Dark matter could be composed of compact dark objects (CDOs). These objects may interact very weakly with normal matter and could move freely {it 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 $m_D$ and or orbital radius $a$ are very small so that $m_D, a < 1.2times 10^{-13}M_oplus R_oplus$. Here $M_oplus$ and $R_oplus$ are the mass and radius of the Earth.