The modern age in astronomy was initiated by the Polish astronomer Nicolaus Copernicus (1473-1543) whose precedent-shattering book De Revolutionibus Orbium Coelestium  ("On the Revolutions of the Celestial Spheres") was published in 1543. According to the Copernican hypothesis, the center of the universe was occupied by the sun; round it revolved the planets and among them the earth, which also rotated daily on its axis (see Fig. 1). At the time of its appearance there were no physical grounds for preferring this hypothesis to the traditional geocentric scheme; but it simplified the construction of planetary tables and thus commended itself to practical astronomers. Copernicus' theory was looked upon with great disfavor by the Church, which preferred to follow a geocentric philosophy.
   The principal complication in a planet's motion was the apparent loops in the planet's path. Copernicus showed that these could be explained if the earth was considered to revolve annually about the sun. He was thus able to eliminate the large epicycle which Ptolemy and other astronomers had been compelled to introduce into each planet's scheme of motion. However, in representing the inequalities now known to arise because a planet's orbit is elliptical, Copernicus still employed the concepts of the epicycle and deferent used by the ancients. From observation he was able to determine the relative sizes of the planetary orbits with reasonable accuracy. He also explained the slow precessional motion of the equinoctial points round the ecliptic by supposing that the earth's axis of rotation described a cone in space in a period of about 26,000 years; this explanation of the precession opened the way for Newton's dynamical interpretation of the phenomenon.
 

Tycho Brahe

   The planetary tables continued to be based upon observations inadequate in both number and accuracy. This deficiency was remedied by the other outstanding 16th-century astronomer Tycho Brahe (1546-1601). Laboring for more than 20 years at his island observatory in the Danish Sound, Tycho observed the moon and planets through all the vicissitudes of their orbits using instruments of his own ingenious design and construction. He discovered two characteristic inequalities in the moon's motion: the variation and the annual equation. Variation arises from the fact that, since the earth and the moon are generally at different distances from the sun, they are accelerated toward it by different amounts, the moon being alternately accelerated and retarded in its orbit. This phenomenon exhibits an annual periodicity (the annual equation) because the distance of the earth-moon system from the sun varies according to the time of year.
   Tycho also established that the temporary star of 1572 (now recognized to have been a supernova) was not an atmospheric explosion, but a cataclysm occurring deep in the heavens where the possibility of such changes was denied by the followers of Aristotle. From his observations of the great comet of 1577 and of later comets, Tycho found that they were at much greater distances than the moon. These discoveries all contributed to the overthrow of the Aristotelian cosmology. Tycho, however, rejected the Copernican theory in favor of a system of his own in which the earth constituted the stationary center of revolution of the sun and moon while the other planets revolved round the sun.
 

Kepler's Law

   Indirectly, Tycho Brahe nevertheless contributed materially to the triumph of the Copernican theory, for at his death his observations came into the possession of his German assistant, Johann Kepler (1571-1630), who employed them to set the planetary motions in an entirely new light. After many months of fruitless attempts to fit an old-time epicyclic system to the motion of Mars, he discovered that each planet revolves in an ellipse with the sun in one of the foci; that the radius vector joining the sun to the planet sweeps out equal areas in equal times; and that the squares of the various planets' periods of revolution are proportional to the cubes of their mean distances from the sun.
 

Physical Explanation of Kepler's Laws

   Kepler's publication of his laws (1609-1619), and his calculation of planetary tables based upon them (1627), did much to establish the Copernican theory. However, his efforts to formulate a physical explanation of his planetary laws reached no satisfactory conclusion; accepting Aristotelian mechanics, he supposed that force was required to maintain the planets in motion, not to retain them in closed orbits.
 

Galileo

   A revolution in mechanical principles was called for, and this was initiated by Kepler's great contemporary Galileo Galilei (1564-1642). Although hardly attaining, in all its generality, to the principle of inertia (which was to be Newton's first law), Galileo was led by his mechanical experiments to recognize that no force was needed to maintain a planet in circulation about the sun. It was Galileo, too, who from 1610 onward achieved the most spectacular results through application of the newly invented telescope to astronomy. With instruments of his own construction he discovered the mountains on the moon, the four largest satellites of Jupiter, the phases of the planet Venus, and anomalous appendages to Saturn. He was also one of the earliest observers to detect sunspots.
   Such discoveries weighed against traditional views of the universe in favor of the Copernican theory, which Galileo brilliantly defended in his great Dialogue Concerning the Two Chief World Systems . The publication of this book in 1632 precipitated a conflict between Galileo and the Roman Inquisition, which compelled Galileo to renounce the Copernican doctrine.
 

