Long-range acceleration induced by a scalar field external to gravity and the indication from Pioneer 10/11, Galileo and Ulysses Data

We suggest an explanation of the "Pioneer effect" based on the interaction of the spacecraft with a long-range scalar field, $\phi$. The scalar field under consideration is external to gravity, coupled to the ordinary matter and undergoes obedience to the weak equivalence principle. In the weak fields limit it result a long-range acceleration $a_{P}$, asymptotically constant within the region of the solar system hitherto crossed by the spacecraft.