The Effects of the Variation of the Gravitational Constant on the Rotation of the Earth in the Post-Newtonian Theories

In this article the effects of the variation of the gravitational constant on the rotation of the Earth in the preferred frames and non-preferred frames of the post-Newtonian gravitational theories are commended, especially the annual periodic variation are expounded. In addition, the theoretical results are made in comparison with the observational results. Finally, a brief discussion and conclusion are made.