Kepler’s laws.

Despite promising beginnings in ancient times, physics was only a descriptive science for astronomy until 1600. But the task of physics is not only to describe the phenomena observed in nature.
It becomes a science in the modern sense of the word only when it begins to penetrate deeply into the essence of things, to know their mutual influence on each other and the connection between them, thereby revealing a universal law, i.e., a physical law. From such laws, by passing to less general, more particular laws, the whole variety of individual facts can be obtained. For this purpose, it is easier and more rational to formulate the law in mathematical form.
Describing the movement of the celestial bodies in the way it appears to the observer, we get a rather disordered picture. If we consider the Earth as a stationary body, then it is hardly possible to establish any single principle of motion. While the stars appear to circle the Earth evenly, the Moon and the planets do not.
To explain why they are now ahead of the Sun in visible motion in the sky, then lag behind the Sun, in ancient times it was assumed that the Moon and the planets move along epicycloids. Such a curve with loops is formed if the center of the circle K2 (epicycle) moves at a constant speed around the circumference of another circle K1, the so-called deferent (Fig. 1), and the circle K2 rotates uniformly. While the small circle will pass a certain segment of the path along the circumference of the large circle, this point P1 of the circle of the epicycle will move to the new position P2.
By means of such epicycles, the visible path of the planets could be fairly correctly represented. We must not forget that the telescope was invented only in 1609, and before that all observations were made with the naked eye. However, in order to achieve a more precise correspondence between this theory and observations, it was necessary to adopt all sorts of additional hypotheses later.
It was necessary to assume that the Earth is not in the center of the deferent, and the planets rotate along the secondary epicycles, which in turn move along the main epicycles. So the epi-epicycloids emerged, and the picture became incredibly confusing. But the system was still built entirely from circular movements, and the Ground stood still. This picture of the world, created by Ptolemy (90-160 AD), was jealously guarded by churchmen in the Middle Ages, because in it the Earth was considered the center of the Universe.
Therefore, the attempt made by Nicolaus Copernicus (1473-1543) to refute the Ptolemaic system and replace it with a fundamentally different theory was at that time extremely bold. Copernicus placed the Sun at the center of a system of planets orbiting the Sun in circular orbits, and thus simplified it strikingly.
As for the cause of this circular motion, Copernicus shared the views of Aristotle: circular motion is “natural” and therefore does not need further explanation.
The correct solution to the problem was found only much later. Copernicus couldn’t figure it out. This is evidenced by this example: in the era of Copernicus, scientists, without a second’s hesitation, rewritten the statement of Aristotle that a fly should have eight legs. It is not surprising that the hypothesis of “natural motion” was then considered a considerable scientific achievement.
The Copernican doctrine was difficult to gain acceptance, not only because it was fiercely attacked by the church, but also because the positions of the planets calculated on this theory did not exactly agree with observations. And the law of motion, which does not give accurate results, cannot satisfy a scientist, and, for example, even such a major astronomer of that time as Tycho Brahe, was also not convinced of the correctness of the Copernican system.
At the time when Tycho Brahe was conducting his observations in Prague, he had a very capable assistant working for him. This was Johann Kepler (1571-1630). It was Kepler who examined the Copernican system again and with extraordinary thoroughness. Since the circular orbits did not correspond to the actual movements of the planets, Kepler investigated other possible forms of trajectory.
He spent six years of hard work studying the orbit of Mars, and eventually discovered that it must be an ellipse of a certain size and shape. In contrast to a circular orbit, the planet in this case rushes around the Sun not at a constant speed, but faster near it and relatively slower in the distance.
If Kepler already knew the law of squares, he wouldn’t have to worry about it. But it was only after an exceptionally laborious comparison of his calculations with observations that he was able to discover that the product of a planet’s distance from the Sun by its speed is always constant.
So the first two laws of planetary motion, named after Kepler, were found. Kepler worked on the discovery of the third law, which relates the distance of the planet from the Sun and the time of its orbit, for another 17 years.
Here are Kepler’s laws: The
First Law. The orbit of each planet is an ellipse, in one of the foci of which is the Sun. The second law. The radius vector of the planet sweeps equal areas at equal intervals. The Third Law. The squares of the times of revolutions of the two planets around the Sun are referred to as cubes of the semimajor axes of their orbits.
It is very difficult to depict the entire solar system on a scale due to too large differences in the size of the orbits. Therefore, Figure 2 shows only the orbits of nearby planets, which are almost circular. Only the orbits of Mercury and Mars are so eccentric that it can be seen in the figure.
But planets with their moons are not the only bodies in the solar system. In the gap between the near and far planets there are many asteroids. These are small and minute bodies of various sizes and shapes that look like the wreckage of a previously existing small planet. To date, it has been possible to accurately determine the orbits of a small part of the asteroids. Since their paths intersect many times, collisions can occur quite often. Some of the fragments fall to the Ground and fall into our hands like meteorites.
The members of the solar system also include numerous comets, which are characterized by highly elongated elliptical orbits. Figure 2 shows only two cometary orbits.
The structure of comets is such that they can easily collapse. When they disintegrate, a whole stream of small meteor bodies is formed, which burn up when they enter the Earth’s atmosphere, forming a rain of”shooting stars”.