The Second Post-Newtonian Light Propagation and Its Astrometric Measurement in the Solar System
Abstract
The relativistic theories of light propagation are generalized by introducing two new parameters 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 (μas) 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 1μas are estimated.