Myths and Marvels of Astronomy

by Richard A. Proctor

In passing, I may remark that the failure of Galileo to ascertain the real shape of these appendages has always seemed to me to afford striking evidence of the importance of careful reasoning upon all observations whose actual significance is not at once apparent. If Galileo had been thus careful to analyse his observations of Saturn, he could not have failed to ascertain their real meaning. He had seen the planet apparently attended by two large satellites, one on either side, 'as though supporting the aged Saturn upon his slow course around the sun.' Night after night he had seen these attendants, always similarly placed, one on either side of the planet, and at equal distances from it. Then in 1612 he had again examined the planet, and lo, the attendants had vanished, 'as though Saturn had been at his old tricks, and had devoured his children.' But after a while the attendant orbs had reappeared in their former positions, had seemed slowly to grow larger, until at length they had presented the appearance of two pairs of mighty arms encompassing the planet. If Galileo had reasoned upon these changes of appearance, he could not have failed, as it seems to me, to interpret their true meaning. The three forms under which the rings had been seen by him sufficed to indicate the true shape of the appendage. Because Saturn was seen with two attendants of apparently equal size and always equi-distant from him, it was certain that there must be some appendage surrounding him, and extending to that distance from his globe. Because this appendage disappeared, it was certain that it must be thin and flat. Because it appeared at another time with a dark space between the arms and the planet, it was certain that the appendage is separated by a wide gap from the body of the planet. So that Galileo might have concluded—not doubtfully, but with assured confidence—that the appendage is a thin flat ring nowhere attached to the planet, or, as Huyghens said some forty years later, Saturn 'annulo cingitur tenui, plano, nusquam cohærente.' Whether such reasoning would have been accepted by the contemporaries of Galileo may be doubtful. The generality of men are not content with reasoning which is logically sound, but require evidence which they can easily understand. Very likely Huyghens' proof from direct observation, though in reality not a whit more complete and far rougher, would have been regarded as the first true proof of the existence of Saturn's ring, just as Sir W. Herschel's observation of one star actually moving round another was regarded as the first true proof of the physical association of certain stars, a fact which Michell had proved as completely and far more neatly half a century earlier, by a method, however, which was 'caviare to the general.'

However, as matters chanced, the scientific world was not called upon to decide between the merits of a discovery made by direct observation and one effected by means of abstract reasoning. It was not until Saturn had been examined with much higher telescopic power than Galileo could employ, that the appendage which had so perplexed the Florentine astronomer was seen to be a thin flat ring, nowhere touching the planet, and considerably inclined to the plane in which Saturn travels. We cannot wonder that the discovery was regarded as a most interesting one. Astronomers had heretofore had to deal with solid masses, either known to be spheroidal, like the earth, the sun, the moon, Jupiter, and Venus, or presumed to be so, like the stars. The comets might be judged to be vaporous masses of various forms; but even these were supposed to surround or to attend upon globe-shaped nuclear masses. Here, however, in the case of Saturn's ring, was a quoit-shaped body travelling around the sun in continual attendance upon Saturn, whose motions, no matter how they varied in velocity or direction, were so closely followed by this strange attendant that the planet remained always centrally poised within the span of its ring-girdle. To appreciate the interest with which this strange phenomenon was regarded, we must remember that as yet the law of gravity had not been recognised. Huyghens discovered the ring (or rather perceived its nature) in 1659, but it was not till 1666 that Newton first entertained the idea that the moon is retained in its orbit about the earth by the attractive energy which causes unsupported bodies to fall earthwards; and he was unable to demonstrate the law of gravity before 1684. Now, in a general sense, we can readily understand in these days how a ring around a planet continues to travel along with the planet despite all changes of velocity or direction of motion. For the law of gravity teaches that the same causes which tend to change the direction and velocity of the planet's motion tend in precisely the same degree to change the direction and velocity of the ring's motion. But when Huyghens made his discovery it must have appeared a most mysterious circumstance that a ring and planet should be thus constantly associated—that during thousands of years no collision should have occurred whereby the relatively delicate structure of the ring had been destroyed.

