  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 $m_D\,
a < 1.2\times 10^{-13}M_\oplus R_\oplus$. Here $M_\oplus$ and $R_\oplus$ are
the mass and radius of the Earth.
