  Weakly Interacting Massive Particles (WIMPs) can be captured by the Earth,
where they eventually sink to the core, annihilate and produce e.g. neutrinos
that can be searched for with neutrino telescopes. The Earth is believed to
capture WIMPs not dominantly from the Milky Way halo directly, but instead from
a distribution of WIMPs that have diffused around in the solar system due to
gravitational interactions with the planets in the solar system. Recently,
doubts have been raised about the lifetime of these WIMP orbits due to solar
capture. We here investigate this issue by detailed numerical simulations.
  Compared to earlier estimates, we find that the WIMP velocity distribution is
significantly suppressed below about 70 km/s which results in a suppression of
the capture rates mainly for heavier WIMPs (above ~100 GeV). At 1 TeV and above
the reduction is almost a factor of 10.
  We apply these results to the case where the WIMP is a supersymmetric
neutralino and find that, within the Minimal Supersymmetric Standard Model
(MSSM), the annihilation rates, and thus the neutrino fluxes, are reduced even
more than the capture rates. At high masses (above ~1 TeV), the suppression is
almost two orders of magnitude.
  This suppression will make the detection of neutrinos from heavy WIMP
annihilations in the Earth much harder compared to earlier estimates.
