  Curvilinear coordinate systems distinct from the rectangular Cartesian
coordinate system are particularly valuable in the field calculations as they
facilitate the expression of boundary conditions of differential equations in a
reasonably simple way when the coordinate surfaces fit the physical boundaries
of the problem. The recently finalized orthogonal similar oblate spheroidal
(SOS) coordinate system can be particularly useful for a physical processes
description inside or in the vicinity of the bodies with the geometry of an
oblate spheroid. Such shape is aproximating well objects investigated within
astrophysics. The solution of the azimuthally symmetric case of the Laplace
equation was found for the interior space in the orthogonal SOS coordinates. In
the frame of the derivation of the harmonic functions, the Laplace equation was
separated by a special separation procedure. A generalized Legendre equation
was introduced as the equation for the angular part of the separated Laplace
equation. The harmonic functions were determined as relations involving
generalized Legendre functions of the first and of the second kind. Several
lower-degree functions are reported. Recursion formula facilitating
determination of the higher-degree harmonic functions was found. The general
solution of the azimuthally symmetric Laplace equation for the interior space
in the SOS coordinates is reported.
