  We present the complete analytical solution of the geodesics equations in the
supersymmetric BMPV spacetime \cite{Breckenridge:1996is}. We study
systematically the properties of massive and massless test particle motion. We
analyze the trajectories with analytical methods based on the theory of
elliptic functions. Since the nature of the effective potential depends
strongly on the rotation parameter $\omega$, one has to distinguish between the
underrotating case, the critical case and the overrotating case, as discussed
by Gibbons and Herdeiro in their pioneering study \cite{Gibbons:1999uv}. We
discuss various properties which distinguish this spacetime from the classical
relativistic spacetimes like Schwarzschild, Reissner-Nordstr\"om, Kerr or
Myers-Perry. The overrotating BMPV spacetime allows, for instance, for
planetary bound orbits for massive and massless particles. We also address
causality violation as analyzed in \cite{Gibbons:1999uv}.
