  Einstein gravitation theory can be extended by preserving its geometrical
nature but changing the relation between curvature and energy-momentum tensors.
This change accounts for radiative corrections, replacing the Newton
gravitation constant by two running couplings which depend on scale and differ
in the two sectors of traceless and traced tensors. The metric and curvature
tensors in the field of the Sun, which were obtained in previous papers within
a linearized approximation, are then calculated without this restriction.
Modifications of gravitational effects on geodesics are then studied, allowing
one to explore phenomenological consequences of extensions lying in the
vicinity of general relativity. Some of these extended theories are able to
account for the Pioneer anomaly while remaining compatible with tests involving
the motion of planets. The PPN Ansatz corresponds to peculiar extensions of
general relativity which do not have the ability to meet this compatibility
challenge.
