Remember the Pioneer anomaly? The anomaly was that spacecraft cruising the outer reaches of the solar system were observed to deviate from their trajectory. I was hoping that the wake from an alien space drive was causing that affect and that possibly we needed to post 'no wake' signs but the universe is more (and less) exciting than that ...
In this work we study the gravitational influence of the material extending from Uranus orbit to the Kuiper belt and beyond on objects moving within these regions. We conclude that a density distribution given by $\rho(r)=\frac{1}{r}$ (for $r\geq 20 UA$) generates a constant acceleration towards the Sun on those objects, which, with the proper amount of mass, accounts for the blue shift detected on the Pioneers space crafts.