orbit, which is effected more slowly by reason of its greater distance from the sun, new appearances will be found to arise, such as the direct motion of those planets in the inferior conjunction; and their retrograde motion in the superior conjunction. See Apparent Station, Station, Retrogradation, &c. The orbits of the superior planets include that of the earth; at the same time that the velocity of the earth is greater than those of the superior planets: hence it results that the earth in its motion passes between these planets and the sun; which causes them to appear in opposition to that luminary. In the opposition they have a motion apparently retrograde; it is direct in the conjunction, as that of Venus and Mercury is in their superior conjunctions. Some of the planets, as the Earth, Jupiter, Saturn and Uranus, have moons or satellites, which turn about them, in like manner as they revolve about the sun. Thus the earth has one moon or satellite, Jupiter four, Saturn seven, and Uranus six. See MOON and SATELLITES. With respect to these satellites or secondary planets, the following remarkable circumstance takes place. The moon, the four satellites of Jupiter, and one of Saturn, are found by observation to turn about an axis in the same time as they respectively revolve about their primaries. And although it has not yet been ascertained from observations whether the same be true for the other satellites of Saturn, and those of Uranus; yet from the uniformity which obviously pervades the system, we conclude that the same is true for all the secondaries. The planet Saturn is emcompassed with a thin flat ring, or, as it is now found, with two rings, lying one within the other edgewise towards the planet, and detached from it. Their planes pass through the centre of Saturn. If a circular annulus. be cut out of a card, and divided into two parts by a concentric circle, leaving the inner breadth about three times that of the outer, and a ball be then put within of such a size that the space between the ball and the annulus may be a little larger than the breadth of the annulus, a representation will thus be obtained of Saturn and his two rings. That side next the sun is bright, like the body of the planet. The rings revolve in their own plane; and not being of a regular figure, their centre of inertia is at a small distance from the centre of Saturn. M. Laplace computed the time of their rotation to be 10h, 33m. 368; agreeing very nearly with the time found by Dr. Herschel from observation. If the mean distances either of the planets or of their satellites be compared with the duration of their sidereal revolutions, it will be easy to trace the beautiful relation discovered by Kepler, namely, that while several bodies turn about the same point, the squares of the periodical times are respectively as the cubes of their mean distances from that point: and, by combining this law with the theorem of Huygens, namely, that when the squares of the periodical times of several bodies circulating about the same point, are respectively as the cubes of the distances from that point, the central forces which animate them are in the inverse ratio of the squares of the same distances, it will be easy to discover the law of gravitation, and, as it were, to unveil the mechanism of the planetary system. We shall now present the reader with some tables exhibiting a brief view of the solar system. II. Semianes major of the planetary orbits, or their about 95 millions of English miles, being represented by mean distances from the sun, that of the earth, which is unity. Mercury Mars Ceres Pallas Juno III. Relations of excentricity to the semiaxis major V. (unity.) - (for 1750) 0.048077 (for 1805) IV Inclination of orbits to the ecliptic. : The actual masses of the planets have been in vestigated upon principles which may be here stated in a narrow compass. The forces which solicit two bodies moving circularly are in a ratio composed of the masses, the distances from the centre, and the inverse square of the periodic times (see CENTRAL FORCES) whence it results that the gravity of one of the satellites towards its planet, is to that of the earth towards the sun, as the mean distance of the satellite from the centre of its planet, divided by the square of its periodic time, is to the mean distance of the earth from the sun, divided by the square of its periodic time: or, expressing these gravitating tendencies by G,g. the mean distances by R, r. the periodic times by By applying this result to the planets which have satellites, it is easy to find the value of their masses; for, we know the radii of the orbits of the satellites, as well as the length of their sidereal revolutions, or their periodic times. Taking the cubes of the radii of these orbits, and dividing them successively by the squares of the periodic times, the quotients will give the values of the masses of the bodies about which the satellites circulate. As to the planets which have not satellites, Laplace has deduced the values of the masses of Venus and Mars, from the secular diminution of the obliquity of the ecliptic, and the acceleration of the moon's mean motion. The mass of Mer cury was inferred from its volume, supposing the densities of that planet and the earth reciprocally as their mean distances from the sun. Mecanique Céleste, tome iii. pa. 64., Exposition du Systeme du Monde, ed. 2. pa. 193. Thus was deduced the following table. VII. Masses of the planets, that of the sun being taken for.unity. Mercury Venus The Earth Mars Jupiter Saturn Uranus The Moon 1 2025810 1 