  The Hannay angle has been previously studied for a celestial circular
restricted three-body system by means of an adiabatic approach. In the present
work, three main results are obtained. Firstly, a formal connection between
perturbation theory and the Hamiltonian adiabatic approach shows that both lead
to the Hannay angle; it is thus emphasised that this effect is already
contained in classical celestial mechanics, although not yet defined nor
evaluated separately. Secondly, a more general expression of the Hannay angle,
valid for an action-dependent potential is given; such a generalised expression
takes into account that the restricted three-body problem is a time-dependent,
two degrees of freedom problem even when restricted to the circular motion of
the test body. Consequently, (some of) the eccentricity terms cannot be
neglected {\it a priori}. Thirdly, we present a new numerical estimate for the
Earth adiabatically driven by Jupiter. We also point out errors in a previous
derivation of the Hannay angle for the circular restricted three-body problem,
with an action-independent potential.
