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equally marked distinction of specific character is preserved, all the interior ones having about the same density as the Earth, while that of all the exterior is very much less, not exceeding a quarter of the Earth, and agreeing in the cases of Jupiter and Uranus) very closely with that of the Sun.
(526.) We shall close this chapter with an illustration calculated to convey to the minds of our readers a general impression of the relative magnitudes and distances of the parts of our system. Choose any well levelled field or bowling-green. On it place a globe, two feet in diameter; this will represent the Sun; Mercury will be represented by a grain of mustard seed, on the circumference of a circle 164 feet in diameter for its orbit; Venus a pea, on a circle of 284 feet in diameter; the Earth also a pea, on a circle of 430 feet; Mars a rather large pin's head, on a circle of 654 feet; the Asteroids, grains of sand, in orbits of from 1000 to 1200 feet; Jupiter a moderate-sized orange, in a circle nearly half a mile across; Saturn a small orange, on a circle of four-fifths of a mile; Uranus a full-sized cherry, or small plum, upon the circumference of a circle more than a mile and a half; and Neptune a good-sized plum, on a circle about two miles and a half in diameter. As to getting correct notions on this subject by drawing circles on paper, or, still worse, from those very childish toys called orreries, it is out of the question. To imitate the motions of the planets, in the above-mentioned orbits, Mercury must describe its own diameter in 41 seconds; Venus in 4m 148; the Earth, in 7 minutes ; Mars, in 4m 48%; Jupiter, 2h 56m; Saturn, in 3h 13m; Uranus, in 2h 16m; and Neptune, in 3h 30m*
* In the “ Penny Encyclopædia,” vol. 22. p. 197, the diameters of the orbits of the planets here set down, are quoted as their distances from the center, and the size of the sun is enlarged to four feet, while the sizes of the planets are unaltered.
OF THE SATELLITES.
OF THE MOON, AS A SATELLITE OF THE EARTH. - GENERAL PROX
IMITY OF SATELLITES TO THEIR PRIMARIES, AND CONSEQUENT SUBORDINATION OF THEIR MOTIONS. MASSES OF THE PRIMARIES CONCLUDED FROM THE PERIODS OF THEIR SATELLITES. -MAINTENANCE OF KEPLER'S LAWS IN THE SECONDARY SYSTEMS. OF JUPITER'S SATELLITES. — THEIR ECLIPSES, ETC. VELOCITY OF LIGHT DISCOVERED BY THEIR MEANS. - SATELLITES OF SATURN
OF URANUS OF NEPTUNE.
(527.) In the annual circuit of the earth about the sun, it is constantly attended by its satellite, the moon, which revolves round it, or rather both round their common center of gravity; while this center, strictly speaking, and not either of the two bodies thus connected, moves in an elliptic orbit, undisturbed by their mutual action, just as the center of gravity of a large and small stone tied together and Aung into the air describes a parabola as if it were a real material substance under the earth's attraction, while the stones circulate round it or round each other, as we choose to conceive the matter.
(528.) If we trace, therefore, the real curve actually described by either the moon's or the earth’s centers, in virtue of this compound motion, it will appear to be, not an exact ellipse, but an undulated curve, like that represented in the figure to article 324., only that the number of undulations in a whole revolution is but 13, and their actual deviation from the general ellipse, which serves them as a central line, is comparatively very much smaller -- so much so, indeed, that every part of the curve described by either the earth or moon is concave towards the sun. The excursions of the earth on either side the ellipse, indeed, are so very small as to be hardly appretiable. In fact, the center of gravity of the earth and moon lies always within the surface of the earth, so that the monthly orbit described by the earth’s center about the common center of gravity is comprehended within a space less than the size of the earth itself. The effect is, nevertheless, sensible, in producing an apparent monthly displacement of the sun in longitude, of a parallactic kind, which is called the menstrual equation; whose greatest amount is, however, less than the sun's horizontal parallax, or than 8:6".
(529.) The moon, as we have seen, is about 60 radii of the earth distant from the center of the latter. Its proximity, therefore, to its center of attraction, thus estimated, is much greater than that of the planets to the sun; of which Mercury, the nearest, is 84, and Uranus 2026 solar radii from its center. It is owing to this proximity that the moon remains attached to the earth as a satellite. Were it much farther, the feebleness of its gravity towards the earth would be inadequate to produce that alternate acceleration and retardation in its motion about the sun, which divests it of the character of an independent planet, and keeps its movements subordinate to those of the earth. The one would outrun, or be left behind the other, in their revolutions round the sun (by reason of Kepler's third law), according to the relative dimensions of their heliocentric orbits, after which the whole influence of the earth would be confined to producing some considerable periodical disturbance in the moon's motion, as it passed or was passed by it in each synodical revolution.
