The limiting case of the double-averaged parabolic restricted three-body problem

The planar case of the parabolic restricted three-body problem is considered. The equations of motion are integrated within the framework of the double-averaged problem taking into account only the first term in the expansion of the perturbing function. It is demonstrated that, at moderate approaches to the central body, the size and the shape of the orbit of the perturbing body are invariable and only the orientation of the orbit changes.