### Pioneer 10 and 11 Spacecraft Anomalous Acceleration in the light of the Nonsymmetric Kaluza-Klein (Jordan-Thiry) Theory *[Cross-Listing]*

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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 mysterious connection between an anomalous acceleration and a Hubble constant is solved in the theory. 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. We resolve also some mysterious coincidence between an anomalous acceleration and the cosmological constant using a paradigm of modern cosmology. 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.