(530.) At the distance at which the moon really is from us, its gravity towards the earth is actually less than towards the sun. That this is the case appears sufficiently from what we have already stated, that the moon's real path, even when between the earth and sun, is concave towards the latter. But it will appear still more clearly if, from the known periodic times * in which the earth completes its annual and
* R and r radii of two orbits (supposed circular), P and p the periodic times ; then the arcs in question (A and a) are to each other as to ; and since the versed sines are as the squares of the arcs directly and the radii inversely, these are to each other as jy to pai and in this ratio are the forces acting on the revolving bodies in either case.
the moon its monthly orbit, and from the dimensions of those orbits, we calculate the amount of deflection in either, from their tangents, in equal very minute portions of time, as one second. These are the versed sines of the arcs described in that time in the two orbits, and these are the measures of the acting forces which produce those deflections. If we execute the numerical calculation in the case before us, we shall find 2.233; 1 for the proportion in which the intensity of the force which retains the earth in its orbit round the sun actually exceeds that by which the moon is retained in its orbit about the earth.
(531.) Now the sun is about 400 times more remote from the earth than the moon is. And, as gravity increases as the squares of the distances decrease, it must follow that at equal distances, the intensity of solar would exceed that of terrestrial gravity in the above proportion, augmented in the further ratio of the square of 400 to 1; that is, in the proportion of 355,000 to 1; and therefore, if we grant that the intensity of the gravitating energy is commensurate with the mass or inertia of the attracting body, we are compelled to admit the mass of the earth to be no more than 35štoo of that of the sun.*
(532.) The argument is, in fact, nothing more than a recapitulation of what has been adduced in Chap. VIII. (art. 448.) But it is here re-introduced, in order to show how the mass of a planet which is attended by one or more satellites can be as it were weighed against the sun, provided we have learned, from observation, the dimensions of the orbits described by the planet about the sun, and by the satellites about the planet, and also the periods in which these orbits are respectively described. It is by this method that the masses of Jupiter, Saturn, Uranus, and Neptune have been ascertained, and from which their densities are concluded. See art. (561.).
(533.) Jupiter, as already stated, is attended by four satellites; Saturn by eight; Uranus certainly by four; and
In the synoptic table at the end of this volume, the mass of the sun is taken somewhat higher, according to the most recent determination. It has not been thought worth while to alter all the figures of the text in conformity with that estimate.
Neptune by one, or possibly more. These, with their respective primaries (as the central planets are called) form in each case miniature systems entirely analogous, in the general laws by which their motions are governed, to the great system in which the sun acts the part of the primary, and the planets of its satellites. In each of these systems the laws of Kepler are obeyed, in the sense, that is to say, in which they are obeyed in the planetary system — approximately, and without prejudice to the effects of mutual perturbation, of extraneous interference, if any, and of that small but not imperceptible correction which arises from the elliptic form of the central body. Their orbits are circles or ellipses of very moderate excentricity, the primary occupying one focus. About this they describe areas very nearly proportional to the times; and the squares of the periodical times of all the satellites belonging to each planet are in proportion to each other as the cubes of their distances. The tables at the end of the volume exhibit a synoptic view of the distances and periods in these several systems, so far as they are at present known; and to all of them it will be observed that the same remark respecting their proximity to their primaries holds good, as in the case of the moon, with a similar reason for such close connection.
(534.) Of these systems, however, the only one which has been studied with attention to all its details, is that of Jupiter; partly on account of the conspicuous brilliancy of its four attendants, which are large enough to offer visible and measurable discs in telescopes of great power; but more for the sake of their eclipses, which, as they happen very frequently, and are easily observed, afford signals of considerable use for the determination of terrestrial longitudes (art. 286.). This method, indeed, until thrown into the background by the greater facility and exactness now attainable by lunar observations (art. 287.), was the best, or rather the only one which could be relied on for great distances and long intervals.
(535.) The satellites of Jupiter revolve from west to east (following the analogy of the planets and moon), in planes