The Story of Astronomy (14 page)

The dissemination of information meant that fierce arguments sometimes arose when conflicting theories were published. For example, when Isaac Newton (1642–1727) published his
Principia
in 1687 he wrote a whole section of his book to discredit the views of the French mathematician and philosopher René Descartes, whose work on astronomy was carried out a generation before Newton's. Descartes suggested that the planets were carried around the Sun by a system of vortices, analogous to the swirling motion of water draining into a hole. Newton studied the motion of liquids and he was able to prove, to his own satisfaction, that the motion of the planets could not be explained from the laws of fluid dynamics and that Descartes' system was therefore wrong.

A second major contribution to science, and to astronomy in particular, was the French Observatoire de Paris, or Paris Observatory. It was founded under the direction of the Académie Royale des Sciences and became the national astronomical observatory of France. Also like the Académie Royale des Sciences, it was founded by Louis XIV at the
instigation of Jean-Baptiste Colbert, and construction began in 1667. The observatory made many important advances in astronomy.

The French, like the English, were very keen to solve the problem of measuring longitude at sea. Gian-Domenico Cassini (1625–1712) studied the satellites of Jupiter and calculated the exact time when the moons were eclipsed by the shadow of the planet. Tables of the eclipses would enable navigators to use Jupiter as a clock in the sky and to tell the time at sea. The method worked well on land, but it was simply not practical to train a long telescope onto Jupiter's moons from the swaying decks of a vessel at sea. The English solution was little better. At Greenwich it was decided to use the position of the Moon to determine longitude. The problem with this method was not the observation itself, but that of predicting the lunar motion as well as the need to make numerous observations before a set of reliable tables could be published.

In the 17th century neither the Greenwich Observatory nor the Paris Observatory solved the longitude problem, but both places made significant contributions to astronomical knowledge. At Paris the astronomer Jean Picard (1620–82) measured the length of a degree of latitude with greater accuracy than any before him, helping to establish the size of the Earth. In 1672 Picard and
Cassini made the first realistic measurement of the astronomical unit, the distance from the Earth to the Sun. This was achieved by measuring a parallax for the planet Mars when it was at its closest approach to the Earth. John Flamsteed (1646–1719) and Richard Towneley (1629–1707) made the same observation in England, but the French were able to publish their results first and claim priority.

In 1676 another very important astronomical constant was measured for the first time. It was the speed of light. The measurement of the velocity of light was one of the great triumphs of the Paris Observatory and it came about almost as an accident. The Danish astronomer Ole Rømer (1644–1710) was working on the longitude problem and was trying to create a set of tables for viewing the satellites of Jupiter. He was puzzled to discover that when Jupiter moved further away from the Earth the times of the eclipses were measurably later than his tables predicted. After some consideration he correctly concluded that the delay was due to the finite velocity of light. It took about 40 minutes for light to travel from Jupiter to Earth, but this time varied according to the distance between the two planets, and the variable distance had not been allowed for in the calculations. Thus, when the Earth and Jupiter
were on the same side of the Sun, the distance between them was far less than when they were on opposite sides of the Sun. When he realized that the light therefore sometimes had further to travel, with the extra distance being as much as the diameter of the Earth's orbit, Rømer was able to calculate the speed at which light traveled from Jupiter to the Earth, and hence the speed of light itself. This was long before Albert Einstein's (1879–1955) discoveries about the speed of light; in Rømer's time nobody knew that the speed of light was the maximum achievable speed, but it was well known how important this constant was to physics and astronomy.

At the beginning of the 18th century there seemed to be very little progress in astronomy. In 1704 Newton at last published his treatise on light, but he had waited for the death of his adversary Robert Hooke (1635–1703) before going to print. Was light a wave motion or did it consist of small particles? Newton was unable to come up with a direct answer to this question. Some experiments suggested a wave motion, but others suggested that light consisted of particles. Newton knew about interference fringes; these were easily explained by the wave theory of light, but not by the particle theory. He was also puzzled as to how light could travel across the distances between the stars. This was easy to explain with the particle theory, but he wondered about how a wave could travel
through the vacuum of empty space where there was no air or other medium to carry it.

The Newtonian model of the universe stood up well to most of the questions about the motions of the planets and the stars, but there was much speculation about the nature of the universe. How far away were the stars? It had been difficult enough to measure parallax for the planets, but there seemed no way to measure the distance to the stars except by the indirect method of assuming that they were bodies with the same brightness as our own Sun. At this time a few astronomers believed that the Sun was a star, but most still believed the Sun to be the largest object in the universe with the stars as much lesser bodies. They could not believe that the universe was so large that a star as bright as the Sun could appear as a tiny dot of light in the sky.

There were other questions being asked about the universe. Why were the stars not drawn together by gravitation? Some suggested that perhaps they were drawn together, and at some time in the future the universe would end in a massive implosion. The theologians calculated from the genealogies in the Bible that the world was nearly 6,000 years old, and from the Book of Revelation they calculated that it would end in about the year 2000. Was
the universe infinite? Later, an astronomer called Heinrich Olber (1758–1840) posed that, if the universe was indeed infinite, but was filled with a constant density of stars, then the night sky should be as bright as the surface of the Sun. The sky would be bright everywhere, not black with tiny spots of light. The problem became known as Olber's paradox. Some suggested that perhaps the stars were contained in a great disc, all of them orbiting a common center, rather like a scaled-up version of the solar system. This was nearer to the reality, but still a long way away from the truth.

