  We study the motion of test particles in the gravitational field of a
rotating and deformed object within the framework of the adiabatic theory. For
this purpose, the Hartle-Thorne metric written in harmonic coordinates is
employed in the post-Newtonian approximation where the adiabatic theory is
valid. As a result, we obtain the perihelion shift formula for test particles
orbiting on the equatorial plane of a rotating and deformed object. Based on
the perihelion shift expression, we show that the principle of superposition is
valid for the individual effects of the gravitational source mass, angular
momentum and quadrupole moment. The resulting formula was applied to the inner
planets of the Solar system. The outcomes are in a good agreement with
observational data. It was also shown that the corrections related to the Sun's
angular moment and quadrupole moment have little impact on the perihelion
shift. On the whole, it was demonstrated that the adiabatic theory, along with
its simplicity, leads to correct results, which in the limiting cases
correspond to the ones reported in the literature.