Newton

   The principle of inertia seems first to have been clearly stated by the French scientist and philosopher René Descartes in 1644. Its application to planetary theory was grasped by the ingenious experimenter Robert Hooke in about 1666; and it was placed first among the laws of motion by Isaac Newton (1642-1727) in his Philosophiae Naturalis Principia Mathematica  (1687; "Mathematical Principles of Natural Philosophy"). Newton proved that the moon's central acceleration could be explained by reference to the familiar force of gravity, diminished conformably to the moon's distance in accordance with the inverse square law. The concept of gravity, generalized into a force of attraction between material particles, accounted for the elliptic orbits of the planets and their satellites and for the precession of the equinoxes. Newton also went some way toward accounting for the tides, for the spheroidal shape of the earth, and for the principal inequalities of motion of the moon. (See also Celestial Mechanics.)
   Gravitational astronomy, established thus by Newton, was greatly advanced in the eighteenth century through the application of mathematical techniques more effective and general than his pure geometry. A group of continental analysts  applied the calculus to the problem of determining the motions of three mutually gravitating bodies, which makes possible approximate solutions for the systems of the earth, moon, and sun, and of the sun and two planets. These developments in lunar and planetary theory were summed up by Pierre Simon de Laplace (1749-1827) in his Traité de Mécanique Céleste ("Treatise on Celestial Mechanics"), published in parts from 1799 to 1825.
 

Royal Observatory at Greenwich

In 1675, King Charles II established the Royal Observatory at Greenwich, near London, largely in the interests of navigation. At the same time, he created the post of astronomer royal.
 

Flamsteed

The first astronomer royal, John Flamsteed (1646-1719), compiled a catalog of nearly 3,000 telescopically determined star locations, and he improved the tables of the moon's motion. At that period it was proposed to utilize the moon's rapidly changing position among the constellations as an index of standard time, comparison of which with the local time would determine the observer's longitude. This method was eventually superseded through the invention of marine chronometers, which were unaffected by the motion of a ship. The marine chronometers constructed by John Harrison in the mid-eighteenth century were the most celebrated. (See also Time.)
 

Halley

Flamsteed was succeeded as astronomer royal by Edmond Halley (1656-1742), best known for his association with the historic comet that bears his name. Newton had shown that comets, like planets, describe orbits under their gravitation toward the sun. Halley suspected that the comets seen in 1531, 1607, and 1682 were in fact the same comet, traveling in an elongated ellipse and making a return to our skies every seventy-six years or so. He predicted that the comet would return about the end of 1758. Its appearance on Christmas Day of that year was a triumphant vindication of Halley's prediction and a proof that comets, like the planets, move in obedience to definite laws. This greatly helped to bring about general acceptance of Newton's hypothesis of universal gravitation, and at the same time was a deathblow to the superstitious belief that the appearance of a comet was the herald of some disaster. Halley also announced in 1718 that, with the lapse of time, certain bright stars had changed their relative positions in the sky; all the stars were later found to be subject to such "proper motion." (See also Comet.)
 

Bradley

Halley's successor at Greenwich was James Bradley (c. 1693-1762); he traced certain periodic fluctuations in the apparent positions of the stars to the optical phenomenon of aberration (1728) and to a nutation which the moon's attraction imposes upon the mean precessional motion of the earth's axis. (See also Earth.)
Bradley's Greenwich observations long remained unsurpassed in accuracy. Classified by Friedrich Wilhem Bessel (1784-1846) in 1818, and later by Arthur Auwers, they served for the accurate determination of the proper motions of stars. Bessel's own observations provided the basis for the Bonner Durchmusterung  (1859-1862; "Astronomical Observations"), a catalog of the positions and magnitudes of some 320,000 stars.