Systems of the Universe

Universe (or "world") is here taken in the astronomical sense, in its narrower or wider meanings, from our terrestrial planet to the stellar universe. The term "systems" restricts the view to the general structure and motions of the heavenly bodies, but comprises all the ages of the world the present, past, and future.

I. HISTORIC TIMES OF THE UNIVERSE

The present system, in the widest sense of the term, forms the subject of universal cosmography. Descriptions of this kind were made by Lambert, the two Herschels, Laplace, Newcomb, and others. The present section treats only of the solar system, and in particular of the disputed theories of Ptolemy and Copernicus, and the proofs in favour of the latter.

A. Ptolemaic and Copernican Systems

(1) Greek astronomy

The earliest astronomical systems are found in the Greek school. No planetary system can be discerned in Chinese or Babylonian records.

The astronomical knowledge of the Greeks shows three periods. Its infancy is represented by Philolaus and Eudoxus, of the fifth and fourth century B.C. The earth is the common centre of the universe, within the celestial sphere of the fixed stars. The great luminaries, sun and moon, and the five planets have each their concentric spheres, upon which they slide in two directions, longitude and latitude, keeping constantly the same distance from the earth.

The flourishing period of Greek astronomy extends from Heraclides Ponticus in the fourth century B.C. to Hipparchus in the second. Observation was made its basis. The different degrees of brilliancy observed in the nearest planets, Mercury, Venus, and Mars, at the times of the opposition and conjunction with the sun, pointed to heliocentric orbits, and analogy demanded the same arrangement for Jupiter and Saturn. The hypothesis was then established, probably by Heraclides himself, that the sun revolved annually, with the five planets, around the earth, while the moon remained on her sphere as before. Heraclides also made an important step in advance by asserting the diurnal rotation of the earth. His system was afterwards known as that of Tycho Brahé. Even the annual motion of the earth around the sun is mentioned by Heraclides as held by some of his contemporaries. The heliocentric system was certainly pronounced and defended by Aristarchus of Samos, although his writings are lost, and known only through Archimedes, whose works were published a year after Copernicus's death (Basle, 1544).

The period of decline had commenced when Hipparchus flashed up as the last genius among the Greek astronomers. The precession of the equinoxes, which he discovered, was made to fit the geocentric system, then prevailing, only a century after Aristarchus. The philosophical schools, in particular the Stoics, began to prefer astrology to observational astronomy. The geometrical knowledge that apparent or relative motion remains unaffected by an interchange of its component motions, as was correctly demonstrated by Apollonius, paved the way to the confusion of the solar system. It must be remembered that the apparent planetary motions are epicyclical, each planet revolving in its own orbit, the epicycle, around the sun, and with the sun, as centre of the epicycle, apparently around the earth in a common orbit, which is called the deferent orbit. These are the correct ideas, and will ever form the basis of spherical astronomy.

The decadence of astronomical concepts among the Greek philosophers appeared in two ways: First, they applied the geometrical fiction of Apollonius to the physical planetary system, supposing that the epicycle must always be the smaller of the two components in apparent motion; and, secondly, they believed that a physical planet could revolve, all alone, around a fictitious point in space. For the outer planets, Mars, Jupiter, and Saturn, the apparent orbit of the sun is the smaller component-the common deferent orbit. It cannot be made the epicycle, without introducing into the system three new circles each with a fictitious centre. This was done, but worse was to come for the inner planets, Venus and Mercury. There was no need for them to dislodge the common deferent circle, or solar orbit, as it was larger than the two planetary epicycles. And yet the centre of the deferent was moved from the sun towards the earth, at the cost of introducing into the system two new circles and two ideal centres of motion. The precession of the equinoxes discovered by Hipparchus even lent support to the concept of fictitious pivots. It seemed to swing the pole of the ecliptic around the pole of the celestial sphere. In this shape the Greek system of the heavenly bodies came down to posterity during the second century of our era through Ptolemy's Syntax . The two fundamental propositions of the geocentric system viz. that the earth has no axial rotation and no translation in space form the sixth chapter of the first book. The Syntax did not pass directly from the Alexandrian school to Europe. Greek astronomy made its round through Syria, Persia, and Tatary, under Albategnius Ibn-Yunis, Ulugh-Beg. The Ptolemaic system was accepted by the Arabic astronomers without criticism and was made known in Europe through their translations. An unintelligible Latin Almagest had taken the place of the Greek Syntax and rested like a tombstone on European astronomy.

