  Detecting the Earth's inner core motions relative to the mantle presents a
considerable challenge due to their indirect accessibility. Seismological
observations initially provided evidence for differential/super-rotation of the
inner core, but recently demonstrated a possibly about 70-year periodic
oscillation. The contrasting results underscore the ongoing enigma surrounding
inner core motion, leaving debates unresolved, including the precise oscillate
period. In parallel to seismic observations, satellite geodesy has accumulated
decades of global high-precision records, providing a novel avenue to probe
inner core motions. Here, we detect an about 6-year oscillation from the
gravitational field degree-2 order-2 Stokes coefficients derived from satellite
observations, and find it has a unique phase correlation with the about 6-year
signal in the Earth's length-of-day variations. This correlation is attributed
to an inner core oscillation which is controlled by the gravitational coupling
between the inner core and lower mantle (mainly due to the density
heterogeneity of the two large low-velocity provinces; LLVPs). That is, we
independently corroborate the inner core periodic oscillation, albeit with a
significantly shorter period than previously suggested. Our findings
demonstrate the dense layer of the LLVPs (mean density anomalies of about +0.9
percent at the bottom), consistent with inversions from tidal tomography and
Stoneley modes. Furthermore, our research reveals equatorial topographic
undulations of about 187 m at the inner core boundary.
