Question

Since the Earth is moving around the Sun, which is moving around Milky Way, etc... What reference frame is used for the complete motion of the begin/end points (which are non-inertial right?)?

Answer 1

They trust the method used by GPS for geodesy, where the claim is they can go down to picosecond and cm accuracy if necessary (for military use).

GPS error analysis takes even general relativity into account.

In GPS signal propagation (PDF) the systematic errors of a simple GPS setup are given, but the OPERA experiment has more sophisticated use of four satellites.

There has been no analysis of the GPS systematics further in the paper published in the archive, that is why I say they trust it.

Among other corrections, GPS corrects back to the velocity of light in vacuum. The meter is defined as a fraction of the velocity of light in vacuum (the second is defined by the caesium clock at normal temperature and pressure).

In my opinion, it is possible that some of the very sophisticated corrections of GPS values might be systematically off, with an end result of effectively redefining the meter. This would not show up in navigation or geodesy because the lengths probed by the OPERA experiment are very large (732 km) and the errors very small, 20 cm. A tiny systematic offset of what a meter is for GPS would not show up in the normal world use of it, but it would show up in measuring the neutrino speed with this method.