# [time-nuts] Einstein Special on PBS

Magnus Danielson magnus at rubidium.dyndns.org
Sat Nov 28 04:37:05 EST 2015

```Hi,

On 11/27/2015 05:03 PM, Tom Van Baak wrote:
>> 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.

As found in IS-GPS-200H:

http://www.gps.gov/technical/icwg/IS-GPS-200H.pdf

8<---
3.3.1.1 Frequency Plan.
For Block IIA, IIR, IIR-M, and IIF satellites, the requirements
specified in this IS shall pertain to the signal contained within two
20.46 MHz bands; one centered about the L1 nominal frequency
and the other centered about the L2 nominal frequency (see Table 3-Vb).
For GPS III and subsequent satellites, the requirements specified in
this IS shall pertain to the signal contained
within two 30.69 MHz bands; one centered about the L1 nominal frequency
and the other centered about the L2 nominal frequency (see Table 3-Vc).
The carrier frequencies for the L1 and L2 signals shall be coherently
derived from a common frequency source within the SV.  The
nominal frequency of this source -- as it appears to an observer on the
ground -- is 10.23 MHz. The SV carrier frequency and clock rates --
as they would appear to an observer located in the SV -- are offset to
compensate for relativistic effects.  The clock rates are offset by
∆ f/f = -4.4647E-10, equivalent to a change in the P-code chipping rate
of 10.23 MHz offset by a ∆f = -4.5674E-3 Hz.  This is equal to
10.2299999954326 MHz.  The nominal carrier frequencies (f0)
shall be 1575.42 MHz, and 1227.6 MHz for L1 and L2, respectively.
--->8

There is however relativistic effects that the user equipment must
compensate for, as it depends on the position of the user observation
and shifts will be different for each user or for that matter for the
user the shift will be different for each satellite.

Cheers,
Magnus
```