In this chapter, we deduce a unified formula which allows to discuss the comparison of clock rates at two different space–time points. In the case of a perturbed Robertson–Walker metric, our formula returns to an equation for the comparison of clock rates at different cosmic space–time points, which includes the Hubble redshift, the Doppler effect, the gravitational redshift, and the Rees–Sciama effects. In the case of the solar system, when the 2PN metric is substituted into the unified formula, the comparison of the clock rates both on the earth and a space station could be made. It might be useful for the discussion on the precise measurement on future ACES and ASTROD.
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Xu, C., Wu, X., Brüning, E. (2008). Unified Formula for Comparison of Clock Rates and Its Applications. In: Dittus, H., Lammerzahl, C., Turyshev, S.G. (eds) Lasers, Clocks and Drag-Free Control. Astrophysics and Space Science Library, vol 349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34377-6_7
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