The two-body problem of a pseudo-rigid body and a rigid sphere K. Uldall Kristiansen †‡ , M. Vereshchagin △ , K. Go´ zdziewski △ , P. Palmer † and M. Roberts ‡ Surrey Space Centre † and Department of Mathematics ‡ , University of Surrey, Guildford, UK and Centre for Astronomy △ , Nicolaus Copernicus University, Toru´ n, Poland Abstract In this paper we consider the two-body problem of a spherical pseudo rigid body and a sphere. Due to the rotational and “re-labelling” symmetries, the system is shown to possess conservation of angular momentum and circulation. We follow a reduction procedure similar to that undertaken in the study of the two-body problem of a rigid body and a sphere so that the computed reduced non-canonical Hamiltonian takes a similar form. We then consider relative equilibria and show that the notions of locally central and planar equilibria coincide. Finally, we show that Riemann’s theorem on pseudo-rigid bodies has an extension to this system in planar relative equilibria. 1