(2) European astronomy

New astronomical life awoke in the fifteenth century in Germany. Nicholas of Cusa rejected the axioms of Ptolemy Peurbach and Muller restored the text of Ptolemy's Syntax and Copernicus made it his life-work to disentangle the cycles and epicycles of the Greek system. The task of Copernicus was harder than that of his predecessor Aristarchus on account of the unanimous acceptance of the geocentric system for more than a thousand years. The first book of Copernicus's great work On the Revolutions of the Celestial Bodies is directed against the Ptolemaic axioms on the centre of the universe and the stability of the earth. He rightly observes that the universe has no geometrical centre. He then gives clear definitions of relative and apparent motion and applies the Apollonian principle of interchanging the component motions in the opposite sense of Ptolemy. The complex heavenly machinery was explained by a triple motion of the earth one around its axis another around the sun and a third a conical motion around the axis of the ecliptic in periods of respectively one day, one year, and 25,816 years. Ptolemy's negative arguments against a moving earth were answered in a masterly manner:

• It had been objected that a disastrous centrifugal force would be created on the surface of the earth. Copernicus retorts that a far greater centrifugal force must be admitted in the outer planets and the fixed stars if they revolved around the earth.
• The resistance of the atmosphere which it was urged would sweep away every object from a moving earth was disposed of by Copernicus exactly as it is today: each planet condenses and carries its own atmosphere.
• A third difficulty was raised about necessary changes in the appearance of the constellations or in modern language about large parallaxes of the stars when viewed from opposite points of the earth's orbit. Copernicus correctly thought the stars so far away as to make the terrestrial orbit comparatively too small to show any effect in the instruments then available.

The negative arguments of Ptolemy being dispelled there remained only one positive argument in favour of Copernicus.

(3) Reaction to Copernicus

The simplicity of the heliocentric system had sufficient weight to convince a genius like Copernicus. He never called his system an hypothesis. The first who exercised censorship on the work De revolutionibus was the Reformer, Osiander. Dreading the opposition of the Wittenberg school he put the word Hypothesis on the title-page and substituted for the preface of Copernicus one of his own-all without authorization. It was more than half a century later that the Congregation of the Index pointed out nine sentences that had either to be omitted or expressed hypothetically before the book might be read freely by all.

The argument of simplicity was greatly strengthened by Kepler when he discovered the ellipticity of planetary orbits. Copernicus had found by long years observation that the inequalities of planetary motion could not be accounted for, after Ptolemaic fashion by simply placing the circular orbits excentrically. Not being prepared to abandon the circle he resorted to small epicycles. Their final removal greatly enhanced the simplicity of the Copernican system. Then came the discoveries of the aberration of light and of stellar parallaxes. While they appeared as natural consequences of the orbital motion of the earth they threw on the Ptolemaic system the condemnation of an almost infinite complexity. The fixed stars were recognized to vibrate in double ellipses their major axes parallel to the ecliptic in periods of exactly one year. The double ellipses are the images of the terrestrial orbit projected on the celestial sphere by the parallactic displacement of the stars and by the finite velocity of light. The former kind is much the smaller of the two and in most cases dwindles to immeasurable dimensions. Some twelve hundred of them have actually been observed. The aberration-ellipses have their apparent major axes all of equal length. The geocentric system not only has no explanation for these phenomena, but cannot even represent them without two epicycles for each star in the firmament. The Copernican argument of simplicity thereby received an overwhelming corroboration.

B. Direct Proofs of the Copernican System

While the argument of greater simplicity is only an indirect criterion between the two opposing systems mechanics has furnished more direct proofs. Copernicus actually had them in mind when he maintained that centrifugal force in a daily rotating celestial sphere would have to be enormous that the atmosphere is condensed around the terrestrial globe and that single planets cannot revolve around fictitious points that have no physical meaning. Kepler was too much preoccupied with geometrical studies and with the favourite idea of cosmical harmonics ( Harmonices mundi ) to recognize in the common focus of his elliptical orbits a governing power. It was reserved for Newton and Laplace to formulate the mechanical laws of celestial motion.

