  (abbreviated) In this paper we develop a consistent WKBJ formalism, together
with a formal first order perturbation theory for calculating the properties of
the inertial modes of a uniformly rotating coreless body (modelled as a
polytrope and referred hereafter to as a planet) under the assumption of a
spherically symmetric structure. The eigenfrequencies, spatial form of the
associated eigenfunctions and other properties we obtained analytically using
the WKBJ eigenfunctions are in good agreement with corresponding results
obtained by numerical means for a variety of planet models even for global
modes with a large scale distribution of perturbed quantities. This indicates
that even though they are embedded in a dense spectrum, such modes can be
identified and followed as model parameters changed and that first order
perturbation theory can be applied. This is used to estimate corrections to the
eigenfrequencies as a consequence of the anelastic approximation, which we
argue here to be small when the rotation frequency is small. These are compared
with simulation results in an accompanying paper with a good agreement between
theoretical and numerical results. The results reported here may provide a
basis of theoretical investigations of inertial waves in many astrophysical and
other applications, where a rotating body can be modelled as a uniformly
rotating barotropic object, for which the density has, close to its surface, an
approximately power law dependence on distance from the surface.

Solar and Stellar Astrophysics;Earth and Planetary Astrophysics