A general solution to non-collinear equilibria in terms of largest root (κ) of confocal oblate spheroid

This paper deals with the existence of non-collinear equilibria in restricted three-body problem when less massive primary is an oblate spheroid and the potential of oblate spheroid is in terms of largest root of confocal oblate spheroid. This is found that the non-collinear equilibria are the solution of the equations r1 = n-2/3 and κ = 1 – a2, where r1 is the distance of the infinitesimal mass from more massive primary, n is mean-motion of primaries, a is semi axis of oblate spheroid and κ is the largest root of the equation of confocal oblate spheroid passes through the infinitesimal mass.