(1) The annual revolution of the earth around the sun is a necessary consequence of celestial mechanics.

(a) Newton computed from the velocity and distance of our satellite the amount of attraction that the earth must exercise upon it to maintain its orbital revolution. Learning then from French geometers the exact dimensions of the earth he found the force that keeps the moon in her orbit to be identical with terrestrial gravity divided by the square of the distance from the centre. The discovery led to the computation of the masses of sun and planets inclusive of the earth the latter turning out more than three hundred thousand times lighter than the sun. The mechanical conclusion is that the lighter body revolves around the heavier and not the reverse; or, in more scientific language that both revolve around their common centre of gravity which in this case lies inside the solar sphere.

(b) Our satellite furnishes another more direct proof of the annual revolution of the earth. Carl Braun shows in the Wochenschrift für Astronomie X (1867) 193 that the moon is attracted nearly three times more forcibly by the sun than by the earth. Our satellite would therefore leave us unless we revolved with it around the sun. The earth is only able to give the annual lunar orbit a serpentine shape so as to have the satellite alternately outside and inside her own orbit.

(c) Newton also alludes to comets and shows that in the Ptolemaic system each of them needs an epicycle parallel to the ecliptic to turn its orbit towards the sun. With our present cometary knowledge of comets the argument can be made stringent. Numerous comets have their orbits well determined. Over two hundred of them have passed the ecliptic within the earth's orbit, and some, like Halley's comet at its last appearance, almost in line between sun and earth. Most of the comets, including Halley's, come to us from distances beyond the orbit of Neptune. Now, computation shows that they all have their common focus in the sun and that the earth is, as a rule, outside their orbits. In the case of Halley's comet the earth was, at one time, even on the convex side of the orbit. The mechanical conclusion is as follows: If, without any regard to the earth, the comets obey the sun, the earth must do the

(2) The daily rotation of the earth

The daily rotation of the earth around its axis is demonstrated in many ways. Once the annual revolution is proved, the daily rotation becomes a matter of course. If the earth has not the power to swing the sun around its own centre once a year, it will be far less able to do so in one day; and if it cannot swing around one sun, what could it do with the countless suns of the universe? Yet, we have direct and special proofs of the diurnal rotation. They all rest on mechanics, partly celestial, partly terrestrial. Celestial mechanics has turned into proofs what formerly seemed to be difficulties. This occurred in the case of stellar parallaxes, the absence of which had been objected by Ptolemy, and the existence of which was shown by Bessel. The precession of the equinoxes also has changed its role. Laplace showed it to be due to the action of the sun on the protuberant equatorial regions of the rotating earth. The similar result of the action of the moon upon the earth is called nutation. Laplace's demonstration was based upon the flatness of the earth, which had been measured in the seventeenth century, and was also theoretically deduced by him from the existence of centrifugal force. We have here a complex reverse of roles. The consequences of centrifugal force, so strongly urged against diurnal rotation by Ptolemy, turned out to be the cause of precession, known to Hipparchus, and of several phenomena, discovered only after the time of Copernicus. Precession was still a matter of special difficulty to Copernicus, and the one of the three terrestrial motions that he could not explain. To him it was the resultant of two annual, slightly different, conical rotations of opposite direction, to which no cause could be assigned.

So much about the proofs from celestial mechanics. There are others, by means of instruments, so-called laboratory experiments. They commenced immediately after the time of Galilei and seem to have received the impulse from his trial. The experiments may be classified chronologically in five periods or groups. From 1640 to 1770 they were crude trials without result. The years from 1790 to 1831 were a period of experiments with falling bodies. The twenty years from 1832 to 1852 were a time of pendulum experiments. Then followed a period, 1852-80, of experiments with more elaborate apparatus; and the last, since 1902, may be called that of modern methods.

