# [time-nuts] Einstein Special on PBS

Tom Van Baak tvb at LeapSecond.com
Sun Nov 29 11:31:18 EST 2015

```Hal,

Right. The orbits are nominally circular -- but not exactly. The set of orbital parameters cover these details. A quick google search suggests the eccentricity for GPS is around 0.01. Still, that's enough to cause +/- 23 ns of accumulated phase error per orbit. I'm pretty sure the receivers take care of this math, since eccentricity is a key part of any orbit model. I wish we could see the source code to a GPS timing receiver.

I'm not sure I understand your elevation question. Are you talking about elevation as in mountain vs. sea level altitude? Or elevation as in satellite Az/El?

GPS satellites in view are about 20,000 km (overhead) to about 25,000 km (horizon) away, so the signal gets to you within about 65 to 85 ms. Whether you apply the full 4.5e-10 relativistic correction or no correction to the SV clock at all, it makes only a 1 cm time-of-arrival difference. That's why I said for trilateral navigation purposes, the relativistic effects are in the noise. For UTC time-transfer, however, an uncorrected 4.5e-10 frequency error would continuously accumulate, giving 38 us/day phase error, the number you often hear.

About survey grade -- I suspect the post-processing takes into account anything you can think of, from the shape of the antennas to space weather to the phase of the moon (literally).

/tvb

----- Original Message -----
From: "Hal Murray" <hmurray at megapathdsl.net>
To: "Discussion of precise time and frequency measurement" <time-nuts at febo.com>
Cc: <hmurray at megapathdsl.net>
Sent: Saturday, November 28, 2015 2:37 PM
Subject: Re: [time-nuts] Einstein Special on PBS

>
> holrum at hotmail.com said:
>> The GPS spec implies the satellites have a fixed frequency offset to
>> compensate for relativistic effects.  But do they actually dynamically and/
>> or individually adjust the frequency to adjust for orbit variations and
>> eccentricities?
>
> I think the orbits are circular so the frequency won't depend on the orbital
> position.
>
> The next question is does the math in the receiver have to correct for
> changes due to elevation?  Does it become relevant if you are trying for