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Seventeenth-century scientists in the wake of the Copernican revolution developed the implications of his new cosmology and worked to refine their models of planetary motion. The German Johannes Kepler, working with data provided by the Danish astronomer Tycho Brahe, abandoned the Ptolemaic dictum that orbits were circular, and argued instead in the Astronomia nova (1609) that planetary orbits were in fact elliptical. Around the same time, Galileo Galilei used one of the telescopes he developed to discover the moons of Jupiter and the phases of Venus, and described the features of the surface of earth's moon. These results, published in Sidereus nuncius (1610), were examined by other astronomers such as Johannes Hevelius, G. B. Riccioli, and Christian Huygens, helped to demonstrate that the planets were similar in kind to the earth.
Serious advances in the understanding of planetary motion depended on more sophisticated astronomical models than were available in antiquity, models made possible by the calculus, independently developed by Sir Isaac Newton and Leibniz. Kepler's theory was largely verified by Newton's Principia Mathematica (1687), which marks the beginning of modern celestial mechanics. The implications of Newton's new theories of motion and gravitation were developed at length by such mathematicians as Jean d'Alembert, Alexis Clairaut, Leonahrd Euler, Joseph Lagrange, and Pierre Laplace.
The new mathematical models led to a considerable interest in astronomical observation among both professionals and amateurs. The eighteenth century therefore saw not only the founding of many official observatories, often in remote parts of the world, but also many observations made by dilettantes, often with homemade telescopes.
Edmond Halley, who predicted the return of the comet that bears his name in 1759, provided an experimental confirmation of Newton's theories of gravitation by predicting the effect of the planets on the comet's orbit. Halley also demonstrated for the first time that the stars were not fixed, but subject to what he called proper motion. His discoveries enabled the English theological Thomas Wright to explain the luminous band known as the Milky Way as a collection of countless stars, the galaxy of which our own sun is a part.
But perhaps the most groundbreaking astronomical observation came in 1781 from Sir William Herschel, who discovered the planet Uranus with a homemade reflecting telescope. (The next planet to be discovered was Neptune, in 1846.)
The single most ambitious application of the new Newtonian science was Laplace's Traité de mécanique céleste (5 vols, 1798-1827), which demonstrated convincingly that the entire solar system could be described accurately according to Newton's laws of gravitation. With the Newtonian thesis firmly in place until it was modified by Einstein early in the twentieth century, astronomers after Laplace were concerned largely with identifying, charting, and measuring the various celestial bodies.