The gravitomagnetic influence on Earth-orbiting spacecrafts and on the lunar orbit
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Gravitomagnetic field is covariantly split in the intrinsic and extrinsic parts, which are generated by rotational and translational currents of matter respectively. The intrinsic component has been recently discovered in the LAGEOS spacecraft experiment. We discuss the method of detection of the extrinsic tidal component with the lunar laser ranging (LLR) technique. Analysis of the gauge residual freedom in the relativistic theory of three-body problem demonstrates that LLR is currently not capable to detect the extrinsic gravitomagnetic effects which are at the ranging level of few millimeters. Its detection requires further advances in the LLR technique that are coming in the next 5-10 years.