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We derive purely gravitational constraints on dark matter and cosmic neutrino profiles in the solar system using asteroid (101955) Bennu. We focus on Bennu because of its extensive tracking data and high-fidelity trajectory modeling resulting from the OSIRIS-REx mission. We find that the local density of dark matter is bound by $ρ_{\rm DM}\lesssim 3.3\times 10^{-15}\;\rm kg/m^3 \simeq 6\times10^6\,\barρ_{\rm DM}$, in the vicinity of $\sim 1.1$ au (where $\barρ_{\rm DM}\simeq 0.3\;\rm GeV/cm^3$). We show that high-precision tracking data of solar system objects can constrain cosmic neutrino overdensities relative to the Standard Model prediction $\bar{n}_ν$, at the level of $η\equiv n_ν/\bar{n}_ν\lesssim 1.7 \times 10^{11}(0.1 \;{\rm eV}/m_ν)$ (Saturn), comparable to the existing bounds from KATRIN and other previous laboratory experiments (with $m_ν$ the neutrino mass). These local bounds have interesting implications for existing and future direct-detection experiments. Our constraints apply to all dark matter candidates but are particularly meaningful for scenarios including solar halos, stellar basins, and axion miniclusters, which predict or allow overdensities in the solar system. Furthermore, introducing a DM-SM long-range fifth force with a strength $\tildeα_D$ times stronger than gravity, Bennu can set a constraint on $ρ_{\rm DM}\lesssim \barρ_{\rm DM}\left(6 \times 10^6/\tildeα_D\right)$. These constraints can be improved in the future as the accuracy of tracking data improves, observational arcs increase, and more missions visit asteroids.