Small as these satellites seem in [Fig. 86], they are really bodies of considerable size, as appears from [Fig. 90], where their dimensions are compared with those of the earth and moon, save that the fifth satellite is not included. This one is so small as to escape all attempts at measuring its diameter, but, judging from the amount of light it reflects, the period printed with the legend of the figure represents a gross exaggeration of this satellite's size.
Fig. 90.—Jupiter's satellites compared with the earth and moon.
Like the moon, each of these satellites may fairly be considered a world in itself, and as such a fitting object of detailed study, but, unfortunately, their great distance from us makes it impossible, even with the most powerful telescope, to see more upon their surfaces than occasional vague markings, which hardly suffice to show the rotations of the satellites upon their axes.
One striking feature, however, comes out from a study of their influence in disturbing each other's motion about Jupiter. Their masses and the resulting densities of the satellites are smaller than we should have expected to find, the density being less than that of the moon, and averaging only a little greater than the density of Jupiter itself. At the surface of the third satellite the force of gravity is but little less than on the moon, although the moon's density is nearly twice as great as that of III, and there can be no question here of accounting for the low density through expansion by great heat, as in the case of the sun and Jupiter. It has been surmised that these satellites are not solid bodies, like the earth and moon, but only shoals of rock and stone, loosely piled together and kept from packing into a solid mass by the action of Jupiter in raising tides within them. But the explanation can hardly be regarded as an accepted article of astronomical belief, although it is supported by some observations which tend to show that the apparent shapes of the satellites change under the influence of the tidal forces impressed upon them.
141. Eclipses of the satellites.—It may be seen from [Fig. 89] that in their motion around the planet Jupiter's satellites must from time to time pass through his shadow and be eclipsed, and that the shadows of the satellites will occasionally fall upon the planet, producing to an observer upon Jupiter an eclipse of the sun, but to an observer on the earth presenting only the appearance of a round black spot moving slowly across the face of the planet. Occasionally also a satellite will pass exactly between the earth and Jupiter, and may be seen projected against the planet as a background. All of these phenomena are duly predicted and observed by astronomers, but the eclipses are the only ones we need consider here. The importance of these eclipses was early recognized, and astronomers endeavored to construct a theory of their recurrence which would permit accurate predictions of them to be made. But in this they met with no great success, for while it was easy enough to foretell on what night an eclipse of a given satellite would occur, and even to assign the hour of the night, it was not possible to make the predicted minute agree with the actual time of eclipse until after Roemer, a Danish astronomer of the seventeenth century, found where lay the trouble. His discovery was, that whenever the earth was on the side of its orbit toward Jupiter the eclipses really occurred before the predicted time, and when the earth was on the far side of its orbit they came a few minutes later than the predicted time. He correctly inferred that this was to be explained, not by any influence which the earth exerted upon Jupiter and his satellites, but through the fact that the light by which we see the satellite and its eclipse requires an appreciable time to cross the intervening space, and a longer time when the earth is far from Jupiter than when it is near.
For half a century Roemer's views found little credence, but we know now that he was right, and that on the average the eclipses come 8m. 18s. early when the earth is nearest to Jupiter, and 8m. 18s. late when it is on the opposite side of its orbit. This is equivalent to saying that light takes 8m. 18s. to cover the distance from the sun to the earth, so that at any moment we see the sun not as it then is, but as it was 8 minutes earlier. It has been found possible in recent years to measure by direct experiment the velocity with which light travels—186,337 miles per second—and multiplying this number by the 498s. (= 8m. 18s.) we obtain a new determination of the sun's distance from the earth. The product of the two numbers is 92,795,826, in very fair agreement with the 93,000,000 miles found in [Chapter X]; but, as noted there, this method, like every other, has its weak side, and the result may be a good many thousands of miles in error.
It is worthy of note in this connection that both methods of obtaining the sun's distance which were given in [Chapter X] involve Kepler's Third Law, while the result obtained from Jupiter's satellites is entirely independent of this law, and the agreement of the several results is therefore good evidence both for the truth of Kepler's laws and for the soundness of Roemer's explanation of the eclipses. This mode of proof, by comparing the numerical results furnished by two or more different principles, and showing that they agree or disagree, is of wide application and great importance in physical science.