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CHAP. VIII.

SOLAR SYSTEM.

243

as to the logical correctness of our argument, in consequence of our temporary neglect of them while working our way upward to the law of gravity from a general consideration of the moon's orbit.

CHAP. VIII.

OF THE SOLAR SYSTEM.

APPARENT MOTIONS OF THE PLANETS. THEIR STATIONS AND RETROGRADATIONS. THE SUN THEIR NATURAL CENTER OF MOTION. INFERIOR PLANETS. -THEIR PHASES, PERIODS, ETC. DIMENSIONS AND FORM OF THEIR ORBITS. TRANSITS ACROSS THE SUN. SUPERIOR PLANETS. THEIR DISTANCES, PERIODS, ETC.- KEPLER'S LAWS AND THEIR INTERPRETATION. ELLIPTIC ELEMENTS OF A PLANET'S ORBIT. ITS HELIOCENTRIC AND GEOCENTRIC PLACE.-BODE'S LAW OF PLANETARY DISTANCES. THE FOUR ULTRA-ZODIACAL PLANETS.-PHYSICAL PECULIARITIES OBSERVABLE IN EACH OF THE PLANETS.

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(387.) THE sun and moon are not the only celestial objects which appear to have a motion independent of that by which the great constellation of the heavens is daily carried round the earth. Among the stars there are several, and those among the brightest and most conspicuous, which, when attentively watched from night to night, are found to change their relative situations among the rest; some rapidly, others much more slowly. These are called planets. Four of them,

-Venus, Mars, Jupiter, and Saturn, are remarkably large and brilliant ; another, Mercury, is also visible to the naked eye as a large star, but, for a reason which will presently appear, is seldom conspicuous; a fifth, Uranus, is barely discernible without a telescope; and four others,- Ceres, Pallas, Vesta, and Juno,- are never visible to the naked eye. Besides these ten, others yet undiscovered may exist; and it is extremely probable that such is the case,—the multitude of telescopic stars

being so great that only a small fraction of their number has been sufficiently noticed to ascertain whether they retain the same places or not, and the five lastmentioned planets having all been discovered within half a century from the present time.

(388.) The apparent motions of the planets are much more irregular than those of the sun or moon. Generally speaking, and comparing their places at distant times, they all advance, though with very different average or mean velocities, in the same direction as those luminaries, i. e. in opposition to the apparent diurnal motion, or from west to east: all of them make the entire tour of the heavens, though under very dif ferent circumstances; and all of them, with the exception of the four telescopic planets,-Ceres, Pallas, Juno, and Vesta (which may therefore be termed ultra-z0diacal),—are confined in their visible paths within very narrow limits on either side the ecliptic, and perform their movements within that zone of the heavens we have called, above, the Zodiac (art. 254.).

(389.) The obvious conclusion from this is, that whatever be, otherwise, the nature and law of their motions, they are all performed nearly in the plane of the ecliptic, that plane, namely, in which our own motion about the sun is performed. Hence it follows, that we see their evolutions, not in plan, but in section; their real angular movements and linear distances being all foreshortened and confounded undistinguishably, while only their deviations from the ecliptic appear of their natural magnitude, undiminished by the effect of perspective.

(390.) The apparent motions of the sun and moon, though not uniform, do not deviate very greatly from uniformity; a moderate acceleration and retardation, accountable for by the ellipticity of their orbits, being all that is remarked. But the case is widely different with the planets: sometimes they advance rapidly; then relax in their apparent speed- come to a momentary stop; and then actually reverse their motion, and run back upon their former course, with a rapidity at

CHAP. VIII. NODES OF A PLANET'S ORBIT.

245

first increasing, then diminishing, till the reversed or retrograde motion ceases altogether. Another station, or moment of apparent rest or indecision, now takes place ; after which the movement is again reversed, and resumes its original direct character. On the whole,

however, the amount of direct motion more than compensates the retrograde; and by the excess of the former over the latter, the gradual advance of the planet from west to east is maintained. Thus, supposing the Zodiac to be unfolded into a plane surface, (or represented as> in Mercator's projection, art. 234., taking the ecliptic EC for its ground line,) the track of a planet, when mapped down by observation from day to day, will offer

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the appearance P Q R S, &c.; the motion from P to Q being direct, at Q stationary, from Q to R retrograde, at R again stationary, from R to S direct, and so on.

