Long-period variations in the geocenter observed from laser tracking of multiple Earth satellites

The geocenter vector represents the translational offset between networks of tracking stations and the mass center of the total Earth system (including the solid, ocean, and atmosphere components). The vector, directed from the Earth's mass center to the origin of the terrestrial reference frame (TRF), is equivalent to degree one geopotential coefficient changes in a crust-fixed system. This vector changes over time due to mass redistribution between the components of the planetary system. Dynamical satellite geodesy can be used to observe geocenter vector changes since satellites are dynamically tied to the Earth's mass center while crust-fixed tracking sites define the TRF. SLR tracking of geodetic satellites provides one of the most precise methods of monitoring these changes. The duality between the geocenter vector and degree one geopotential coefficients is developed analytically and demonstrated numerically through simulations. Time-varying errors in real-world geopotential models make the geocenter vector difficult to observe. Therefore observed geocenter variations must be interpreted as linear combinations of several low degree and order geopotential coefficients. Precise observations of geocenter motion from Lageos-1 are presented spanning the years 1983-1995. Shorter span solutions over the years 1993-1995 computed from Lageos-1, Lageos-2, TOPEX/Poseidon, and Ajisai tracking are presented along with multi-satellite combination solutions. Observed variations in the axial z-direction are consistently larger than in the equatorial x- and y-directions. The equatorial time-series show a consistent RMS variability of 5-8 mm. Frequency spectra of the time-series are dominated by semi-annual and annual variations. Motion of the geocenter vector represents a new and significant geodetic observable. Geocenter mismodeling can cause significant errors in the axial centering of TOPEX orbits, in mean sea level estimates, and in mean sea level slope calculations. Future altimetric missions must model geocenter vector changes during the orbit determination process. Along with polar motion, universal time, precession, and nutation, modeling the geocenter vector is needed to complete the transformation from the terrestrial reference frame to the local inertial celestial reference frame.