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In the context of relativistic positioning, the coordinates of a given usermay be calculated by using suitable information broadcast by a 4-tuple ofsatellites. Our 4-tuples belong to the Galileo constellation. Recently, weestimated the positioning errors due to uncertainties in the satellite worldlines (U-errors). A distribution of U-errors was obtained, at various times, ina set of points covering a large region surrounding Earth. Here, thepositioning errors associated to the simplifying assumption that photons movein Minkowski space-time (S-errors) are estimated and compared with theU-errors. Both errors have been calculated for the same points and times tomake comparisons possible. For a certain realistic modeling of the world lineuncertainties, the estimated S-errors have proved to be smaller than theU-errors, which shows that the approach based on the assumption that theEarth's gravitational field produces negligible effects on photons may be usedin a large region surrounding Earth. The applicability of this approach -whichsimplifies numerical calculations- to positioning problems, and the usefulnessof our S-error maps, are pointed out. A better approach, based on theassumption that photons move in the Schwarzschild space-time governed by anidealized Earth, is also analyzed. More accurate descriptions of photonpropagation involving non symmetric space-time structures are not necessary forordinary positioning and spacecraft navigation around Earth.

Approaches to relativistic positioning around Earth and error estimations