On the Possibility to Explain "The Pioneer Anomaly" within the Framework of Conformal Geometrodynamics

Einstein-Infeld-Hoffmann method is used to solve the problem of motion of two bodies when the equations of general relativity are of the generalized form: they have been reduced to a form invariant under conformal transformations. It is proved that not only metric degrees of freedom, but also derivatives of vector $A_{\alpha }$ appearing in the generalized equations can exert influence on the motion of bodies in a certain space-time domain. This influence can account for the recently observed anomalous acceleration of spacecrafts Pioneer 10, Pioneer 11. The impact of vector $A_{\alpha }$ on the motion of bodies is interpreted as a consequence of viscosity in geometrodynamic continuum.