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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 connection between an anomalous acceleration and a Hubble constant is solved in the theory together with a relation to a cosmological constant in CDMΛ model. 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 a 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. We consider also a full formalism of the Nonsymmetric Jordan–Thiry Theory for the problem and present a relativistic model of an anomalous acceleration. We consider the model for General Relativity approximation, i.e.g   μ  ν    ≠   η   μ  ν(    g   μ  ν    =   g   ν  μ). In this model there are no contradictions with General Relativity tests in the Solar System. Pioneer 10/11 spacecrafts will come back in 10 6  years (a time scale of our periodic solutions is 10 6  years). Moreover, almost relativistic or relativistic spacecrafts can escape from the Solar System. We consider also a model of a relativistic acceleration which is more complicated, withg   μ  ν    ≠   g   ν  μtaken into account.

Pioneer 10 and 11 Spacecraft Anomalous Acceleration in the light of the Nonsymmetric Kaluza–Klein (Jordan–Thiry) Theory