Only six years later a discovery was made by two English observers, William and Thomas Ball, which enhanced the mystery. Observing the northern face of the ring, which was at that time turned earthwards, they perceived a black stripe of considerable breadth dividing the ring into two concentric portions. The discovery did not attract so much attention as it deserved, insomuch that when Cassini, ten years later, announced the discovery of a corresponding dark division on the southern surface, none recalled the observation made by the brothers Ball. Cassini expressed the opinion that the ring is really divided into two, not merely marked by a dark stripe on its southern face. This conclusion would, of course, have been an assured one, had the previous observation of a dark division on the northern face been remembered. With the knowledge which we now possess, indeed, the darkness of the seeming stripe would be sufficient evidence that there must be a real division there between the rings; for we know that no mere darkness of the ring's substance could account for the apparent darkness of the stripe. It has been well remarked by Professor Tyndall, that if the moon's whole surface could be covered with black velvet, she would yet appear white when seen on the dark background of the sky. And it may be doubted whether a circular strip of black velvet 2000 miles wide, placed where we see the dark division between the rings, would appear nearly as dark as that division. Since we could only admit the possibility of some substance resembling our darker rocks occupying this position (for we know of nothing to justify the supposition that a substance as dark as lampblack or black velvet could be there), we are manifestly precluded from supposing that the dark space is other than a division between two distinct rings.

Yet Sir W. Herschel, in examining the rings of Saturn with his powerful telescopes, for a long time favoured the theory that there is no real division. He called it the 'broad black mark,' and argued that it can neither indicate the existence of a zone of hills upon the ring, nor of a vast cavernous groove, for in either case it would present changes of appearance (according to the ring's changes of position) such as he was unable to detect. It was not until the year 1790, eleven years after his observations had commenced, that, perceiving a corresponding broad black mark upon the ring's southern face, Herschel expressed a 'suspicion' that the ring is divided into two concentric portions by a circular gap nearly 2000 miles in width. He expressed at the same time, very strongly, his belief that this division was the only one in Saturn's ring-system.

A special interest attached at that time to the question whether the ring is divided or not, for Laplace had then recently published the results of his mathematical inquiry into the movements of such a ring as Saturn's, and, having proved that a single solid ring of such enormous width could not continue to move around the planet, had expressed the opinion that Saturn's ring consists in reality of many concentric rings, each turning, with its own proper rotation rate, around the central planet. It is singular that Herschel, who, though not versed in the methods of the higher mathematics, had considerable native power as a mathematician, was unable to perceive the force of Laplace's reasoning. Indeed, this is one of those cases where clearness of perception rather than profundity of mathematical insight was required. Laplace's equations of motion did not express all the relations involved, nor was it possible to judge, from the results he deduced, how far the stability of the Saturnian rings depended on the real structure of these appendages. One who was well acquainted with mechanical matters, and sufficiently versed in mathematics to understand how to estimate generally the forces acting upon the ring-system, could have perceived as readily the general conditions of the problem as the most profound mathematician. One may compare the case to the problem of determining whether the action of the moon in causing the tidal wave modifies in any manner the earth's motion of rotation. We know that as a mathematical question this is a very difficult one. The Astronomer Royal, for example, not long ago dealt with it analytically, and deduced the conclusion that there is no effect on the earth's rotation, presently however, discovering by a lucky chance a term in the result which indicates an effect of that kind. But if we look at the matter in its mechanical aspect, we perceive at once, without any profound mathematical research, that the retardation so hard to detect mathematically must necessarily take place. As Sir E. Beckett says in his masterly work, Astronomy without Mathematics, 'the conclusion is as evident without mathematics as with them, when once it has been suggested.' So when we consider the case of a wide flat ring surrounding a mighty planet like Saturn, we perceive that nothing could possibly save such a ring from destruction if it were really one solid structure.

To recognise this the more clearly, let us first notice the dimensions of the planet and rings.

