Limits on dark matter, ultralight scalars, and cosmic neutrinos with gyroscope spin and precision clocks

Dark matter (DM) within the solar system induces deviations in the geodetic drift of a gyroscope spin due to its gravitational interaction. Considering a constant DM density as a minimal scenario, we constrain DM overdensity within the Gravity Probe B (GP-B) orbit around the Earth and for Earth's and Neptune's orbits around the Sun. The presence of electrons in gravitating sources and test objects introduces an electrophilic scalar-mediated Yukawa potential, which can be probed from the measurement of geodetic drift as well as using terrestrial and space-based precision clocks. We derive projected DM overdensity (eta) limits from Sagnac time measurements using onboard satellite clocks, highlighting their dependence on the source mass and orbital radius. The strongest sensitivity, eta similar to 4.45 x 103, is achieved at Neptune's orbit (similar to 30 AU), exceeding existing constraints. Correspondingly, the cosmic neutrino overdensity is xi similar to 5.34 x 1010, surpassing results from KATRIN and cosmic ray studies. The strongest sensitivity on the electrophilic scalar coupling, g similar to 7.09 x 10-24, is achieved for a scalar mass m phi less than or similar to 1.32 x 10-18 eV. This result, obtained from the projected precision clock studies probing non-gravitational potentials, is competitive with the leading bounds from fifth-force searches. These precision measurements offer a robust framework for testing gravity at solar system scales and probing DM in scenarios inaccessible to direct detection experiments.