  The Nonsymmetric Kaluza-Klein (Jordan-Thiry) Theory leads to a model of a
modified acceleration that can fit an anomalous acceleration experienced by the
Pioneer 10 and 11 spacecraft. The future positions of those spacecrafts are
predicted using distorted hyperbolic orbit. A connection between an anomalous
acceleration and a Hubble constant is solved in the theory together with a
relation to a cosmological constant using a paradigm of modern cosmology. . In
the paper we consider an exact solution of a point mass motion in the Solar
System under an influence of an anomalous acceleration. We find two types of
orbits: periodic and chaotic. Both orbits are bounded. This means there is no
possibility to escape from the Solar System. Some possibilities to avoid this
conclusion are considered. Relativistic effects and a cosmological drifting of
a gravitational constant are considered.The model of an anomalous acceleration
does not cause any contradiction with Solar System observations. We give a full
statistical analysis of the model.
