By the end of the XVIII century, astronomers received powerful research tools — both observational (improved reflectors) and theoretical (celestial mechanics, photometry, etc.). The development of methods of celestial mechanics continued. As the accuracy of observations increased, deviations of the planets' motion from Keplerian orbits were revealed. The theory of perturbation accounting for the many—body problem was created by the efforts of Euler, A. Clerault, Lagrange, but above all by Pierre Simon Laplace, who investigated the most complex cases, including the most obscure problem — the stability of the system. After Laplace's work, the last doubts disappeared that Newton's laws are sufficient to describe all celestial movements. Among other things, Laplace developed the first complete theory of the motion of Jupiter's moons, taking into account the mutual influence and disturbances from the Sun. This problem was very urgent, since it was the basis of the only known accurate method of determining longitude at sea, and the previously compiled tables of the positions of these satellites became obsolete very quickly.

William Herschel

An important role in the development of astronomy was played by the great English scientist of German origin William Herschel. He built reflectors unique for that time with a mirror diameter of up to 1.2 m and masterfully used them. Herschel discovered the seventh planet — Uranus (1781) and its satellites (1787), rotating "in the wrong direction" (1797), several satellites of Saturn, discovered seasonal changes in the polar caps of Mars, explained the stripes and spots on Jupiter as clouds, measured the rotation period of Saturn and its rings (1790). He discovered that the entire Solar system is moving towards the constellation Hercules (1783), while studying the spectrum of the Sun discovered infrared rays (1800), established the correlation of solar activity (by the number of spots) and terrestrial processes — for example, wheat harvest and prices for it. But his main occupation for all thirty years of observations was the study of stellar worlds. He has registered over 2,500 new nebulae. Among them were doubles and multiples; some were connected by jumpers, which Herschel interpreted as the formation of new star systems. However, at that time this discovery was ignored; interacting galaxies were rediscovered already in the XX century.
Herschel was the first to systematically apply statistical methods in astronomy (introduced earlier by Michel), and with their help concluded that the Milky Way is an isolated stellar island that contains a finite number of stars and has a flattened shape. He estimated the distances to nebulae at millions of light-years. In 1784, Herschel noted that the world of nebulae has a large—scale structure - clusters and belts ("layers"); now the largest belt is considered as the equatorial zone of the Metagalaxy. He explained the variety of forms of clusters and nebulae by the fact that they are at different stages of development. Some round-shaped nebulae, sometimes with a star inside, he called planetary and considered clusters of diffuse matter in which a star and a planetary system are formed. In fact, almost all the nebulae he discovered were galaxies, but in essence Herschel was right — the process of star formation is happening today.
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