The Formation of Theoretical Astronomy: the Renaissance and Early Modern Times

Early Revival

In the XV century, the German philosopher, Cardinal Nicholas of Cusa, noticeably ahead of his time, expressed the opinion that the universe is infinite, and it has no center at all — neither the Earth, nor the Sun, nor anything else occupies a special position. All celestial bodies consist of the same matter as the Earth, and, quite possibly, are inhabited. A century before Galileo, he claimed that all the luminaries, including the Earth, move in space, and every observer on it has the right to consider stationary. In the XV century, a great role in the development of observational astronomy was played by the works of Georg Purbach, as well as his student and friend Johann Muller (Regiomontane). By the way, they became the first scientists in Europe who did not have a spiritual dignity. After a series of observations, they were convinced that all the available astronomical tables, including the Alphonsine ones, were outdated: the position of Mars was given with an error of 2 °, and the lunar eclipse was an hour late. To improve the accuracy of calculations, Regiomontan compiled a new table of sines (in 1') and a table of tangents. The newly appeared book printing contributed to the fact that the corrected textbook of Purbach and the "Ephemerides" of Regiomontanus were the main astronomical guides for Europeans for decades. The Regiomontane tables were much more accurate than the previous ones and served regularly until Copernicus. They were used by Columbus and Amerigo Vespucci. Later, the tables were used for some time even for calculations based on the heliocentric model. Regiomontan also proposed a method for determining longitude by the difference between tabular and local time corresponding to a given position of the Moon. He stated that the Julian calendar diverged from the solar year by almost 10 days, which made the church think about calendar reform. Such a reform was discussed at the Lateran Council (Rome, 1512-1517) and was implemented in 1582.

The Copernican Revolution

By the 16th century, it became clear that Ptolemy's system was inadequate and led to unacceptably large calculation errors. Nicolaus Copernicus was the first to propose a detailed alternative, and based on a completely different model of the world. Copernicus' main work, On the Rotation of the Celestial Spheres (Latin De Revolutionibus Orbium Coelestium), was mostly completed in 1530, but only before his death Copernicus decided to publish it. However, in 1503-1512 Copernicus distributed among friends a handwritten summary of his theory ("A small commentary on hypotheses relating to celestial movements"), and his disciple Reticus published a clear exposition of the heliocentric system in 1539. Apparently, rumors about the new theory were widely spread already in the 1520s. According to the structure, Copernicus' main work almost repeats the Almagest in a somewhat abbreviated form (6 books instead of 13). The first book also contains axioms, but instead of the position about the immobility of the Earth, another axiom is placed — the Earth and other planets rotate around the axis and around the Sun. This concept is argued in detail, and the "opinion of the ancients" is more or less convincingly refuted. Copernicus mentions only the ancient philosophers Philolaus and Niketas as his allies. From heliocentric positions Copernicus easily explains the return motion of the planets. The following is the same material as Ptolemy's, only slightly refined: spherical trigonometry, a star catalog, the theory of the movement of the Sun and Moon, an estimate of their size and distance to them, the theory of precession and eclipses. In book III, devoted to the annual movement of the Earth, Copernicus makes an epochal discovery: he explains the "precession of the equinoxes" by shifting the direction of the earth's axis. In books V and VI, devoted to the motion of the planets, thanks to the heliocentric approach, it became possible to estimate the average distances of the planets from the Sun, and Copernicus gives these data, quite close to modern values. The Copernican world system, from the modern point of view, is not yet radical enough. All orbits are circular, the movement along them is uniform, so epicycles had to be preserved — however, instead of 80 there were 34. The mechanism of rotation of the planets is kept the same — the rotation of the spheres to which the planets are attached. But then the Earth's axis must rotate during the annual rotation, describing a cone; to explain the change of seasons, Copernicus had to introduce a third (reverse) rotation of the Earth around an axis perpendicular to the ecliptic, which he also used to explain precession. Copernicus placed a sphere of fixed stars on the boundary of the world. Strictly speaking, the Copernican model was not even heliocentric, since he did not place the Sun in the center of the planetary spheres. Ptolemaic displacement of the center of the orbit (equant) Copernicus, of course, excluded, and this was a step back — initially more accurate than Ptolemy's, Copernicus' tables soon diverged significantly from observations, which puzzled and cooled her enthusiastic fans a lot. And yet, on the whole, the Copernican model of the world was a colossal step forward. The Catholic Church initially reacted to the revival of "Pythagoreanism" complacently, some of its pillars even patronized Copernicus. Pope Clement VII, concerned about the clarification of the calendar, instructed Cardinal Wigmannstadt to give a lecture to the higher clergy on the new theory, which was listened to with attention. However, there were also ardent opponents of heliocentrism among Catholics. However, already in the 1560s, lectures on the Copernican system began at several universities in Switzerland and Italy. The mathematical basis of the Copernican model was somewhat simpler than that of Ptolemy, and this was immediately used for practical purposes: refined astronomical ("Prussian") tables were issued (1551, E. Reinhold). Among other events of the turbulent XVI century, we note that on October 5, 1582, a long-planned calendar reform was carried out (October 5 became the 15th). The new calendar was named Gregorian in honor of Pope Gregory XIII, but the real author of the project was the Italian astronomer and physician Luigi Lillio.

