Equations of deviation of geodesic lines, describing relative oscillations of two free particles, was obtained earlier by Synge .
The mathematical model for such an antenna consists of two free test-particles moving on neighbouring geodesic lines located infinitely close to one another.
As Synge had deduced, a deviation of the geodesic line [GAMMA](v +dv) from the geodesic line [GAMMA](v) can be found as the solution of his obtained equation
If there are two free mass-bering particles, they fall freely along neighbour geodesic lines in a gravitational field.
More generally, the trajectories of the geodesic lines are determined by the metric which works in the geometrical structure used as a modeling metric space.
The navigable trajectories as great ellipse or great circle are the examples of geodesic lines on the spheroid and sphere, respectively.
The geodesic lines
joining the 3 sensors give the Delaunay triangle, which is the dual of conventional Voronoi diagram.
The exact solution of non-null geodesic lines describing the motion of a satellite in a state of weightlessness is obtained.
It follows from exact solutions of the isotropic geodesic lines equations for the obtained metric, that an anisotropy of the velocity of light exists in the z-direction.
As Borissova recently showed  by the Synge equation for deviating geodesic lines and the Synge-Weber equation for deviating non-geodesics, Weber's experimental statement on gravitational waves  is inadequate.
alpha]] = 0), they move along neighbouring geodesic lines, according to the geodesic equations of motion