There was another dilemma put forward in Newton's lifetime. It involved the force of gravity. Basically every star or planet has what is called an escape velocity. Any orbiting object traveling at this speed can escape from the gravitational pull of the star or planet. For example, an object traveling at above 6.8 miles per second (11 km/sec) with no air resistance can escape from the Earth. It needed a higher velocity to escape from the Sun, but comets were discovered with velocities high enough to make their escape and they were never seen again. The escape velocity from a star of any given mass could easily be calculated by classical mechanics. The dilemma was that if a star was sufficiently massive then the escape velocity could be greater than the velocity of light. It meant that even light itself could not get away from such a massive star. It was an
idea first surmised by John Michell (1724–93) in the 18th century, but for over 200 years it was no more than a fanciful concept, for such a vast object had not been, nor could be, observed. What Michell had envisaged, however, was the phenomenon later to be known as a black hole.

In Britain, mathematics had been given a great boost by the publication of Newton's
Principia
. Although he had developed the calculus to arrive at many of his conclusions, he chose not to use the methods in the
Principia
for he feared that nobody would be able to understand them. It happened that at the same time as Newton was developing calculus there was another mathematician, Gottfried Leibniz (1646–1716) of Germany, who was working along the same lines. In spite of warnings from people like John Wallis at the Royal Society, Newton persistently refused to publish his work on calculus and the result was that Leibniz published the discovery of calculus before him. There followed a great feud as both parties tried to establish their priority, which did little to enhance the image of either Newton or Leibniz. One result of the dispute was that the British used a different notation from the rest of Europe. In the 18th century, after the death of Newton, the continental notation was the one that came into general use and British mathematicians found themselves out of
step with the rest of Europe. Thereafter, British mathematics fell into a decline, and toward the end of the century the key developments came from the Continent and from the French in particular.

The leading mathematicians of the century all wanted to make a contribution toward the theoretical aspects of astronomy. The Swiss mathematician Leonhard Euler (1707–83) was born at Basel. He worked on analytical geometry and the theory of complex numbers, but possibly his greatest work was on the mechanics of rotating bodies. He showed how to calculate their motion from their three principal axes and moments of inertia. He did much work on calculus and he tried to solve the three-body problem that had defeated Newton in the previous century. Euler was the most prolific mathematician of the century, but he was closely challenged in this field by two French mathematicians, Joseph-Louis Lagrange (1736–1813) and Pierre Simon Laplace (1749–1827).

Joseph-Louis Lagrange was born in Italy to a French family. He moved to Paris and in 1764 won an academy prize for his essay on the libration of the Moon (the small oscillation of the Moon about its mean position). His greatest work was his
Méchanique analytique
published 1788, in which he showed how to formulate mechanical problems in terms of generalized coordinates of position and momentum.

Pierre Simon Laplace was the son of a peasant farmer in Normandy. Laplace was a precocious child. He quickly left his agricultural roots behind him and arrived in Paris at the age of 17 to study mathematics. He worked on gravitational problems and the anomalies of the planetary orbits. He was able to show that the errors in the orbits of Jupiter and Saturn could be accounted for by the gravitational attraction between them. His great work was the
Méchanique celeste;
it consisted of five volumes published between 1798 and 1827.

Throughout the 18th century it was the French who produced the best mathematical theories of the mechanics of the universe. Lagrange's equations were developed to solve mechanical systems, and Laplace developed a very powerful tool for solving problems related to gravitational fields. Although the British lagged behind in mathematics at this time—relying instead on Newton's
Principia
—in terms of solving practical problems such as finding longitude and building larger and more powerful telescopes, they would continue to make great strides forward.

Italian-born French astronomer Gian-Domenico Cassini (1625–1712) was the first of four generations of his family to hold the post of director of the Paris Observatory. He discovered the true nature of the rings of Saturn, and his
telescope was powerful enough to see the gap between the rings that became known as the Cassini division. He also discovered four of Saturn's satellites and made an accurate estimate of the distance to the Sun. Amongst his other achievements, he was first to record observations of the zodiacal light and he laid down three rules that accurately describe the rotation of the Moon.

Jacques Cassini (1677–1756) succeeded his father Gian-Domenico as head of the Paris Observatory in 1712. He compiled the first tables of the orbital motions of Saturn's satellites, and in 1718 he completed the measurement of the arc of the meridian—the line of longitude passing between Dunkirk and Perpignan. In his paper
De la grandeur et de la figure de la terre
, published in 1720, he argued that the Earth was not a true sphere but was elongated at the poles.

Cassini de Thury (1714–84), sometimes known as Cassini III, continued the surveying work undertaken by his father Jacques, and he began the construction of a great topographical map of France. He, his father and his grandfather had defended the Cartesian view that the Earth was slightly elongated, but Cassini de Thury abandoned the position in the face of growing evidence that favored the opposite—the so-called Newtonian view that the Earth is flattened at the poles. Cassini de Thury succeeded his father as director of the Paris Observatory
in 1771. The
Carte géométrique de la France
(
Geometric Map of France
), or
La Carte de Cassini
, was the first map of an entire country drawn up on the basis of extensive triangulation and topographic surveys. It was published in 1789, the year of the French Revolution.

Jean-Dominique, comte de Cassini (1748–1845) succeeded his father as director of the observatory in 1784. He completed his father's map of France, which formed the basis for the
Atlas national
of 1791, depicting France's departments.

Mapping the world using a grid of intersecting circles was first implemented in the ancient world. The astronomer Ptolemy was not the first to suggest that the Earth was a sphere, but we must give him the credit for suggesting that the grid of lines we now know as latitude and longitude was the best way of mapping a set of points on such a surface. Thus one of the greatest requirements facing geographers and explorers was the need to determine the latitudes and longitudes of points on the surface of the Earth.