Re: How GPS works


Tom Roberts wrote:
Koobee Wublee wrote:

** c^2 (T1 - t)^2 = (x - X1)^2 + (y - Y1)^2 + (z - Z1)^2
** c^2 (T2 - t)^2 = (x - X2)^2 + (y - Y2)^2 + (z - Z2)^2
** c^2 (T3 - t)^2 = (x - X3)^2 + (y - Y3)^2 + (z - Z3)^2
** c^2 (T4 - t)^2 = (x - X4)^2 + (y - Y4)^2 + (z - Z4)^2

Note you used 4 satellites, not 3.

Good observation. However, only three is needed if you can synchronize
your clock with the GPS, or you don't care about the accuracy.

** No GR

Because you ignored it. GR came in where you said "all satellites should
have their time synchronized with each other" -- GR is necessary so
differential GPS will work, which involves a ground-based "satellite",
and yields much better accuracy than standard GPS. Empirically, it is
also used in the actual GPS system, because the control segment is on
the ground. <shrug>

All satellites reside in the same altitude. As Androcles said, any
effect cancels out. Synchronization can be done with adjacent
satellite by each where all satellites in the same orbit are stationary
to each other. There are two such orbits of satellites. How does one
satellite from one orbit synchronize its clock with one satellite from
the other orbit?

** No SR

Your assumption that the signals travel at c in the ECI frame is the
essence of SR. But as I've said before, one must use GR here, not SR.

Since it is essential to synchronize all clocks for all satellites even
if in different orbits, this proves SR wrong. However, you can argue
that the satellites in one orbit are moving relatively slowly with
satellites from the other orbit.

** Sagnac lack of effect

You did not convert to rotating-earth coordinates, which is where it
enters.

Just when is Sagnac non-effect coordinate dependent?

People want position in latitude and longitude, not in ECI
coordinates as you gave above.

True. Use spherically symmetric polar coordinate instead of the
rectangular coordinate then. <shrug>

.

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