Perturbations

The principal motion of the planets is, as we have seen, determined by the gravitation of each of them towards the focus of its orbit. The regularity of this movement must be impaired by the mutual gravitation of the bodies of the system. The most striking of these derangements were observed by the School of Alexandria, in the first days of Mathematical Astronomy; others have been observed, in proportion as our knowledge became more precise; and now, all are explained with such completeness by the theory of gravitation, that the smallest perturbations are known before they are observed. This is the last possible test and triumph of the Newtonian system.

Instantaneous

There are, as Lagrange pointed out, two principal kinds of perturbations, which differ as much in their mathematical theory as in the circumstances which constitute them; instantaneous changes, from shocks or explosions, and gradual changes or perturbations properly so called, caused by secondary gravitation, requiring time. The first kind may never have taken place in our system; but it is necessary to consider it, not only because it is of possible occurrence, but because it is a necessary preliminary to the study of the other kind,—the gradual perturbations being treated theoretically as a series of little shocks.

The first case is easy of treatment. No collision or explosion would affect Kepler's laws: and, if the form of the orbit was altered, the accelerating forces would remain the same; and thus, the new variation once understood, our calculations might proceed as before.