The invention of the telescope. Galileo

The great Italian scientist Galileo Galilei accepted the Copernican system with enthusiasm, and immediately rejected the fictitious "third movement", showing by experience that the axis of a moving top retains its direction by itself. To prove the correctness of Copernicus, he used a telescope. Polished glass lenses were known to the Babylonians; the oldest of the lenses found during excavations dates back to the VII century BC. In 1608, a telescope was invented in Holland; after learning about it in the summer of 1609, Galileo independently built a significantly improved version of it, creating the world's first refractor telescope. The magnification of the telescope was at first threefold, later Galileo brought it to 32 times. Galileo presented the results of his research in a series of articles "The Starry Messenger" (1610), causing a real flurry of optical observations of the sky among scientists. It turned out that the Milky Way consists of clusters of individual stars, that there are mountains on the Moon (up to 7 km high, which is close to the truth) and depressions, there are spots on the Sun, and Jupiter has satellites (the term "satellite" was introduced later by Kepler). Especially important was the discovery that Venus has phases; in the Ptolemaic system, Venus as the "lower" planet was always closer to the Earth than the Sun, and "fullness" was impossible. Galileo noted that the diameter of stars, unlike planets, does not increase in the telescope, and some nebulae, even in enlarged form, do not break up into stars; this is a clear sign that the distances to stars are colossal even compared to the distances in the Solar System. Galileo discovered protrusions near Saturn that he took for two moons. Then the protrusions disappeared (the ring turned), Galileo considered his observation an illusion and did not return to this topic anymore; the Saturn ring was discovered in 1656 by Christian Huygens. Galileo did not accept Kepler's ellipses, continuing to believe in the circular orbits of the planets. The reason for this may have been Kepler's excessive fascination with mystical numerology and "world harmony". Galileo recognized only positive knowledge and did not respect Pythagoreanism. Personally, he highly valued Kepler and conducted a lively correspondence with him, but he did not mention him anywhere in his works. The image in the Galileo telescope was not very clear, mainly due to chromatic aberration. For this and other reasons, the announcement of Galileo's discoveries caused many to distrust and even ridicule. Galileo was also, which was much more unpleasant, accused of heresy. He was repeatedly forced to travel to Rome, personally and in writing to explain himself to the higher clergy and the Inquisition. On March 5, 1616, the Roman congregation officially banned heliocentrism as a dangerous heresy: To assert that the Sun stands motionless in the center of the world is an absurd opinion, false from a philosophical point of view and formally heretical, since it directly contradicts St. Scripture. To assert that the Earth is not in the center of the world, that it does not remain stationary and even has a diurnal rotation, is an opinion equally absurd, false from a philosophical and sinful from a religious point of view. The book of Copernicus was included in the Index of Banned Books "before its correction". At first, the enormous scientific authority and patronage of notable persons, including Cardinal Barberini (who later became Pope Urban VIII) saved Galileo from repression. But the publication of the Dialogues on the Two Most Important Systems of the World (January-February 1632), although permitted by papal censorship, provoked the fury of the Inquisition and Pope Urban himself, who suspected that it was he who was brought out in the book under the name simpleton Simplicio. Despite the demonstratively neutral position of the author, the arguments of the Copernican Salviati in the book are clearly more convincing than his opponents. Moreover, the "Dialogue" contained assumptions about the infinity of the Universe and the multiplicity of inhabited worlds. Already in August of the same year 1632, the Dialogues were included in the notorious "Index", the negligent censor was fired, the book was withdrawn from sale, and in October the 69-year-old Galileo was summoned to the Roman Inquisition. Attempts by the Tuscan duke to delay the trial due to the poor health of the scientist and the plague quarantine in Rome were unsuccessful, and in February 1633 Galileo was forced to come to Rome. Galileo's trial lasted until June 1633. According to the verdict, Galileo was found guilty of having supported and disseminated false, heretical and contrary St. The teaching of Scripture. The scientist was forced to publicly repent and renounce the "heresy". Then he was sent to prison, but a few days later Pope Urban allowed Galileo to be released under the supervision of the Inquisition. In December, he returned to his homeland, to a village near Florence, where he spent the rest of his life under house arrest.

