erification of the priority and controllability of analytical solutions determined for active parts in the gravitational field of a spheroidal planet.

This paper presents analytical solutions to the problem of optimal trajectory design
for a point mass representing the center of mass of a spacecraft during intermediate-thrust motion in
the gravitational field of an axisymmetric spheroidal planet. The mathematical model incorporates
the perturbative influence of the second zonal harmonic J 2 , accounting for the oblateness of the
attracting body. The variational problem is formulated within the framework of optimal control
theory, and a class of particular analytical solutions is obtained using the Levi-Civita regularization
method. Special attention is devoted to the qualitative analysis of the derived analytical solutions.
The obtained program motions are examined with respect to stability and controllability. It is shown
that certain solutions exhibit regions of dynamic instability in the neighborhood of the nominal
trajectory. The controllability properties of the system are analyzed in the linear approximation,
and conditions under which stabilization is achievable are identified. A linear feedback regulator is
constructed to ensure asymptotic stability of the investigated program motion. The results provide
a theoretical basis for assessing the practical applicability of the derived analytical solutions in
spacecraft guidance problems under non-central gravitational perturbations.