• The first period is represented by the names of Calignon, Mersenne, Viviani, and Newton. Calignon (1643) experimented with plumb lines, without knowing what their variations should tell. Mersenne (1643) had pieces of artillery directed to the zenith, rightly expecting a westerly deviation of the balls. Foucault's pendulum experiment was materially forestalled by Viviani at Florence (1661) and Poleni at Padua (1742), but was not formally understood. The easterly deviation of falling bodies was explicitly announced by Newton, but unsuccessfully tried by Hooke (1680). Galilei had alluded to it before, in his "Dialogo" (Opere, VII 1897), in a contradictory manner. In one place {p. 170) he denied the possibility of the experiment, in another (p. 259) he affirmed it. Lalande missed the opportunity of first making Newton's experiment at the Paris observatory. The honour was reserved to Abbate Guglielmini.
• The second period comprises the experiments with falling bodies, made by Guglielmini at Bologna (1790-2), by Benzenberg at Hamburg (1802) and Schlebusch (1804), and by Reich at Freiburg (1831) The general drift of the balls towards the east side of the meridian was unmistakable. It proved the rotation of the earth from west to east, but only in a qualitative manner. Quantitative proofs were obtained in the next period.
• Three kinds of pendulum experiments filled the third period. The horizontal pendulum was invented and tried by Hengler, in 1832, for the effects of the centrifugal force. The instrument is still waiting for a more delicate manipulator. Foucault's vertical pendulum dates from 1851, and was tried first in a cellar, then in the Paris Observatory, and last in the Pantheon. The deviation of the pendulum from the original vertical plane was clockwise, as expected by Foucault, but no quantitative measures were ever published by him. They were made in many places, chiefly in large cathedrals. The best results known are those of Secchi in Rome (1851) and of Garthe in Cologne (1852). Secchi experimented in San Ignazio, in presence of many Italian scientists, and Garthe in the cathedral, before Cardinal Geissel, royal princes, and numerous spectators. The counterproof in the southern hemisphere, where the deviation of the pendulum must be counter-clockwise, has not been made to this day. The attempt at Rio de Janeiro (1851) cannot be regarded as such. A conical pendulum was set in motion by Bravais in the same meridian room of the observatory and in the same year as the vertical pendulum of Foucault. The experiment had the advantage of being reversible. Swinging clockwise, the pendulum appeared to move faster than in the opposite sense, for the reason that the theodolite, in which it was observed, followed the rotation of the earth. Two pendulums used simultaneously, and moving in opposite directions, yielded the correct value of the diurnal rotation within a tenth of one per cent, a result never reached by Foucault's pendulum.
• The second half of the nineteenth century, the fourth period, is remarkable for complicated experiments and profound theories. The instruments were the gyroscope and the compound pendulum. The invention of the former is due to Foucault, and furnished a new proof of the diurnal rotation. It was constructed by him in three forms: the universal, the vertical, and the horizontal gyroscope, so called according to their degrees of freedom. The vertical gyroscope was perfected by Gilbert (1878) into his barogyroscope, while the horizontal gyroscope was lately introduced on warships as an astronomical compass. The proofs of Foucault and Gilbert could only be qualitative, for want of electric motors. The delicate experiment made in 1879 with the compound pendulum by Kamerlingh Onnes, comprises those of Foucault and Bravais as special cases, and in general all the movements between the plane and the circular pendulum vibrations (see "Specola Vaticana", I, 1911, Appendix 1).
• The fifth and last period of experiments falls within the early twentieth century and presents no less than four proofs, all widely different among themselves. The difficult experiment with falling bodies was brought within the walls of the physical laboratory by E. H. Hall in 1902. Under improved facilities, a fall of only twenty-three metres showed the easterly deviation better than all the preceding trials with heights from three to seven times as large. In 1904 the gyroscope was made to yield quantitative results by Föppl. An electric motor gave to a double wheel of 160 pounds a speed of over two thousand turns a minute. The rotation of the earth was strong enough to deviate the horizontal axis, which was suspended on a triple wire, six and a half degrees from the primevertical. A novel scheme had been tried by Perrot in 1859. He made a liquid flow through the central orifice of a circular vessel, and rendered the currents visible by means of floating dust. We have to take his word, that the currents were spiral-shaped, and ran counter-clockwise. The experiment was repeated by Tumlirz in Vienna (1908), and its result photographed and compared with theory. While the experiments of Hall, Föppl, and Tumlirz are repetitions of former ones, with improved methods, the next proof of the diurnal rotation is new as an experiment, although forecast in the idea by Poinsot as early as 1851. It was carried out at the Vatican Observatory in 1909. Its principle is that of equal areas described in equal times, applied to a horizontal beam suspended in form of a torsion balance, on which heavy masses can be moved. The shifting of the masses from extremity to centre will make the beam turn faster than the earth; the opposite will happen in the reverse case. The last proof had never been proposed before, and consists in observing the thread of the Atwood machine in a telescope. Viewed in the meridian, the thread of the falling weight is seen to come down east of the plumb-line, but viewed in the prime vertical it remains exactly plumb. This experiment was likewise carried out at the Vatican Observatory in 1912 (see "Specola Vaticana", I, 1911, appendix II, 1912).

