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About Small Corrections to General Relativity: Gravitational Acceleration Depends of the Accelerated Bodies Masses (Principle of Equivalence is Not Absolute in the Multifractal Universe)

In the frame of the multifractal theory of time and space ( in this model our universe is consisting of real time and space ﬁelds and is the multifractal universe) in the works [1]- [ ? ] some of problems were analyzed: how the fractional dimensions of real ﬁelds of time and space inﬂuence on behavior of diﬀerent physical phenomena. In this paper it is shown that in the multifractal theory of time and space the corrections of general relativity to Newton gravitational forces are explaining very simple in Newton approach. It is shown also that there is dependence (though very small) of bodies gravitational acceleration from their masses, so the principle of equivalence in multifractal universe is not absolute and it is only a very good approach. Thus taking into account the multifractal dimensions of time gives small corrections to gravitation forces of Einstein general relativity and explain it in Newton approach. These corrections are equal to F g ( r 0 ma )( Mr m ) − 1 where F g is the gravitational force originated by mass M at the distance r where the mass m is located, r 0 is the gravitational radius of the mass M and the r m is the mean radius of the mass m , a is a numerical factor depending of distribution of masses of m . The possibility of experimental checking this eﬀect in weak gravitational ﬁelds is analyzed . It makes for perihelion of Mercury rotation the correction to known results of Einstein relativity. This correction is equal ∼ 0 , 5 of percent of Einstein corrections.