  Analyzing the static spherically symmetric and rotating ellipsoid solutions
in the Newtonian limit of Jordan, Brance - Dicke theory we find the following.
In empty space scalar-tensor theories have trivial solution of field equation
with constant scalar potential (efficient value of gravitation constant). In
this case no celestial-mechanical experiments to reveal a difference between
scalar-tensor theories and Einstein theory is not presented possible. However,
scalar field, inside the matter, has characteristics like gravitation
permeability of material similar electromagnetic permeability of material in
Maxwell theories of electromagnetism. Investigation of obtained exact solutions
for given functions of a matter distributions in the Newtonian limit of Jordan,
Brance - Dicke theory show the efficient value of gravitation constant depends
on density of matter, sizes and form of object, as well as on the value of
theories coupling constant. That for example led to weakening gravitation force
in the central regions of a Galaxies. This assumption constitutes the way to
explain observed rotation curves of Galaxies without using cold dark matter.
