Abstract
This paper deals with the existence and stability of the libration points in the restricted-three body problem when the smaller primary is a finite straight segment and bigger primary is an oblate spheroid. We have observed that five libration points do exist in this problem, out of which three are collinear and two are non-collinear with the primaries. The collinear libration points are unstable for all values of mass parameter /u and the non-collinear libration points are stable if jU < /Jc, where jU is a critical value of mass parameter /u. The range of stability depends length of the finite straight segment and oblateness factor.
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