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Relativistic Correction of Newton’s Law of Gravitation


А.А. Sazanov

In aspiration to widen the relativity principle up to affirming an equality of inertial and noninertial systems of counting out space and time coordinates, Einstein applied to geometrical model of the curved four-dimensional space with pseudo-Riemann metrical properties. And just from these positions it was constructed by him the theory of gravitation. But in the present offered article likewise in developing it article about gravitational decreasing of electromagnetic radiation frequency attention is paid to possibility of understanding relativistic effects of gravitation in terms of nonlinear geometrical constructions, having the physical sense in pseudo-Euclidian space of Minkowski. The point of departure for this lies in comprehending the invariant sense of parameters in Newton’ law of gravitation in the framework of Minkowski’s model and in using universal dependence of acceleration observed upon velocity. With taking in account these considerations it was deduced refined differential equation of the world line, corresponding to free falling of the body in spherically symmetric gravitation field. The integral form of this equation reveals existence of the limit for approaching to the source of gravitation. If free falling of the body begins from infinity with initial velocity near to zero, then this limit will be equal to radius of Schwarz¬schild. The world line corresponding to such initial condition was named as «normal line». The «normal world line» plays role of proper characteristic of the field of gravity mentioned and gives the reason to determine new significant notion discussed in the next article. Under other initial conditions, when the body in its free falling has a zero velocity at restricted distance from the source of gra¬vitation, or does not has a zero velocity at whatever distance, the limit for approaching to the source of gravitation may be less or more than Schwarz¬schild radius, though practically negligibly.

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