Motion of a Particle in the Field of a Massive Rotating Body

The geometry of the two-dimensional space surrounding the axis of rotation passing through the center of mass of a spheroidal body is described. Only a cylindrically symmetric one-sheet hyperboloid can be such a space. It is shown that sections of this space by planes passing through the center are divided into two groups by the angle between the cutting plane and the axis of rotation. The boundary value of the angle is determined by the ratio of the principal radii of the spheroid. The trajectory formed by the section by a plane whose angle with the axis of rotation is less than the boundary value is a hyperbola. Otherwise, the trajectory is a closed regular ellipse. If the angle is equal to pi/2, the ellipse becomes a circle whose radius is the maximum radius of the spheroid. If a particle moves along a hyperbola, its trajectory is not closed. An ellipsoidal trajectory is a trajectory of a planet.