Recent years have witnessed the rapid development of observation and the quick improvement of the advanced methods for measurement. It is time for astrometry to unfold a new era indubitably.

  Presently, the satellite laser ranging like LAser GEOdynamics Satellite (LAGEOS) has achieved accuracies of 0.5 milliarcsecond (mas) for orbit determination, the precision of lunar laser ranging (LLR) has approached one millimeter, and the very long baseline interferometry (VLBI) has attained to the precision of 0.1 mas and higher. Beyond the current thresholds, astrometric observation will be able to attain the accuracy of few microarcsecond or higher for some astrometric missions in the near future, such as the Laser Astrometric Test Of Relativity (LATOR), the Phobos Laser Ranging (PLR) and the Beyond Einstein Advanced Coherent Optical Network (BEACON). On the other hand, when light ray passes the limb of the Sun, the two-post-Newtonian (2PN) deflection contributed by the Sun is about few micro-arcsecond. Thus, a whole 2PN approximation framework should be construceted in order to meet these accuracy levels.

   Inspired by these ideas, within the framework of the scalar-tensor theory with an intermediate-range force, its 2PN approximation is obtained with Chandrasekhar’s approach. It includes the 2PN metric and equations of motion for general matter without specific equation of state. The conserved quantities to the 2PN order are isolated with the aid of the energy-momentum complex. Besides, the research also discuss the prospect of testing and distinguishing the intermediate-range force with the orbital motions of celestial bodies and spacecrafts. Basically, the intermediate-range force depend on the scale of testing system. In galactic scale, the force parameters would play a big role in explaining the flat rotation curve. However, in the outer solar system, the force could provide to

a certain extent the Pioneer anomalous constant acceleration. Then, in the inner solar system, the strength coupled with gravitation about the force. These results lead to the force negligible in an inner Solar System. If future experiments confirm the nonentity of dark matter in the Universe, it will provide a possible existence of the force. Until then, the intermediate-range force must work in galactic scale even cosmological scale.