2.4656 For Dr. Hutton's results on this subject, the reader may consult O. Gregory's Astronomy, pa. 247. Besides the bodies which revolve completely round the sun, within the limits of our observa tion, there are others, of which we only conclude from analogy that they perform such revolutions. These are the comets: they generally appear attended by a nebulous light, either surrounding them as a coma, or stretched out to a considerable length as a tail; and they sometimes seem to consist of such light only. Their orbits are so eccentric, that in their remoter situations the comets are no longer visible to us, although at other times they approach much nearer to the sun than any of the planets: for the comet of 1680, when at its perihelion was at the distance of only one sixth of the sun's diameter from his surface. Their tails are often of great extent, appearing as a faint light, directed always towards a point nearly opposite to the sun. Ít is quite uncertain of what substance they consist; and it is difficult to determine which of the conjectures respecting them is the least improbable. See СОМЕТ. Nearly 500 comets are recorded to have been seen at different times, and the orbits of about 100 have been ascertained with tolerable correctness but we have no opportunity of observ ing a sufficient portion of the orbit of any comet, to determine with accuracy the whole of its form limits of our observation does not sensibly differ as an ellipsis; since the part which is within the from the parabola. The last comet which has been observed was seen in the autumn of 1807. It was distinctly seen by the naked eye for about six weeks in September and October; and the elements, as far as they had been determined when this treatise was sent to press, were as below: 383130 Longitude of the ascending node 8 27 15 65 27 8 27 45 60763030 Sept. 17d 0h 02m Two comets at least, or perhaps three, have been recognised in their return. A comet ap1067.09 peared in 1770 which Prosperin suspected to 1 move in an orbit materially different from a pa3359-40 rabola: Mr. Lexell determined its period to be five years and seven months, and its extreme distances to be between the orbits of Jupiter and of Mercury: but it does not appear that any subsequent observations have confirmed his theory. 19504 1 X 68.5 1 329620 The densities of bodies are in the direct ratio of their masses, and the inverse ratio of the volumes; and when bodies are nearly spherical, the volumes are as the cubes of their radii; whence it results that the densities are then as the masses divided by the cubes of the radii. By Dr. Halley foretold the return of a comet about 1758, which had appeared in 1531, in 1607, and in 1682, at intervals of about seventy-five years; and with Clairaut's farther correction for the perturbations of Jupiter and Saturn, the time agreed within about a month. The mean distance of this comet from the sun must be less than that of Uranus or Herschel. Dr. Halley also supposed the comet of 1680 to have been seen in 1106, in 531, and in the year 44 before Christ, having a period of 575 years; and it has been conjectured that the comets of 1556 and 1264 were the same, the interval being 292 years; a conjecture which will either be confirmed or confuted in the year 1848. T. Young's Lectures, I. 513. Some useful information on the subject of comets is given in Ch. 21. of O. Gregory's Astronomy, and several very striking conjectures in Lambert's Letters on Cosmogony. But after all, it must be acknowledged that the philosophy of comets is, at present, very imperfect. The prediction of Seneca remains yet to be accomplished, wherein he says, "The time will come when the nature of comets and their magnitudes will be ⚫ demonstrated, and the routs they take, so different from the planets, explained. Posterity will then wonder, that the preceding ages should be ignorant of matters so plain and easy to be known." On the Laws of Gravitation. It now remains that we endeavour to explain to the reader, the nature and operation of that extensive and general principle from which the analogies that obtain in the motion of the heavenly bodies naturally flow; that invisible chain which = binds together so many bodies in an indissoluble connection, and yet does not oblige them to come into immediate contact. This explanation 畔 we shall give nearly in the words of Dr. T. ■Young, as below. It was first systematically demonstrated by sir Isaac Newton, that all the motions of the heavenly bodies, which have been described, may be deduced from the same force of gravitation which causes a heavy body to fall to the earth: he has shewn that, in consequence of this universal property of matter, all bodies attract each other with forces decreasing as the squares of the distances increase; and of later years, the same theory has been still more accurately applied to the most complicated phenomena. We are at present to take a general view of the operation of this law, in the same order in which the affections of the celestial bodies have been enumerated. The bodies which exist in nature are never single gravitating points; so that, in order to determine the effects of their attraction, we must suppose the actions of an infinite number of such points to be combined. It was shewn by Newton, that all the matter of a spherical body, or of a spherical surface, may be considered, in estimating its attracting force on other matter, as collected in the centre of the sphere. The steps of the demonstration are these: a particle of matter, placed at the summit of a given cone or pyramid, is attracted