I GPS system and general relativity

[cianfa72]

Actually, as you state this, it's too strong. The correct statement is that, given a spacelike hypersurface, one can always find some open neighborhood of that hypersurface in which Gaussian normal coordinates, i.e., a "synchronous coordinate chart", can be constructed. But one cannot guarantee that such coordinates will be valid for any open neighborhood, of any size whatever.

Ok, let me say the point is that, given an open patch in spacetime, it might be so much larger that timelike geodesics starting orthogonal from a spacelike hypersurface within it will intersect inside that region, though.

 

[PeterDonis]

the point is that, given an open patch in spacetime, it might be so much larger that timelike geodesics starting orthogonal from a spacelike hypersurface within it will intersect inside that region, though.

It doesn't have to be "so much" larger, just large enough for geodesics to intersect.

This is getting pretty far off the original topic of this thread, btw. The frames used in GPS are not examples of synchronous coordinates.

 

[binis]

Hi, we had a thread some time ago about GPS satellite system.
One starts considering the ECI coordinate system in which the Earth's center is at rest with axes pointing towards fixed stars. One may assume it is an inertial frame in which the Earth's surface undergoes circular motion.

Do you mean this ? I would thank you for your contribution.

 

[cianfa72]

Do you mean this ? I would thank you for your contribution.

No, the thread I was referring to is this.