Kinematics of a Planet in Space Surrounding a Rotating Star

It is shown that the center of mass of a star without rotation creates a gravitational field in which inertial motion occurs along a large circle of the sphere determined by the initial conditions. A rotating star is represented mathematically as an axis of rotation passing through the center of mass. The trajectories of the planets pass along a second-order surface that envelops the axis of rotation without intersecting with it. Such a surface is an one-sheet hyperboloid. The standard equation of such a hyperboloid is known. It is shown that only the section of the hyperboloid by a plane perpendicular to the axis of rotation is an ellipse whose parameters depend on the parameters of the hyperboloid and the distance of the section plane from the center of mass. If the section plane contains the axis of rotation, then the trajectory of the planet in this plane is a hyperbola. It is concluded that the stationary closed orbit of the planet is an ellipse in a plane perpendicular to the axis of rotation.