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 $ς$ and $η$ in the second post-Newtonian (2PN) order, in addition to the parameterized post-Newtonian parameters $γ$ and $β$. This new 2PN parameterized (2PPN) formalism includes the non-stationary 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 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 microacrsecond ($μ$as) for space astrometry missions in the near future, we further consider a model of angular measurement, LATOR-like missions. In this case, all terms with aimed at the accuracy of $\sim1μ$as are estimated.

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