content_image/419734.jpg content_image/419735.jpg
provided, the Eq. (38) and Eq. (39) give the relation 

for determining the function ˜ r ( r ) . We must now turn to the actual correspondence between the expression (39) for the line element surrounding an attracting central body and the observational facts of astronomy. The in- vestigating methods are so well known that it will be sufficient for our purposes merely to indicate the classi- cal tests of GR conducted in solar-system dealing only with the shape of the trajectories of photons and plan- ets. All these tests are carried out in empty space and in gravitational fields that are to a good approximation static and spherically symmetric. Therefore, in sufficient approximation, at great distances from the central body 

we may take expansion of function ω ( F ) = λ$_{1}$F + λ$_{2}$F $^{2}$+ · · · , and that from Eq. (40) we obtain 

<img src='content_image/419734.jpg'>

<img src='content_image/419735.jpg'>

the tests of gravity via astrometric VLBI observations. Detailed analysis of VLBI data have yielded a consis- tent stream of improvements γ = 1 . 0000 . 003 [47, 48], γ = 0 . 99960 . 0017 [45], γ = 0 . 999940 . 00031 [43] and γ = 0 . 999830 . 00045 [50] resulting in the accuracy of bet- ter than ∼ 0 . 045%. The major advances in several dis- ciplines notably in microwave spacecraft tracking, high precision astrometric observations, and lunar laser rang- ing (LLR) suggest new experiments. LLR, a continuing legacy of the Apollo program, provided improved con- straint on the combination of parameters 4 β − γ − 3 [52– 55]. The analysis of LLR data [53] constrained this com- bination as 4 β − γ − 3 = (4 . 0 ± 4 . 3) × 10 − $^{4}$, leading to an ac- curacy of ∼ 0 . 011% in verification of general relativity via precision measurements of the lunar orbit. A significant improvement was reported in 2003 from Doppler tracking of the Cassini spacecraft while it was on its way to Sat- urn [41], with a result γ − 1 = (2 . 1 ± 2 . 3) × 10 − $^{5}$. This was made possible by the ability to do Doppler measurements using both X-band (7175 MHz) and Ka-band (34316 MHz) radar, thereby significantly reducing the dispersive effects of the solar corona. In addition, the 2002 superior conjunction of Cassini was particularly favorable: With the spacecraft at 8.43 astronomical units from the Sun, the distance of closest approach of the radar signals to the Sun was only 1 . 6 $^{R}$⊙ . This experiment has reached the current best accuracy of ∼ 0 . 002% [42]. Keeping in mind aforesaid, the best fit for satisfactory agreement be- tween the proposed theory of gravitation and observation can be reached at λ$_{1}$ − 1 / 4 = (2 . 95 ± 3 . 24) × 10 − $^{5}$. 

## IV. THE RELATIVISTIC FIELD THEORY OF INERTIA 

As we mentioned in Sect.2, in the proposed theory of gravitation, the preferred systems and group of transfor- mations of the real-curvilinear coordinates relate only to the real gravitational fields. This prompts us to intro- duce separately the distortion inertial fields , which have other physical source than that of gravitation, and con- struct the relativistic field theory of inertia. The latter, similarly to gravitation theory, treats the inertia as a dis- tortion of local internal properties of flat M$_{2}$ space. The geometry of Sect.3 is a language which is almost indis- pensable for the treatment of this problem. 

## A. The case of unbalanced net force other than gravitational 

First, we shall discuss the inertia effects in particu- lar case when the relativistic test particle accelerated in the flat space under unbalanced net force other than gravitational. Let us concentrate our attention on the first observer in two-dimensional Minkowski flat space M$_{2}$ = R 1 (+) ⊕ R 1 $^{(}$−) = R 1 ⊕ T $^{1}$, being regarded as in a state of rest or uniform motion. Suppose this unaccel- 

