Some future space missions will measure distances of laser links and angles among these links with very high precision. For example, LATOR mission will reach a level of 0.1 pico-arcsecond. And when light ray passes the limb of the Sun, the 2PN deflection contributed by the Sun is about few micro-arcsecond. So, a whole 2PN light propagation should be considered. On the other hand, although Einstein’s general relativity (GR) has passed nearly all the tests in the Solar System, there are many important reasons to question it. Especially, in the cosmological scale, two big problems challenge the GR. So, testing and distinguishing different gravity theories is needed. Among these theories, STT is the simplest and most natural way to modify GR. And deviation of the PPN parameter γ from 1 might range for 10-7 to 10-5. And this deviation needs to be considered at 2PN order. From the practial and theoretical points of view, it is a natural development to build a 2PN theory of a N-body system for its dynamics and light propagation within it which might show some subtle but interesting effects due to the coupling terms in the 2PN order.

This research shows the 2PN 2-body effect in the Solar System is one order of magnitude less than future ~1 nano-arcsecond experiments, while this effect could be comparable with first post-Newtonian component of δθSTT in a binary system with two Sun-like stars and separation by ~0.1 AU if an experiment would be able to measureγ-1 down to ~10-6. Besides, the deviation from the general relativity δθSTT does not depend on the PPN parameter β at 2PN level in a case that the light propagation time is much less than the time scale of its orbital motion. For more details, please see the following link:

http://prd.aps.org/abstract/PRD/v86/i4/e044007