  The Hubble law is extended to massive particles based on the de Broglie
wavelength. Due to the expansion of the universe the wavelength of an unbound
particle would increase according to its cosmological redshift. Based on the
navigation anomalies of the Pioneer 10 & 11 spacecraft it is postulated that an
unbound massive particle has a cosmological redshift z = (c / v_0) H_0 t, where
c is the speed of light in vacuum, v_0 is the initial velocity of the particle,
H_0 is Hubble's constant and t is the duration of time that the particle has
been unbound. The increase in wavelength of the particle corresponds to a
decrease in its speed by delta_v = - c H_0 t. Furthermore, it is hypothesized
that the solar system has escaped the gravity of the Galaxy as evidenced by its
orbital speed and radial distance and by the visible mass within the solar
system radius. This means that spacecraft which become unbound to the solar
system would also be galactically unbound and subject to the Hubble law. This
hypothesis and the extended Hubble law may explain the anomalous acceleration
found to be acting upon the unbound Pioneer 10 & 11 spacecraft. Thus, the
Pioneer anomaly may be a counter example to the dark matter hypothesis.
  Because photons have a speed which make them unbound to the Galaxy, it is
predicted that the navigation beam in open space would undergo a cosmological
redshift in its frequency which would be detectable with modern clocks.
