very nearly, although not exactly, coincident with that of the equator of the planet, or parallel to its belts. This latter plane is inclined 3° 5' 30" to the orbit of the planet, and is therefore but little different from the plane of the ecliptic. Accordingly, we see their orbits projected very nearly into straight lines, in which they appear to oscillate to and fro, sometimes passing before Jupiter, and casting shadows on his disc (which are very visible in good telescopes, like small round ink spots, the circular form of which is very evident), and sometimes disappearing behind the body, or being eclipsed in its shadow at a distance from it. It is by these eclipses that we are furnished with accurate data for the construction of tables of the satellites' motions, as well as with signals for determining differences of longitude. (536.) The eclipses of the satellites, in their general conception, are perfectly analogous to those of the moon, but in their detail they differ in several particulars. Owing to the much greater distance of Jupiter from the sun, and its greater magnitude, the cone of its shadow or umbra (art. 420.) is greatly more elongated, and of far greater dimension, than that of the earth. The satellites are, moreover, much less in proportion to their primary, their orbits less inclined to its ecliptic, and (comparatively to the diameter of the planet) of smaller dimensions, than is the case with the moon. Owing to these causes, the three interior satellites of Jupiter pass through the shadow, and are totally eclipsed, every revolution; and the fourth, though, from the greater inclination of its orbit, it sometimes escapes eclipse, and may occasionally graze as it were the border of the shadow, and suffer partial eclipse, yet does so comparatively seldom, and, ordinarily speaking, its eclipses happen, like those of the rest, each revolution. (537.) These eclipses, moreover, are not seen, as is the case with those of the moon, from the center of their motion, but from a remote station, and one whose situation with respect to the line of shadow is variable. This, of course, makes no difference in the times of the eclipses, but a very great one in their visibility, and in their apparent situations with respect to the planet at the moments of their entering and quitting the shadow. (538.) Suppose S to be the sun, E the earth in its orbit EFGK, J Jupiter, and a b the orbit of one of its satellites. The cone of the shadow, then, will have its vertex at X, a point far beyond the orbits of all the satellites; and the penumbra, owing to the great distance of the sun, and the consequent smallness of the angle (about 6' only) its disc subtends at Jupiter, will hardly extend, within the limits of the satellites' orbits, to any perceptible distance beyond the shadow, for which reason it is not represented in the figure. A satellite revolving from west to east (in the direction of the arrows) will be eclipsed when it enters the shadow at a, but not suddenly, because, like the moon, it has a considerable diameter seen from the planet; so that the time elapsing from the first perceptible loss of light to its total extinction will be that which it occupies in describing about Jupiter an angle equal to its apparent diameter as seen from the center of the planet, or rather somewhat more, by reason of the penumbra; and the same remark applies to its emergence at b. Now, owing to the difference of telescopes and of eyes, it is not possible to assign the precise moment of incipient obscuration, or of total extinction at a, nor that of the first glimpse of light falling on the satellite at b, or the complete recovery of its light. The observation of an eclipse, then, in which only the immersion, or only the emersion, is seen, is incomplete, and inadequate to afford any precise information, theoretical or practical. But, if both the immersion and emersion can be observed with the same telescope and by the same person, the interval of the times will give the duration, and their mean the exact middle of the eclipse, when the S J X, i. e. the true moment of its Such observations, and such only, are satellite is in the line opposition to the sun. of use for determining the periods and other particulars of the motions of the satellites, and for affording data of any material use for the calculation of terrestial longitudes. The intervals of the eclipses, it will be observed, give the synodic periods of the satellites' revolutions; from which their sidereal periods must be concluded by the method in art. 418. (539.) It is evident, from a mere inspection of our figure, that the eclipses take place to the west of the planet, when the earth is situated to the west of the line S J, i. e. before the opposition of Jupiter; and to the east, when in the other half of its orbit, or after the opposition. When the earth approaches the opposition, the visual line becomes more and more nearly coincident with the direction of the shadow, and the apparent place where the eclipses happen will be continually nearer and nearer to the body of the planet. When the earth comes to F, a point