On the one-body problem in the field of a tall cylinder in orbit

We describe the motion of a material point that is attracted by a tall, homogeneous cylinder. The cylinder moves on a circular orbit and points in the radial direction. The finite solution can be expanded in powers of two small parameters: the initial eccentricity of the orbital motion about the cylinder and the coupling parameter of the Coriolis force. Such expansions are given for the case of the indifferent longitudinal location. Solutions periodic in the polar angle are constructed. We do not find resonance effects or other large cumulative amplitude variations that might be due to the gravity-gradient and Coriolis force.