Abstract
We consider the motion of a test particle in a central field of arbitrary physical nature. In constrast to the usual statement of the classical two-body problem assuming an infinite range of the field about a central point, real conditions are considered when the sphere of effective influence of the field about a given center is bounded and when the central body itself has finite dimensions. Motion in such a central field is called stable and the corresponding orbits stationary if the total energy and angular momentum remain constant and the particle itself does not leave the sphere of effective influence. Representing one of the vectors of the Laplace integral as a scalar product of a symmetric tensor with the radius vector, the equation for the stationary orbits are obtained after a transformation, which are analogous to the equations of field-dynamic equilibrium and are formally very similar to the Shroedinger wave equation.
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