We have in Saturn a globe about 70,000 miles in mean diameter, an equatorial diameter being about 73,000 miles, the polar diameter 66,000 miles. The attractive force of this mighty mass upon bodies placed on its surface is equal to about one-fifth more than terrestrial gravity if the body is near the pole of Saturn, and is almost exactly the same as terrestrial gravity if the body is at the planet's equator. Its action on the matter of the ring is, of course, very much less, because of the increased distance, but still a force is exerted on every part of the ring which is comparable with the familiar force of terrestrial gravity. The outer edge of the outer ring lies about 83,500 miles from the planet's centre, the inner edge of the inner ring (I speak throughout of the ring-system as known to Sir W. Herschel and Laplace) about 54,500 miles from the centre, the breadth of the system of bright rings being about 29,000 miles. Between the planet's equator and the inner edge of the innermost bright ring there intervenes a space of about 20,000 miles. Roughly speaking, it may be said that the attraction of the planet on the substance of the ring's inner edge is less than gravity at Saturn's equator (or, which is almost exactly the same thing, is less than terrestrial gravity) in about the proportion of 9 to 20; or, still more roughly, the inner edge of Saturn's inner bright ring is drawn inwards by about half the force of gravity at the earth's surface. The outer edge is drawn towards Saturn by a force less than terrestrial gravity in the proportion of about 3 to 16—say roughly that the force thus exerted by Saturn on the matter of the outer edge of the ring-system is equivalent to about one-fifth of the force of gravity at the earth's surface.

It is clear, first, that if the ring-system did not rotate, the forces thus acting on the material of the rings would immediately break them into fragments, and, dragging these down to the planet's equator, would leave them scattered in heaps upon that portion of Saturn's surface. The ring would in fact be in that case like a mighty arch, each portion of which would be drawn towards Saturn's centre by its own weight. This weight would be enormous if Bessel's estimate of the mass of the ring-system is correct. He made the mass of the ring rather greater than the mass of the earth—an estimate which I believe to be greatly in excess of the truth. Probably the rings do not amount in mass to more than a fourth part of the earth's mass. But even that is enormous, and subjected as is the material of the rings to forces varying from one-half to a fifth of terrestrial gravity, the strains and pressures upon the various parts of the system would exceed thousands of times those which even the strongest material built up into their shape could resist. The system would no more be able to resist such strains and pressures than an arch of iron spanning the Atlantic would be able to sustain its own weight against the earth's attraction.

It would be necessary then that the ring-system should rotate around the planet. But it is clear that the proper rate of rotation for the outer portion would be very different from the rate suited for the inner portion. In order that the inner portion should travel around Saturn entirely relieved of its weight, it should complete a revolution in about seven hours twenty-three minutes. The outer portion, however, should revolve in about thirteen hours fifty-eight minutes, or nearly fourteen hours. Thus the inner part should rotate in little more than half the time required by the outer part. The result would necessarily be that the ring-system would be affected by tremendous strains, which it would be quite unable to resist. The existence of the great division would manifestly go far to diminish the strains. It is easily shown that the rate of turning where the division is, would be once in about eleven hours and twenty-five minutes, not differing greatly from the mean between the rotation-periods for the outside and for the inside edges of the system. Even then, however, the strains would be hundreds of times greater than the material of the ring could resist. A mass comparable in weight to our earth, compelled to rotate in (say) nine hours when it ought to rotate in eleven or in seven, would be subjected to strains exceeding many times the resistances which the cohesive power of its substance could afford. That would be the condition of the inner ring. And in like manner the outer ring, if it rotated in about twelve hours and three-quarters, would have its outer portions rotating too fast and its inner portions too slowly, because their proper periods would be fourteen hours and eleven hours and a half respectively. Nothing but the division of the ring into a number of narrow hoops could possibly save it from destruction through the internal strains and pressures to which its material would be subjected.

Even this complicated arrangement, however, would not save the ring-system. If we suppose a fine hoop to turn around a central attracting body as the rings of Saturn rotate around the planet, it may be shown that unless the hoop is so weighted that its centre of gravity is far from the planet, there will be no stability in the resulting motions; the hoop will before long be made to rotate eccentrically, and eventually be brought into destructive collision with the central planet.