We suggest a numerical and analytical algorithm of searching for stationary space station orbits in the vicinity of an oblate asteroid, when these orbits correspond to relative equilibrium positions of the space station on the plane defined by the asteroid precession and proper rotation axes, in the case of the asteroid being represented by a solid body of an approximately dynamically symmetric shape, compressed along the axis of dynamic symmetry. The algorithm is based on representing the asteroid gravitational potential by a composition of two complex conjugate point masses and consists of sequential variable substitution steps, reducing the problem to solving algebraic equations analytically and numerically. We supply a number of facts concerning evolution of stationary orbits in cases of changes in precession angular velocity.
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