determined by drawing 6 F to touch the body of the planet, the emersions will cease to be visible, and will thenceforth, up to the time of the opposition, happen behind the disc of the planet. Similarly, from the opposition till the time when the earth arrives at I, a point determined by drawing a I tangent to the eastern limb of Jupiter, the emersions will be concealed from our view. When the earth arrives at G (or H) the immersion (or emersion) will happen at the very edge of the visible disc, and when between G and H (a very small space), the satellites will pass uneclipsed behind the limb of the planet. (540.) Both the satellites and their shadows are frequently observed to transit or pass across the disc of the planet. When a satellite comes to m, its shadow will be thrown on Jupiter, and will appear to move across it as a black spot till the satellite comes to n. But the satellite itself will not appear to enter on the disc till it comes up to the line drawn from E to the eastern edge of the disc, and will not leave it till it attains a similar line drawn to the western edge. It appears then that the shadow will precede the satellite in its progress over the disc before the opposition of Jupiter, and vice versa. In these transits of the satellites, which, with very powerful telescopes, may be observed with great precision, it frequently happens that the satellite itself is discernible on the disc as a bright spot if projected on a dark belt; but occasionally also as a dark spot of smaller dimensions than the shadow. This curious fact (observed by Schroeter and Harding) has led to a conclusion that certain of the satellites have occasionally on their own bodies, or in their atmospheres, obscure spots of great extent. We say of great extent; for the satellites of Jupiter, small as they appear to us, are really bodies of considerable size, as the following comparative table will show:*— From which it follows, that the first satellite appears, when on Jupiter's horizon, as large as our moon to us; the second and third nearly equal to each other, and of somewhat more than half the apparent diameter of the first, and the fourth about one quarter of that diameter. So seen, they will frequently, of course, eclipse one another, and cause eclipses of the sun (the latter visible, however, only over a very small portion of the planet), and their motions and aspects with respect to each other must offer a perpetual variety and singular and pleasing interest to the inhabitants of their primary. (541.) Besides the eclipses and the transits of the satellites across the disc, they may also disappear to us when not eclipsed, by passing behind the body of the planet. Thus, when the earth is at E, the immersion of the satellite will be seen at a, and its emersion at b, both to the west of the Main. Do. xxv. p. 51. *Struve, Mem. Art. Soc. iii. 301. planet, after which the satellite, still continuing its course in the direction b, will pass behind the body, and again emerge on the opposite side, after an interval of occultation greater or less according to the distance of the satellite. This interval (on account of the great distance of the earth compared with the radii of the orbits of the satellites) varies but little in the case of each satellite, being nearly equal to the time. which the satellite requires to describe an arc of its orbit, equal to the angular diameter of Jupiter as seen from its center, which time, for the several satellites, is as follows: viz., for the first, 2h 20m; for the second, 2h 56m; for the third, 3h 43m; and for the fourth, 4h 56m; the corresponding diameters of the planets as seen from these respective satellites being, 19° 49′; 12° 25′; 7° 47′; and 4° 25'.* Before the opposition of Jupiter, these occultations of the satellites happen after the eclipses: after the opposition (when, for instance, the earth is in the situation K), the occultations take place before the eclipses. It is to be observed, that, owing to the proximity of the orbits of the first and second satellites to the planet, both the immersion and emersion of either of them can never be observed in any single eclipse, the immersion being concealed by the body, if the planet be past its opposition, the emersion if not yet arrived at it. So also of the occultation. The commencement of the occultation, or the passage of the satellite behind the disc, takes place while obscured by the shadow, before opposition, and its re-emergence after. All these particulars will be easily apparent on mere inspection of the figure (art. 536.). It is only during the short time that the earth is in the arc G H (i.e. between the sun and Jupiter, that the cone of the shadow converging (while that of the visual rays diverges) behind the planet, permits their occultations to be completely observed both at ingress and egress, unobscured, the eclipses being then invisible. (542.) An extremely singular relation subsists between the mean angular velocities or mean motions (as they are termed) These data are taken approximately from Mr. Woolhouse's paper in the supplement to the Nautical Almanack for 1835. |