PERTURBATIONS (Lat. perturbatio, con fusion, from perturbare, to confuse, from per, through --F. turbare, to disturb, from turbo, throng, tumult). In astronomy, a term used to describe disturbances in the orbital motion of the planets or other celestial bodies. The sim plest kind of motion imaginable tinder the law of gravitation would he that of a small material particle revolving about a larger central attract ing body. if this particle is so small that its mass may be neglected altogether, as being in appreciable in comparison with that of the cen tral body, then the particle will describe an elliptic orbit having the larger body in one of its foci. lf, however. both bodies have masses so large that neither is negligible, then each body will describe an elliptic orbit having the common centre of gravity of the two bodies in the com mon focus, and its distance from either body will he inversely proportional to that body's mass. Thus the larger body will describe proportional ly the smaller orbit. The problem of determin ing mathematically all the circumstances of mo tion in such a system is called the 'problem of two bodies,' and its complete solution is possible. When the number of bodies in a system is in creased to three. we have the famous 'problem of three bodies,' whose complete mathematical so lution has never been made. It is not even certain whether our inability to solve this problem com pletely is due to the lack of sufficient power in the known methods of mathematical analysis, or to the fact that the problem is actually in soluble. Fortunately, astronomers have been able to obtain au approximate solution of the problem as it actually exists in the solar system, and this approximate solution is sufficiently exact for all practical purposes of predicting planetary phenomena. This solution is made by taking advantage of the fact that all the planets in the solar system are very small in comparison with the central body, the sun. The effect of this is to make such planet describe an orbit very near ly the same as the elliptic curve in which it would move if that planet and the sun were the only bodies in the system. Consequently. astrono mers can predict planetary phenomena on the as sumption that the orbit is a true ellipse, and then calculate the small Iiisturbances or perturba tions produced by the gravitational attraction of the other phinets in the system. The continuing action of perturbative attraction may in time produce certain changes in the size. shape, and position of an orbit. Suppose, for instance, that in the ease of a given planet perturtintive action should suddenly eease. Then the planet would go on front that moment in a true elliptic orbit which would never undergo further change. But the ellipse would not he the same ellipse if the perturbative action were to stop to-day as it \\Mild have been if that cessation of action had occurred ten thousand ago. For in that
long interval the size. shape and position of the orbit would have been changed appreciably. It follows from these considerations that we may consider pertuthative action, if we choose, from the following point of view : We may regard each planet as traveling for the moment in a certain elliptic orbit, and consider the pertur bations as disturbing the orbit instead of the itself. Having then deduced from obser vation the elements (q.v.) of the orbit at a given epoch, we can calculate the changes of the orbit in another epoch, and thus predict the ac tual motion of the planet for any future time.
The principal planetary perturbations are of several kinds: some change a planet's position on the sky alternately forward and backward every few years (periodic perturbations); others require a longer cyele to art forward and back ward (long inequalities): and lastly there are the secular inequalities, whose effects are so slow that hundreds of thousands of years are in cluded in their nation. The planetary pe riodic perturbations may displace the planets as seen from the sun by 15" in the case of Mer cury, 30" for Venus, 60" for the earth, and 120" for Mars. The most important 'long inequality' is that existingbetween Jupiter and Saturn. It may displace the former planet 28' and the la lter as much as 48'. The long-period secular inequali ties do not alter either the mean distances of the rivulets from the sun or their periods of revolu tion. But the nodes (q.v.) and perihelia (q.v.) of the orbits move continuously. The perihelia of all the planets except Venus are gradually increasing their celestial longitudes, and all the nodes are moving in the opposite direction on the ecliptic. At the same time, the inclinations of the planetary orbits to the ecliptic plane are os cillating through narrow limits in very long pe riods of time and the eccentricities are similar ly affected. But, on the whole, the mathematical researches so far made indicate that the con tinued effect of gravitational perturbative action will not end in the disruption of our solar sys tem. But its permanent existence might be jeoparded by other than gravitational forces, or by forees operating from outside the system. In the ease of the moon, perturbations are more complex and larger than they are in the plane tary orbits. The moon is so near uua that the slightest error in her predicted position is ob served with ease and certainty; and therefore her motion offers a much severer test to mathe matical calculations than do the planetary phe nomena. (See Moos.) Consult Tisserand, Traitd di oenaniqnc raeste ( 1889-1894).