Does PIONEER measure local spacetime expansion?
  There is a longstanding mystery connected with the radiotracking of distant interplanetary spaceprobes like ULYSSES, Galileo and especially the two NASA probes PIONEER 10 and 11. Comparing radiosignals outgoing from the earth to the probe and ingoing again from the probes do show anomalous frequency shifts which up to now have been explained as caused by anomalous non-Newtonian decelerations of these probes recognizable at solar distances beyond 5 AU. In this paper we study cosmological conditions for the transfer of radiosignals between the Earth and these distant probes. Applying general relativity, we derive both the geodetic deceleration as well as the cosmological redshift and compare the resulting frequency shift with the observed effect. We find that anomalous decelerations do act on these probes which are of cosmological nature, but these are, as expected from standard cosmology, much too low to explain the observed effect. In contrast, the cosmological redshift of radiophotons suffered during the itinerary to the probe and back due to the local spacetime expansion reveals a frequency shift which by its magnitude is in surprisingly good agreement with the long registered phenomenon, and thus explains the phenomenon well, except for the sign of the effect. Problems of a local Hubble expansion may give the reason for this. 
Hans-Joerg Fahr and Mark Siewert (Argelander-Institut f. Astronomie,   Abt. Astrophysik)