An efficient method for determining the distance between a trajectory and a point on the surface of a spheroid is proposed to address some ensuing control problems. An error assessment for the spherical approximation is obtained. The time gained through applying the gnomonic projection with the initial spherical approximation and without it is estimated. The limits of applicability of the spherical and the gnomonic projections for the method are shown. Detection of multiple extrema in the proposed problem and the causes of their occurrence are described. The algorithm for the solution of this problem under such conditions is suggested. The method demonstrates high accuracy of the solution and can be recommended for use in commercial navigation and geodetic software products that comply with international standards. The technique extends to control problems associated with target intercepting.