A particle which flies from a point C to point L in the Earth gravitation should submit to the brachistochrone problem decision. 

Well-known that the particle flying in a gravitational field of the Earth on a cycloid, spends less time, than flying on direct line. It concerns as neutrino so photon. Hence, why not to direct on the same way photons (for example, impulses of centimetric radio-waves over the Earth between the same points) and to compare time of their flight to time of these neutrinos?