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MOST IMPORTANT SCIENTIFIC DISCOVERIES
The laws of planetary motion. History and essence of scientific discovery
Directory / The most important scientific discoveries The planets, due to their outwardly complex movements, played a decisive role in astronomy and in general in building the foundation of mechanics and physics. Even the ancient Greek astronomers raised the question whether the observed complex movements across the sky are only a reflection of the more regular movements of the planets in space. From this time begins the theoretical construction of schemes of the planetary system, or, as we said above, the kinematics of planetary motions in space. One of the first Copernicans, the German mathematician and astronomer Erasmus Reinhold (1511–1553) compiled in 1551, based on the heliocentric system Copernicus, tables of the motion of the planets, which he called "Prussian Tables". These tables turned out to be more accurate than all the previous ones based on old schemes, and this greatly contributed to the strengthening of the idea of heliocentrism, which with great difficulty makes its way through the views that have been established for centuries and familiar to those times, as well as overcoming the reactionary ideological pressure of the church. Nevertheless, astronomers soon discovered a discrepancy between these tables and observational data on the movement of celestial bodies. For advanced scientists it was clear that the teachings of Copernicus were correct, but it was necessary to investigate more deeply and find out the laws of planetary motion. This problem was solved by the great German scientist Kepler. Johannes Kepler (1571-1630) was born in the small town of Vejle near Stuttgart. Kepler was born into a poor family, and therefore, with great difficulty, he managed to finish school and enter the University of Tübingen in 1589. Here he enthusiastically studied mathematics and astronomy. His teacher Professor Mestlin was secretly a follower of Copernicus. Of course, at the university, Mestlin taught astronomy according to Ptolemy, but at home he introduced his student to the basics of the new teaching. And soon Kepler became an ardent and staunch supporter of the Copernican theory. Unlike Maestlin, Kepler did not hide his views and beliefs. The open propaganda of the teachings of Copernicus very soon brought on him the hatred of local theologians. Even before graduating from university, in 1594, Johann was sent to teach mathematics at a Protestant school in the city of Graz, the capital of the Austrian province of Styria. Already in 1596, he published The Cosmographic Secret, where, accepting Copernicus's conclusion about the central position of the Sun in the planetary system, he tries to find a connection between the distances of the planetary orbits and the radii of the spheres, in which regular polyhedra are inscribed in a certain order and around which are described. Despite the fact that this work of Kepler was still a model of scholastic, quasi-scientific sophistication, it brought fame to the author. The famous Danish astronomer-observer Tycho Brahe (1546–1601), who was skeptical about the scheme itself, paid tribute to the young scientist’s independent thinking, knowledge of astronomy, skill and perseverance in calculations and expressed a desire to meet him. The meeting that took place later was of exceptional importance for the further development of astronomy. In 1600, Brahe, who arrived in Prague, offered Johann a job as his assistant for sky observations and astronomical calculations. Shortly before this, Brahe was forced to leave his homeland of Denmark and the observatory he built there, where he conducted astronomical observations for a quarter of a century. This observatory was equipped with the best measuring instruments, and Brahe himself was a most skilful observer. The scientist was very interested in the teachings of Copernicus, but he was not a supporter. He put forward his own explanation of the structure of the world: he recognized the planets as satellites of the Sun, and considered the Sun, Moon and stars to be bodies revolving around the Earth, behind which, thus, the position of the center of the entire Universe was preserved. Brahe did not work with Kepler for long: he died in 1601. After his death, Kepler began to study the remaining materials with data from long-term astronomical observations. Working on them, especially on materials on the motion of Mars, Kepler made a remarkable discovery: he derived the laws of planetary motion, which became the basis of theoretical astronomy. Kepler's starting point was a comparison of theory and observation. The fact is that by the end of the 4th century, the Prussian tables, compiled, as mentioned above, began to predict the motion of the planets very inaccurately. The positions of the planets observed and calculated from these tables differed by 5–XNUMX degrees, which was unacceptable in astronomical practice. It followed from this that the planetary theory of Copernicus needed to be corrected and supplemented. At the beginning, Kepler took the path of refining and complicating the Copernican scheme. Of course, he was deeply convinced of the truth of the principle of heliocentrism and began to select new combinations of circles (epicycles, eccentres). He managed to pick up, in the end, such a combination that his scheme gave an error compared to