Semi-analytic treatments of weakly interacting massive particle (WIMP) orbits in 
the solar system (e.g., Damour 
& Krauss 1999, Gould 1991, Lundberg & Edsjo 2004) suggest that the WIMPs 
bound to solar system may 
enhance the direct detection rate relative to that of the unbound population by 
up to a factor of order unity, as 
well as boost the flux of neutrinos from WIMP annihilation in the Earth up to 
two orders of magnitude.  Given 
these intriguing implications, it is worthwhile to check the semi-analytic 
approximations with numerical 
integrations of particle orbits in the solar system.  We present the results of a 
suite of numerical experiments to 
explore the size of the bound WIMP population as a function of WIMP mass and 
the elastic scattering cross section 
with baryonic matter.  For regions of WIMP parameter space not yet excluded by 
experiments, we find that the 
bound WIMP population enhances the direct detection rate by at most $\approx 
1\%$ relative to the halo WIMP 
rate.  It is unlikely that neutrinos from WIMP annihilation in the Earth will be 
observed in upcoming km$^3$-
scale neutrino telescopes.  The event rate from neutrinos from WIMP 
annihilation in the Sun will depend on the 
WIMP mass and elastic cross section in ways that have not been previously 
explored.