(391.) In the midst of the irregularity and fluctuation of this motion, one remarkable feature of uniformity is observed. Whenever the planet crosses the ecliptic, as at N in the figure, it is said (like the moon) to be in its node; and as the earth necessarily lies in the plane of the ecliptic, the planet cannot be apparently or uranographically situated in the celestial circle so called, without being really and locally situated in that plane. The visible passage of a planet through its node, then, is a phenomenon indicative of a circumstance in its real motion quite independent of the station from which we view it. Now, it is easy to ascertain, by observation, when a planet passes from the north to the south side of the ecliptic: we have only to convert its right ascensions and declinations into longitudes and latitudes, and the change from north to south latitude on two successive days will advertise us on what day the transition took place; while a simple proportion, grounded on the observed state of its motion in latitude in the interval,

will suffice to fix the precise hour and minute of its arrival on the ecliptic. Now, this being done for several transitions from side to side of the ecliptic, and their dates thereby fixed, we find, universally, that the interval of time elapsing between the successive passages of each planet through the same node (whether it be the ascending or the descending) is always alike, whether the planet at the moment of such passage be direct or retrograde, swift or slow, in its apparent movement.

(392.) Here, then, we have a circumstance which, while it shows that the motions of the planets are in fact subject to certain laws and fixed periods, may lead us very naturally to suspect that the apparent irregularities. and complexities of their movements may be owing to our not seeing them from their natural center (art. 316.), and from our mixing up with their own proper motions movements of a parallactic kind, due to our own change of place, in virtue of the orbitual motion of the earth about the sun.

(393.) If we abandon the earth as a center of the planetary motions, it cannot admit of a moment's hesitation where we should place that center with the greatest probability of truth. It must surely be the sun which is entitled to the first trial, as a station to which to refer them. If it be not connected with them by any physical relation, it at least possesses the advantage, which the earth does not, of comparative immobility. But after what has been shown in art. 380., of the immense mass of that luminary, and of the office it performs to us as a quiescent center of our orbitual motion, nothing can be more natural than to suppose it may perform the same to other globes which, like the earth, may be revolving round it; and these globes may be visible to us by its light reflected from them, as the moon is. Now there are many facts which give a strong support to the idea that the planets are in this predicament.

(394.) In the first place, the planets really are great globes, of a size commensurate with the earth, and several of them much greater. When examined through

CH. VIII. APPARENT DIAMETERS OF THE PLANETS. 247

powerful telescopes, they are seen to be round bodies, of sensible and even of considerable apparent diameter, and offering distinct and characteristic peculiarities, which show them to be solid masses, each possessing its individual structure and mechanism; and that, in one instance at least, an exceedingly artificial and complex one. (See the representations of Jupiter, Saturn, and Mars, in Plate I.) That their distances from us are great, much greater than that of the moon, and some of them even greater than that of the sun, we infer from the smallness of their diurnal parallax, which, even for the nearest of them, when most favourably situated, does not exceed a few seconds, and for the more remote ones is almost imperceptible. From the comparison of the diurnal parallax of a celestial body, with its apparent semidiameter, we can at once estimate its real size. For the parallax is, in fact, nothing else than the apparent semidiameter of the earth as seen from the body in question (art. 298. et seq.); and, the intervening distance being the same, the real diameters must be to each other in the proportion of the apparent ones. Without going into particulars, it will suffice to state it as a general result of that comparison, that the planets are all of them incomparably smaller than the sun, but some of them as large as the earth, and others much greater.

(395.) The next fact respecting them is, that their distances from us, as estimated from the measurement of their angular diameters, are in a continual state of change, periodically increasing and decreasing within certain limits, but by no means corresponding with the supposition of regular circular or elliptic orbits described by them about the earth as a center or focus, but maintaining a constant and obvious relation to their apparent angular distances or elongations from the sun. For example; the apparent diameter of Mars is greater when in opposition (as it is called) to the sun, i. e. when in the opposite part of the ecliptic, or when it comes on the meridian at midnight,-being then about 18′′, —but diminishes rapidly from that amount to about

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