by a thin surface, composed also of attracting matter, occupying the base of the cone, with equal force, whatever may be the length of the cone, provided that its angular position remain unaltered: hence it is easily inferred that if a gravitating point be placed any where within a hollow sphere, it will remain in equilibrium, in consequence of the opposite and equal action of the infinite number of minute surfaces, terminating the opposite pyramids into which the sphere may be divided: it is also demonstrable, by the assistance of a fluxional calculation, that a point placed within the surface is attracted by it, precisely in the same manner as if the whole matter which it contains were collected in the centre; consequently the same is true of a solid sphere, which may be supposed to consist of an infinite number of such hollow spheres. If, however, the point were placed within a hollow sphere, it would be urged towards the centre, by a force which is simply proportional to its distance from that centre. This proposition tends very much to facilitate all calculations of the attractions of the celestial bodies, since all of them are so nearly spherical, that their action on any distant bodies is the same as if the whole of the matter of which they consist were condensed into their respective centres; but, if the force of gravity varied according to any other law than that which is found to prevail, this simplification would no longer be admissible, even with respect to a sphere. It can scarcely be doubted that the power of gravitation extends from one fixed star to another, although its effects may in this case be far too inconsiderable to be perceived by us. It may possibly influence the progressive motions of some of the stars; and if, as Dr. Herschel supposes, there are double and triple stars revolving about a common centre, they must be retained in their orbits by the force of gravity. Dr. Herschel also imagines that the motion of our sun is in some measure derived from the same cause, being directed nearly towards a point in which two strata of the milky way meet; the attraction of the stars, other things being equal, must, however, be proportional to their brightness, and that part of the heavens to which the sun is probably moving appears to afford less light than almost any other part, nor does the hemisphere of which it is the centre abound so much in bright stars as the opposite hemisphere. If Sirius were a million times as far from the sun as the earth, and if he should descend towards the sun by means of their mutual gravitation only, he would move, on a rough estimate, but about forty feet in the first year, and in 1000 years only 8000 miles. The sun's change of place dependent on the relative situation of the planets is so inconsiderable, that it escaped observation until its existence had been deduced from theory. Not bu that this change would be sufficiently conspicuous if we had any means of detecting it, since it may amount in the whole to a distance equal to twice the sun's diameter, or seven times the distance of the moon from the earth; and this change is generally deducible from the general and unquestionable law of mechanics, that the place of the centre of inertia of a system cannot be changed by any reciprocal or mutual action of the bodies composing it, the action of gravity being found to be perfectly reciprocal. But the earth accompanies the sun in great measure in this aberration, and the other planets are also more or less affected by similar motions; so that the relative situations are much less disturbed than if the sun described this irregular orbit by the operation of a cause foreign to the rest of the system. The simple revolution of a body in a given plane, indicates at first sight the existence of an attractive force directed to some point within the orbit; and the Keplerean law of the equality of the areas described in equal times by a line drawn from each planet to the sun, agrees precisely with what is demonstrable of the effects of central forces, and points at once to the sun as the centre of attraction of the system. And since the orbits of the planets are elliptical, and the sun is placed in one of the foci of each, it may be mathemati cally demonstrated that the force directed to the sun must increase as the square of the distance decrcases, and vice versa. See ATTRACTION. sun. The times of the revolution of the planets are also in perfect conformity with the laws of gravitation, that is, the squares of the times are proportional to the cubes of the mean distances from the It was easy to infer, from what Huygens had already demonstrated of centrifugal forces, that this Keplerean law must be true of bodies revolving in circles by the force of gravitation; but Newton first demonstrated the same proportion with respect to elliptic orbits, and shewed that the time of revolution in an ellipsis is equal to the time of revolution in a circle, of which the diameter is equal to the major axis of the ellipse, or the semidiameter to the mean distance of the planet. The universality of the laws of gravitation, as applied to the different planets, shews also that the matter of which they are composed is equally subjected to its power; for if any of the planets contained a portion of an inert substance, requiring a force to put it in motion, and yet not liable to the force of gravitation, the motion of the planet would be materially different from that of any other planet similarly situated. The deviations of each planet from the plane of its orbit, and the motions of its nodes or the