  Some writers have expressed surprise that Catholic scientists were allowed to take part in the experiments, e.g. that Bonfioli, domestic prelate to Pius VI assisted Guglielmini in measuring the impressions of the balls on the plate of wax, or that Secchi demonstrated the rotation of the earth in Rome "before all the people" (Wolf, "Handbuch", I, Zurich, 1890, no. 262 c). We must remember, however, that what was condemned in a former age was not the experiment but a then gratuitous assertion.

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II. PAST AND FUTURE OF THE WORLD

How the world has developed into its present shape, and how it will pass out of it, science may never tell. Cosmogony is the accepted name for all the hypotheses on the past (from kosmos world, and gignesthai to originate). A corresponding form from the Greek, to designate the speculations on the future of the world, cosmothany (world's death), has been used; more correct formations are perhaps: cosmophthory ( phthora , corruption) or cosmodysy ( dysis, occasus , decline). World must here be taken in all its narrower or wider meanings, as earth, solar system, stellar system, universe.

A. Cosmogony

No cosmogony can really claim to be a scientific theory or even hypothesis, in the proper sense of a systematic development of the details from a definite number of assumed principles. Proposition and rejection are alike vague and uncertain, and must be so, as processes of extrapolation from laboratory laws to the fabric of the Creator.

For more information on mythical cosmogony, the reader is referred to the article COSMOGONY. For Biblical cosmogony, see HEXAEMERON.

B. Cosmodysy

This is the proposed name for all the hypotheses on the future of the world. The literature on cosmodysy is far less extensive than that on cosmogony. The youth of the world seems to exert a stronger charm on human speculation than its old age and decline. There does not seem to exist any mythical cosmodysy, and very little can be found on scientific cosmodysies. So much the more explicit and detailed is Biblical cosmodysy (see DIVINE JUDGMENT, IV). And yet, from a scientific point of view, the prospective conclusion from the known premises of the present world would seem to be better warranted than retrospective speculations upon cosmical conditions entirely unknown.

One such theory is the extinction theory. This theory rests on a certain irreversible process, common to all natural phenomena, called entropy. While the sum total of cosmical energy is supposed to remain constant, the amount of potential energy is steadily diminishing. It is the unstable condition of potential energy that animates all activity in the universe. Drifting as it is towards stability. it will end in exhaustion and repose. The process is not reversible and consequently not cyclical. Applying it to the earth but abstracting from organic life, it will mean the extinction of its interior plutonic power and of its rotary speed. The raising and shifting of continents, the continual tremors, occasional earthquakes and volcanic eruptions, the gradual shrinkage of the crust and the wandering of the polar ice caps, are so many irretrievable losses of potential energy.

Our scanty science of cosmodysy might be a temptation to look for further information in the Scripture. Will the darkening of sun and moon, and the falling of stars, lend support to the extinction theory, for instance? The like question may be raised in cosmogony. Can Genesis be consulted to decide between the various hypotheses?

The answer is given by an attempt, made three centuries ago, in cosmography. The Scriptural decision of the controversy, whether the solar system be geocentric or heliocentric, was bound to be a failure either way. Cosmogonic revelation was given to impress on the human race its physical and moral dependency upon the Creator. Likewise has cosmodysic revelation the purpose of holding out to mankind the final administration of justice. Purely scientific curiosity will find no satisfaction in Scripture.