laws of mechanics, Newton's law of universal gravitation and the law of conservation of angular momentum by rigorous mathematical calculations. And if so, we can be sure that Kepler's laws apply equally to any planetary system anywhere in the universe. Astronomers who are looking for new planetary systems in space (and there are already quite a few of them) use Kepler's equations over and over again, as a matter of course, to calculate the parameters of the orbits of distant planets, although they cannot observe them directly.

Kepler's third law has played and still plays an important role in modern cosmology. When observing distant galaxies, astrophysicists detect faint signals emitted by hydrogen atoms orbiting very far from the galactic center - much further than stars usually are. Using the Doppler effect in the spectrum of this radiation, scientists determine the rotation speeds of the hydrogen periphery of the galactic disk, and using them, the angular velocities of galaxies as a whole ( cm. also dark matter). I am glad that the works of the scientist who firmly put us on the path to a correct understanding of the structure of our solar system, and today, centuries after his death, play such an important role in studying the structure of the vast Universe.

Between the spheres of Mars and the Earth is a dodecahedron (dodecahedron); between the spheres of the Earth and Venus - the icosahedron (twenty-sided); between the spheres of Venus and Mercury is an octahedron (octahedron). The resulting construction was presented by Kepler in a section on a detailed three-dimensional drawing (see figure) in his first monograph, The Cosmographic Mystery (Mysteria Cosmographica, 1596).— Translator's note.

Historically, Kepler's laws (like the principles of thermodynamics) are numbered not according to the chronology of their discovery, but in the order in which they were understood in scientific circles. In reality, the first law was discovered in 1605 (published in 1609), the second - in 1602 (published in 1609), the third - in 1618 (published in 1619).— Translator's note.

He formulated three laws of planetary motion relative to the sun. Kepler's laws. space speeds

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