The second post-Newtonian light propagation and its astrometric measurement in the solar system

The relativistic theories of light propagation are generalized by introducing two new parameters zeta and eta in the second post-Newtonian (2PN) order, in addition to the parametrized post-Newtonian (PPN) parameters gamma and beta. This new 2PN parametrized (2PPN) formalism includes the nonstationary gravitational fields and the influences of all kinds of relativistic effects. The multipolar components of gravitating bodies are taken into account as well at the first post-Newtonian (1PN) order. The equations of motion and their solutions of this 2PPN light propagation problem are obtained. Started from the definition of a measurable quantity, a gauge-invariant angle between the directions of two incoming photons for a differential measurement in astrometric observation is discussed and its formula is derived. For a precision level of a few microarcsecond (mu as) for space astrometry missions in the near future, we further consider a model of angular measurement, the Laser Astrometric Test of Relativity (LATOR)-like missions. In this case, all terms with aimed at the accuracy of similar to 1 mu as are estimated.