observations up to 8 minutes. But Kepler was sure that Tycho Brahe could not make such mistakes in his observations. Therefore, Kepler concluded that the theory was "guilty" because it did not agree with astronomical practice. He completely abandoned the scheme based on epicycles and eccentrics, and began to look for other schemes. Kepler came to the conclusion about the incorrectness of the opinion established since antiquity about the circular shape of planetary orbits. By calculations, he proved that the planets do not move in circles, but in ellipses - closed curves, the shape of which is somewhat different from a circle. In solving this problem, Kepler had to meet a case that, generally speaking, could not be solved by the methods of mathematics of constants. The matter was reduced to calculating the area of the sector of the eccentric circle. If this problem is translated into modern mathematical language, we will arrive at an elliptic integral. Kepler, of course, could not give a solution to the problem in quadratures, but he did not retreat before the difficulties that arose and solved the problem by summing an infinitely large number of "actualized" infinitesimals. This approach to solving an important and complex practical problem represented in modern times the first step in the prehistory of mathematical analysis. Kepler's first law suggests that the Sun is not at the center of the ellipse, but at a special point called the focus. From this it follows that the distance of the planet from the Sun is not always the same. Since the ellipse is a flat figure, the first law implies that each planet moves while remaining in the same plane all the time. The second law sounds like this: the radius vector of the planet (that is, the segment connecting the Sun and the planet) describes equal areas in equal intervals of time. This law is often called the law of areas. The second law indicates, first of all, the change in the speed of the planet in its orbit: the closer the planet comes to the Sun, the faster it moves. But this law actually gives more. It entirely determines the motion of the planet in its elliptical orbit. Both Kepler's laws have become the property of science since 1609, when his famous "New Astronomy" was published - a presentation of the foundations of new celestial mechanics. However, the release of this remarkable work did not immediately attract due attention: even the great Galileo, apparently, until the end of his days did not accept the laws of Kepler. Kepler intuitively felt that there are patterns that connect the entire planetary system as a whole. And he has been looking for these patterns in the ten years that have passed since the publication of the New Astronomy. The richest fantasy and great zeal led Kepler to his so-called third law, which, like the first two, plays a crucial role in astronomy. Kepler publishes "Harmony of the World", where he formulates the third law of planetary motions. The scientist established a strict relationship between the time of revolution of the planets and their distance from the Sun. It turned out that the squares of the periods of revolution of any two planets around the sun are related to each other as the cubes of their average distances from the Sun. This is Kepler's third law. “Kepler's third law plays a key role in determining the masses of planets and satellites,” E.A. Grebennikov and Yu.A. Ryabov write in their book. “Indeed, the periods of revolution of planets around the Sun and their heliocentric distances are determined using special mathematical processing methods observations, and the masses of the planets cannot be obtained directly from observations. We do not have grandiose cosmic scales at our disposal, on one bowl of which we would put the Sun, and on the other planets. Kepler's third law compensates for the absence of such cosmic scales, since with its help we we can easily determine the masses of celestial bodies that form a single system. Kepler's laws are also remarkable in that they are, so to speak, more accurate than reality itself. They represent the exact mathematical laws of motion for an idealized "solar system" in which the planets are material points of infinitely small mass compared to the "Sun". In reality, the planets have an appreciable mass, so that in their actual motion there are deviations from Kepler's laws. This situation takes place in the case of many currently known physical laws. Today we can say that Kepler's laws accurately describe the motion of the planet within the framework of the two-body problem, and our solar system is a multiplanetary system, so these laws are only approximate for it. It is also paradoxical that it is for Mars, whose observations led to their discovery, that Kepler's laws are less accurate. Kepler's work on the creation of celestial mechanics played an important role in the approval and development of the teachings of Copernicus. He prepared the ground for subsequent research, in particular for the discovery Newton the law of universal gravitation. Kepler's laws still retain their significance: having learned to take into account the interaction of celestial bodies, scientists use them not only to calculate the movements of natural celestial bodies, but, most importantly, also artificial ones, such as spaceships, witnesses of the emergence and improvement of which our generation is. Author: Samin D.K.
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