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In this last paper in a series of three on weakly interacting massiveparticle (WIMP) dark matter in the solar system, we focus on WIMPs bound to thesystem by gravitationally scattering off of planets. We present simulations ofWIMP orbits in a toy solar system consisting of only the Sun and Jupiter. Asprevious work suggested, we find that the density of gravitationally capturedWIMPs at the Earth is small and largely insensitive to the details of elasticscattering in the Sun. However, we find that the density of gravitationallycaptured WIMPs may be affected by external Galactic gravitational fields. Ifsuch fields are unimportant, the density of gravitationally captured WIMPs atthe Earth should be similar to the maximum density of WIMPs captured in thesolar system by elastic scattering in the Sun. Using standard assumptions aboutthe halo WIMP distribution function, we find that the gravitationally capturedWIMPs contribute negligibly to direct detection event rates. While these WIMPsdo dominate the annihilation rate of WIMPs in the Earth, the resulting eventrate in neutrino telescopes is too low to be observed in next-generationneutrino telescopes.

Dark matter in the solar system III: The distribution function of WIMPs at the Earth from gravitational capture