The Trouvelot astronomical drawings manual

by E. L. Trouvelot

The shadows cast by the planet on the ring, and by the ring on the planet, are very interesting phenomena, inasmuch as they enable the astronomer to recognize the form of the surface which receives them. The shadow cast by the ring on the ball is not quite so interesting as the other, although it has served to prove that the surface of this globe is not smooth, as is likewise suggested by its mottled appearance. I have sometimes found, as have also other observers, that the outline of this shadow upon the ball was irregular and indented, an observation which proves either that the surface of the ball is irregular, or that the border of the ring casting the shadow was jagged. The shadow of the globe on the rings has much more interest, as it enables us to get at some knowledge of the form of the surface of the rings, which otherwise is very difficult to discover, owing to the oblique position in which we always see them.

In general, the shadow of the ball on the middle ring has its outline concave towards the planet; while on the outer ring it is usually slanting, and at a greater distance from the limb than on the middle, and dusky rings. This form of the shadow evidently proves that the middle ring stands at a higher level than the two others, especially towards its outer margin. The system seems to increase gradually in thickness from the inner border of the dusky ring to the vicinity of the outer margin of the middle ring, after which it rapidly diminishes on this border, while the surface of the outer ring is almost level.

But this surface is by no means fixed, as its form sometimes changes, as proved by my observations and those of others. As may be noticed on Plate X., the outline of the shadow of the planet on the rings is strongly deviated towards the planet, near the outer margin of the middle ring; the notch indicating an abrupt change of level, and a rise of the surface at that point. Some observers have endeavored to explain these deviations by the phenomena of irradiation, from which it would follow that the maximum effect of deviation should be observed where the ring is the brightest, which does not accord with observation; as the deepest depression in the shadow is not to be found usually at the brightest part, which is towards the outer border of the middle ring, but occurs near its centre. From these observations it is undoubtedly established that the surface of the rings is far from being flat throughout, and is, besides, not permanent, but changes, as would, for instance, the surface of a large mass of clouds seen from the top of a high mountain. In general, the system is thickest not very far from the outer border of the intermediary ring.

Some interesting phenomena which I had occasion to observe before and after the passage of the Sun through the plane of the rings, on February 6th, 1878, conclusively show that the surface of this system cannot be of a uniform level, but must be thicker towards the outer border of the middle ring, thence gradually sloping towards the planet. Many of my observations irresistibly lead to this conclusion. As it would, however, be out of place to have them recorded here in detail, I will simply give one of the most characteristic among them.

From December 18th, 1877, when the Sun was about 41' above the plane of the rings, to February 6th, 1878, the day of its passage through their plane, the illuminated surface of this system gradually decreased in breadth with the lowering of the Sun, until it was lost sight of, February 5th, on the eve of the passage of the Sun through their plane. The phenomenon in question consisted in the gradual invasion of their illuminated surface by what appeared to be a black shadow, apparently cast by the front part of the outer portion of the middle ring the nearest to the Sun. On January 25th, when the elevation of the Sun above the plane of the rings was reduced to 15', the shadow thus cast had extended so far on their surface that it reached the shadow cast by the globe on the opposite part of the ring in the east, and accordingly the remaining portion of the illuminated surface of the eastern ansa then appeared entirely disconnected from the ball, by a large dark gap, corresponding in breadth to that of the globe's shadow on the rings. On February 4th, when the Sun was only 5' above the plane of the rings, their illuminated and only visible surface was reduced to a mere thread of light, which on the 5th appeared broken into separate points. It is evident that the phenomenon was not caused by the obliquity of the ring as seen from our globe, since the elevation of the Earth above the plane of the rings—which on December 18th was 3° 20'—was still 1° 20' on the 4th of February. In ordinary circumstances, when the Sun is a little more elevated, and the rings seen at this last angle, they appear quite broad and conspicuous, and even the dark open space separating the dusky ring from the planet is perfectly visible on the ansæ, where the Earth's elevation above their plane is reduced to 40'. It is also evident that the phenomenon was not to be attributed to the reduction of the light which they received from the Sun, although the illumination in February might be expected to be comparatively feeble, since the Sun then shone upon the rings so obliquely; yet (on the supposition that their surface is flat) they should have been illuminated throughout, and if not very brightly, sufficiently so, at least, to make them visible and as bright as was the narrow thread of light observed on the 4th of February. The phenomenon actually observed may be explained most readily by assuming, as other phenomena also indicate, that the surface of the ring is not flat, but more elevated towards, or in the vicinity of its outer border, from which place it slopes inwardly towards the planet. On this assumption, it is evident that the elevated part of the ring the nearest to the Sun would cast a shadow, which, with the increasing obliquity of the Sun, would gradually cover the whole surface comprised within the elevated part, and thus become invisible to us. Several observations made by Bond and other observers undoubtedly show the same phenomenon, and do not seem to be intelligible on any other supposition. From my observations made in 1881 it would appear, however, that the opposite surfaces of the rings do not exactly correspond in form, but this may not be a permanent feature, as the surface of this system is subject to changes, as already shown.

