Because of the presence of an ocean below the ice shell of icy satellites such as Europa, Callisto, Ganymede and Titan the solid interior of these satellites can be displaced with respect to the ice shell, similarly to the translational oscillation of the inner core of the Earth called the Slichter modes of the Earth. We construct a set of interior structure models of Europa, Callisto, Ganymede and Titan satisfying the observed mass, radius and moment of inertia and study the properties of the Slichter mode for these models. The periods obtained range from a few hours to a few tens of hours depending mainly on the ocean thickness. Ganymede has two Slichter modes since it is thought to have a liquid outer core besides a global subsurface ocean. The second Slichter mode describes essentially the oscillation of the solid inner core inside the liquid outer core and its period is determined principally by the thickness of the outer core. We study the possible observation of these modes with a lander on the surface or a spacecraft in orbit about Europa, Callisto, Ganymede or Titan. We show that an impactor with a radius of at least a few kilometers to a few tens of kilometers could excite the Slichter modes to a level observable by a lander. Such impacts occur on average once in >30 My for Europa, once in >70 My for Callisto, once in >40 My for Ganymede and once in >0.4 Gy for Titan. Observation of the Slichter mode would allow constraining the thickness of the ocean.
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