points in which the orbit intersects the plane of the ecliptic, as well as the motions of the aphelion, or the point where the orbit is remotest from the sun, have also been deduced from the attractions of the other planetary bodies; but the calculations of the exact quantities of these perturbations are extremely intricate, In general, each of the disturbing forces causes the nodes to have a slight degree of retrograde motion; but on account of the peculiar situation of the orbits of Jupiter and Saturn, it happens that the ret: ograde motion of Jupiter's node, on the plane of the orbit of Saturn, produces a direct motion on the ecliptic, so that the action of Saturn tends to lessen the effect of the other planets in causing a retrograde motion of Jupiter's nodes on the ecliptic. The secular diminution of the obliquity of the ecliptic, or that slow variation of its position, which is only discovered by a comparison of very distant observations, is occasioned by the change of position of the earth's orbit, in consequence of the attractions of the other planets, especially of Jupiter. It has been computed that this change may amount in the course of many ages to 10 or 11, with respect to the fixed stars: but the obliquity of the ecliptic to the equator can never vary more than two or three degrees, since the equator will follow, in some measure, the motion of the ecliptic. The mutual attraction of the particles of matter composing the bulk of each planet would naturally dispose them, if they were either wholly or partially fluid, to assume a spherical form; but their rotatory motion would require, for the preservation of this form, an excess of attraction in the equatorial parts, in order to balance the greater centrifugal force arising from the greater velocity of their motion: but since the attractive force of the sphere on the particles at an equal distance from its centre is every where equal, the equatorial parts would necessarily recede from the axis, until the greater number of particles, acting in the same column, compensated for the greater effect of the centrifugal force. The form would thus be changed from a sphere to an oblate or fattened shperoid; and the surface of a fluid either wholly or partially covering a solid b must assume the same figure, in order that it m remain at rest. The surface of the sea is, the fore, spheroidal, and that of the earth only . ates so far from a spheroidal figure, as it is abo or below the general level of the sea. The action of the sun and moon on the nent parts about the earth's equator, produci slight change of the situation of its axis, int same manner as the attraction of the other plan occasions a deviation from the plane of its Hence arises the precession of the equinoxes, “ the retrograde motion of the equinoctial porta amounting annually to about 50 seconds. Th nutation of the earth's orbit is a small perioda change of the same kind, depending on the pos tion of the moon's nodes; in consequence which, according to Dr. Bradley's original vations, the pole of the equator describes in the heavens a little ellipsis of which the diameters a 16 and 20 seconds. The same cause is also ca cerned in modifying the secular variation of the obliquity of the ecliptic; and, on the other had this variation has a considerable effect on the ap parent precession of the equinoxes. On account of the different quantity of the precession at e ferent times, the actual length of the tropical year is subjected to a slight variation; it is now 5 seconds shorter than it was in the time of Hp. parchus. The utmost change that can bigges from this cause amounts to 43 seconds. The exact computation of the moon's motion a one of the most difficult as well as important pro blems in astronomy; but it is easy to underta in general, how the difference in the quantity and direction of the sun's actions on the moon ad earth may cause such a derangement of the moon's gravitation towards the earth, that the 10clination of the orbit must be variable, that the nodes must have a retrograde, and the apidesa direct motion; and that the velocity of the mo must often be different from that which she wok have, according to the Keplerean law, in a s elliptic orbit. For, the sun's attraction, as far as it nets equa ly on the earth and the moon, can have so tika in disturbing their relative position, being alwart employed in modifying their common meal volution; but the difference of the forces 02sioned by the difference of distances, always tendr to diminish the effect of their mutual attractios; since the sun acts more powerfully on the neare than on the remoter of the two bodies. The d fercnce of the directions in which the sun atsa the earth and moon, produces also a force whe tends in some degree to bring them nearer gether; but this force is, on the whole, much m er than the former; and the result of both the disturbing forces, is always directed to some po in the line which joins the earth and the sun, th same side of the earth with the moon. It is con ous that when the nodes are also in this line, disturbing force can have no effect, either on ther position or on the inclination of the orbit, sne acts wholly in the plane of that orbit; but they are in any other situation, the disturbing force must cause a deviation from the plane, D wards the side on which the sun is situated, that the inclination of the orbit increases and as creases continually and equally; but whatev may be the position of the nodes, it will ap that they must recede during the greater part the moon's revolution, and advance during the smaller. |