Authors’ abstract: “Using Melnikov’s method we are able to prove the existence of transverse homoclinic orbits and therefore the existence of a horseshoe in a special restricted three-body problem. This analysis is an alternative to the one described by J. Moser [Stable and random motions in dynamical systems, Princeton Univ. Press, Princeton (1973; Zbl 0271.70009)], based on K. Sitnikov’s original work [Sov. Phys., Dokl. 5, 647-650 (1960); translation from Dokl. Akad. Nauk SSSR 133, No. 2, 303-306 (1960; Zbl 0108.186)], where the task is accomplished using a more direct construction of the horseshoe”.