The dimensions of the rings are great, the diameter of the outer one being no less than 172,982 miles, the distance from the centre of the globe to the outer border of the system being, therefore, 86,491 miles. The breadth of the outer ring is 9,941 miles; that of the principal division, 2,131 miles; that of the middle ring, 19,902 miles, and that of the dusky ring, 8,772 miles. The breadth of all the rings taken together is, therefore, 40,746 miles. The interval between the surface of Saturn and the inner border of the dusky ring is 7,843 miles.

The thickness of the system of rings has been variously estimated by astronomers, on account of the great difficulties attending its determination. While Sir John Herschel estimated it at more than 250 miles, G. P. Bond reduces it to 40 miles. Both of these numbers are evidently too small, as so slight a thickness cannot explain the observed phenomenon of the shadow cast by a portion of the ring on its own surface, when the Sun is very low in its horizon, as shown above.

The plane of the system of rings is inclined 27° to the planet's orbit, and is parallel, or at least very nearly so, with the equator of the planet, passing, therefore, through its centre, and dividing its globe into northern and southern hemispheres. Seen from the Earth, a portion of the ring always appears projected in front of the planet, thus concealing a small part of its globe, while the opposite portion passes behind the globe, which hides it from sight.

As the plane of the ring is not affected by the motion of the planet around the Sun, but always remains parallel to itself, it follows that as Saturn advances in its orbit the rings must successively present themselves to us under various angles of inclination, appearing, therefore, more or less elliptical, and presenting two maxima and two minima of inclination in the course of one of its revolutions. As the revolution of Saturn is accomplished in 29½ years, the maxima and the minima must recur every 14 years and 9 months; the maxima being separated from the minima by an interval of 7 years and 4½ months.

When Saturn arrives at the two opposite points of its orbit, where the major axis of its ring is at right angles to the line joining its centre to that of the Sun, the ring, which is then viewed at an inclination of 27°, the greatest angle at which it can ever be seen, has reached its maximum opening, the smaller diameter of its ellipse being then about half that of the larger. At this moment the outer ring projects north and south beyond the globe, which is then completely enclosed in its ellipse. The maximum opening of the northern surface of the ring takes place, at present, when Saturn arrives in longitude 262°, in the constellation Sagittarius, and that of the southern surface when it arrives in longitude 82° in the constellation Taurus. When, on the contrary, Saturn reaches the two opposite points of its orbit, where the plane of its ring is parallel to the line joining its centre to that of the Sun, the opening vanishes, as only the thin edge of the ring is then presented to the Sun and receives its light, the rest being in darkness. At this moment the ring disappears, except in the largest telescopes, where it is seen as an exceedingly thin thread of light; and the Saturnian globe, having apparently lost its ring, appears solitary in the sky, like the other planets. The disappearance of the ring from this cause occurs now when Saturn arrives at 90° from either of the positions of maximum inclination, that is, in longitude 352° in the constellation Pisces, and in longitude 172° in the constellation Leo.