19 - On the Perturbation of a Comet in the Neighbourhood of a Planet

Summary

In Chapter ii. of Book ix. of the Mécanique Céleste, Laplace considers the transformation of the orbit of a comet when it passes a large planet. His object is to show that the action of Jupiter suffices to account for the disappearance of Lexell's comet after 1779.

He remarks that if a comet passes very near to Jupiter, it will throughout a small portion of its orbit move round the planet almost as though it were unperturbed by the sun, and that both before its approach to and after its recession from the planet it will move round the sun almost as though it were unperturbed by the planet. The nature of the orbit of the comet will usually be much transformed by its encounter with the planet. It is clear then that there must be some surface surrounding the planet which separates the region, inside which the comet moves nearly round the planet, from the region in which it moves nearly round the sun. Such a surface is to be found by the comparison of the ratio of the perturbing force to the central force in the motion round the sun with its value in the motion round the planet. There is a certain surface at which this ratio will be the same in the two cases, and this is the surface required for the proposed approximate treatment of the problem.