  We study a simple model of dark matter that is gravitationally clustered
around the sun in the form of a spherical halo of a degenerate gas of heavy
neutrinos. It is shown that for neutrino masses $m_{\nu} \stackrel {\textstyle
<}{\sim} 16~{\rm keV}/c^{2}$, the resulting matter distribution is consistent
with the constraints on the mass excesses within the orbits of the outer
planets, as obtained from astrometrical and the Pioneer 10/11 and Voyager 1/2
(Anderson et al. 1995) ranging data. However, the anomalous acceleration
recently detected in the Pioneer 10/11 data that is approximately constant
between 40 AU and 60 AU (Anderson et al. 1998; Turyshev et al. 1999) is
incompatible with both our model and earlier Pioneer 10/11 ranging data for the
outer planets. We then calculate the planetary and asteroidal perihelion shifts
generated by such a neutrino halo. For $m_{\nu} \stackrel{\textstyle
<}{\sim}16~{\rm keV}/c^{2}$, our results are consistent with the observational
data on Mercury, Venus, Earth and Icarus.Finally, we propose to detect this
neutrino halo directly with a dedicated experiment on Earth, observing the
X-rays emitted in the radiative decay of the heavy neutrino into a light
neutrino and a photon.