Kepler 's Laws

Until the middle of the XVI century, astronomical observations in Europe were not very regular. The Danish astronomer Tycho Brahe was the first to conduct systematic observations using the specially equipped Uraniborg Observatory in Denmark (Ven Island). He built large, unique instruments for Europe, thanks to which he determined the position of the luminaries with unprecedented accuracy. By this time, not only the "Alphonsine", but also the newer "Prussian tables" gave a big error. To improve the accuracy, Brahe applied both technical improvements and a special technique for neutralizing observation errors. Brahe was the first to measure the parallax of the comet of 1577 and showed that it was not an atmospheric body, as previously believed (even Galileo), but a cosmic body. Thus, he destroyed the idea, shared even by Copernicus, of the existence of planetary spheres — comets were clearly moving in free space. He measured the length of the year with an accuracy of 1 second. In the motion of the Moon, he discovered two new inequalities — the variation and the annual equation, as well as the oscillation of the inclination of the lunar orbit to the ecliptic[54]. Brahe compiled an updated catalog for 1000 stars, with an accuracy of 1'. But the main merit of Tycho Brahe is the continuous (daily), for 15-20 years [54], registration of the position of the Sun, Moon and planets[56]. For Mars, whose movement is the most uneven, observations have accumulated over 16 years, or 8 full revolutions of Mars. Brahe was familiar with the Copernican system from the "Small Comment", but immediately pointed out its shortcomings — the stars do not have parallax, Venus does not have a phase change (since there was no telescope at that time, this point of view existed), etc. At the same time, he appreciated the computational convenience of the new system and in 1588 proposed a compromise version close to the "Egyptian model" of Heraclides: the Earth is stationary in space, rotates around an axis, the Moon and the Sun revolve around it, and the other planets revolve around the Sun. Some astronomers supported this option. Brahe failed to verify the correctness of his model due to insufficient knowledge of mathematics, and therefore, having moved to Prague at the invitation of Emperor Rudolf, he invited a young German scientist Johann Kepler there (in 1600). The following year, Tycho Brahe died, and Kepler took his place. Kepler was more attracted to the Copernican system — as less artificial, more aesthetic and corresponding to the divine "world harmony" that he saw in the universe. Using observations of the Martian orbit made by Tycho Brahe, Kepler tried to find the shape of the orbit and the law of change in the velocity of Mars that best agreed with experimental data. He rejected one model after another, until, finally, this persistent work was crowned with the first success — two Kepler's laws were formulated: Each planet describes an ellipse, in one of the foci of which is the Sun. For equal intervals of time, the straight line connecting the planet with the Sun describes equal areas. The second law explains the uneven motion of the planet: the closer it is to the Sun, the faster it moves. He outlined Kepler's main ideas in the work "New Astronomy, or Physics of the Sky" (1609), and, for the sake of caution, attributed them only to Mars. Later, in the book "Harmony of the World" (1619), he extended them to all the planets and announced that he had discovered the third law: The squares of the orbital times of the planets are referred to as cubes of their average distances from the Sun. This law actually sets the velocity of the planets (the second law regulates only the change in this velocity) and allows them to be calculated if the velocity of one of the planets (for example, the Earth) and the distance of the planets to the Sun are known. Kepler published his astronomical tables dedicated to the Emperor Rudolf ("Rudolphin"). A year after Kepler's death, on November 7, 1631, Gassendi observed the passage of Mercury predicted by him across the disk of the Sun. Kepler's contemporaries were already convinced of the accuracy of the laws discovered by him, although their deep meaning remained unclear before Newton. There were no more serious attempts to resuscitate Ptolemy or propose a different system of movement.