Future horseshoe behavior for the nominal orbit. Top panel: future evolution of the value of the relative mean longitude, λ_r, with respect to Saturn for the nominal orbit of 2013 VZ₇₀. Middle panel: Trajectory in three-dimensional space during the time interval (0, 800) yr in a frame of reference centered on the Sun and rotating with Saturn. Bottom panel: the path followed by 2013 VZ₇₀ (which moves counterclockwise) is in a frame of reference centered on the Sun and rotating with Saturn, projected onto the ecliptic plane, during the same time interval. Since Saturn follows an eccentric orbit, it is represented in the panels by a blue trace (middle) or ellipse (bottom). The output time-step size is 0.01 yr.