# [time-nuts] Einstein Special on PBS

Tom Van Baak tvb at LeapSecond.com
Fri Nov 27 11:03:45 EST 2015

```> They mentioned some "6 miles per day" offset due to GPS relativity effects.
> I think this is the sum of both special relativity (time dilation) and
> general relativity (gravitational) effects. The GR correction is 45
> microseconds a day fast; the SR correction is 7 microseconds slow. 38
> microseconds seconds is 11 kilometers which is indeed 6 or 7 miles. While
> time drifts 38 microseconds a day, I'm not sure that GPS coordinates would
> drift that fast - aren't most of the corrections in the same direction?

Hi Tim,

Correct. Here's from the "rel" program (in my http://leapsecond.com/tools/ folder):

C:\tvb\NPR>rel 20000km 14000kph
** Altitude 20000000.000 m (65616797.900 ft, 12427.424 mi) 5.274e-010 blueshift
1898630.424377 ps/hour
45567.130185 ns/day
** Velocity 3888.889 m/s (14000.000 km/h, 8699.197 mph) -8.414e-011 redshift
-302888.070815 ps/hour
-7269.313700 ns/day
** Net effect (GR+SR) 4.433e-010 shift
1595742.353562 ps/hour
38297.816485 ns/day

What this means is that as a *source of UTC*, GPS would in fact be off by 38 us per day if you forgot about relativity when you designed it.

But, you're right, you cannot blindly turn that "38 us/day" into "11 km/day". As long as *all* the GPS clocks are running too fast or too slow and as long as the receivers know what that offset is, the navigation system would still work just fine, relativity or not. This is true for any sort of triangulation (actually, trilateration) system.

GPS is a PNT (Position, Navigation, and Timing) system. So while GPS is really cool, and relativity is really cool, the navigation part of GPS does not "depend" on relativity, per-se.

/tvb

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