Second-order post-newtonian equations of light ray

A series of space astrometric missions have been proposed recently, in some of which second-order contribution to light propagation in multiple systems should be considered, i.e., second-order post-Newtonian ( 2PN ) equations of light ray have to be discussed under the recent extension of the DSX scheme, founded in early 1990ʹs to investigete a complete first-order post-Newtonian (1PN) celestial mechanics for N arbitrarily composed and shaped, rotating deformable bodies. In this paper, the iterative method is taken to establish and calculate the 2PN equations of light ray. The 2PN equations for the solar system have been deduced from the metric tensor and Christoffel symbols. When the higherorder terms are neglected, the 2PN equations reduce to the well-known 1PN equations. By using these equations, the light propagation in the solar system can be calculated.