Dark matter could be composed of compact dark objects (CDOs). These objects may interact very weakly with normal matter and could move freely inside the Earth. A CDO moving in the inner core of the Earth will have an orbital period near 55 min and produce a time dependent signal in a gravimeter. Data from superconducting gravimeters rule out such objects moving inside the Earth unless their mass mD and or orbital radius a are very small so that mD a < 1.2 × 10 −13 M⊕R⊕.Here M⊕ and R⊕ are the mass and radius of the Earth.