« PreviousContinue »
lunar orbit, for example, is the point in which the moon rises above the plane of the ecliptic in going towards the north; and her descending node is that in which she sinks below the same plane in moving towards the south. The orbits of the recently discovered planets deviate more from the ecliptic than those of the ancient planets : that of Pallas, for instance, has an inclination of 35° to it; on which account it is more difficult to determine their motions. These little planets have no sensible effect in disturbing the rest, though their own motions are rendered very irregular by the proximity of Jupiter and Saturn.
The planets are subject to disturbances of two kinds, both resulting from the constant operation of their reciprocal attraction; one kind, depending upon their positions with regard to each other, begins from zero, increases to a maximum, decreases and becomes zero again, when the planets return to the same relative positions. In consequence of these, the disturbed planet is sometimes drawn away from the sun, sometimes brought nearer to him ; at one time it is drawn above the plane of its orbit, at another time below it, according to the position of the disturbing body. All such changes, being accomplished in short periods, some in a few months, others in years, or in hundreds of years, are denominated Periodic Inequalities.
The inequalities of the other kind, though occasioned likewise by the disturbing energy of the planets, are entirely independent of their relative positions: they depend upon the relative positions of the orbits alone, whose forms and places in space are altered by very minute quantities in immense periods of time, and are, therefore, called Secular Inequalities.
In consequence of the latter kind of disturbances, the apsides, or extremities of the major axes of all the orbits, have a direct but variable motion in space, excepting those of the orbit of Venus, which are retrograde; and the lines of the nodes move with a variable velocity in a contrary direction. The motions of both are extremely slow; it requires more than 114755 years for the major axis of the earth's orbit to accomplish a sidereal revolution, that is, to return to the same stars; and 21067 years to complete its tropical motion, or to return to the same equinox. The major axis of Jupiter's orbit requires no less than 200610 years to perform its sidereal revolution, and 22748 years to accomplish its tropical revolution, from the disturbing action of Saturn alone. The periods in which the nodes revolve are also very great. Besides these, the inclination and eccentricity of every orbit are in a
state of perpetual but slow change. At the present time the inclinations of all the orbits are decreasing, but so slowly that the inclination of Jupiter's orbit is only about six minutes less now than it was in the age of Ptolemy. The terrestrial eccentricity is decreasing at the rate of about 41:44 miles annually; and, if it were to decrease equably, it would be 37527 years before the earth's orbit became a circle. But, in the midst of all these vicissitudes, the major axes and mean motions cf the planets remain permanently independent of secular changes; they are so connected by Kepler's law of the squares of the periodic times being proportional to the cubes of the mean distances of the planets from the
without affecting the other.
With the exception of these two elements, it appears that all the bodies are in motion, and every orbit in a state of perpetual change. Minute as these changes are, they might be supposed to accumulate in the course of ages sufficiently to derange the whole order of nature, to alter the relative positions of the planets, to put an end to the vicissitudes of the seasons, and to bring about collisions which would involve our whole system, now so harmonious, in chaotic confusion. It is natural to inquire what proof exists that nature will be preserved from such a catastrophe? Nothing
can be known from observation, since the existence of the human race has occupied comparatively but a point in duration, while these vicissitudes embrace myriads of ages. The proof is simple and convincing. All the variations of the solar system, secular as well as periodic, are expressed analytically by the sines and cosines of circular arcs, which increase with the time; and, as a sine or cosine can never exceed the radius, but must oscillate between zero and unity, however much the time may increase, it follows that when the variations have, by slow changes, accumulated, in however long a time, to a maximum, they decrease, by the same slow degrees, till they arrive at their smallest value, and again begin a new course, thus for ever oscillating about a mean value. This, however, would not be the case if the planets moved in a resisting medium, for then both the eccentricity and the major axes of the orbits would vary with the time, so that the stability of the system would be ultimately destroyed. The existence of such a fluid is now clearly proved; and although it is so extremely rare that hitherto its effects on the motions of the planets have been altogether insensible, there can be no doubt that, in the immensity of time, it will modify the forms of the planetary orbits, and may at last even cause the destruction of our system, which in itself contains no principle of decay.
Three circumstances have generally been supposed necessary to prove the stability of the system : the small eccentricities of the planetary orbits, their small inclinations, and the revolutions of all the bodies, as well planets as satellites, in the same direction. These, however, though sufficient, are not necessary conditions; the periodicity of the terms in which the inequalities are expressed is enough to assure us that, though we do not know the extent of the limits, nor the period of that grand cycle which probably embraces millions of
years, yet they never will exceed what is requisite for the stability and harmony of the whole, for the preservation of which every circumstance is so beautifully and wonderfully adapted.
The plane of the ecliptic itself, though assumed to be fixed at a given epoch for the convenience of astronomical computation, is subject to a minute secular variation of 45':7, occasioned by the reciprocal action of the planets; but, as this is also periodical, and cannot exceed 39, the terrestrial equator, which is inclined to it at an angle of about 23° 27' 34"-5, will never coincide with the plane of the ecliptic: so there never can be perpetual spring. The rotation of the earth is uniform ;