Frequently asked questions on Relativity

Why do we need two reference systems - GCRS and BCRS?

One can argue in different ways. Basically, one can use any relativistic reference system to describe physical phenomena since there is no preferred one in general relativity. However, some of the reference systems are more convenient than others. In this sense the BCRS is convenient to describe solar system ephemerides. Although phenomena located in a certain vicinity of the Earth can be described in the BCRS as well, that description is not physically adequate. For example, because of the time-dependent barycentric velocity of the Earth, the Earth's figure in the BCRS is time-dependent because of the Lorentz contraction. This effect has nothing to do with the physics of the Earth. To avoid this and similar effects a special reference systems - called GCRS - was introduced. The influences of external matter (Sun, Moon, etc.) and the translational motion of the Earth are effaced in the GCRS coordinates as much as it is possible in general relativity: as it is usual in Newtonian theory the external gravitational potentials in the GCRS are reduced to tidal ones. Further explanations can be found in Soffel et al. 2003, Astron.J, 126, 2687.

What would be a good qualitative description of the time-dependent directions of the GCRS spatial axes as viewed in the BCRS? (George Kaplan, USNO)

There is no rotation matrix between the spatial axes of the BCRS and those of the GCRS; the orientation of the BCRS spatial axes (determined by the ICRS) completely determines the orientation of GCRS axes.