There are two kinds of geocentric frames: local inertial and non-inertial geocentric frames. Ashby et al successfully constructed a local inertial geocentric frame in the neighborhood of the gravitating Earth. In the frame with origin at the Earth's center, the gravitational effects of the sun and of planets other than the Earth are basically reduced to their tidal forces, with very small relativistic corrections.

However, the spatial base vectors of the local inertial frame essentially experience the geodesic (or deSitter) precession with respect to the solar system barycentric frame. Hence the realization of the local inertial frame requires that the general precession should exclude the geodesic precession. This requirement is inconsistent with the convention that the amount of geodesic precession is included in that of the general precession given by Lieske et al.