Collinear equilibria and their characteristic exponents in the restricted three-body problem when the primaries are oblate spheroids

Abstract

In this paper location of the collinear libration points is investigated numerically, by taking the oblateness of the primaries into consideration, for 19 systems of astronomical interest. It is found that in some of the systems the shifts are significant. These equilibria are shown to be unstable in general, though the existence of conditional, infinitesimal (linearized) periodic orbits around them can be established, in the usual way. It is shown that the eccentricity and synodic period of these orbits are functions of oblateness too. Numerical study, in this connection, with the above systems, revealed that the orbits around the libration point, which is farthest from the primary whose oblateness effect is included, exhibit a different trend from those around the other two points.