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From: "Paul.B.Andersen" <relativity@paulba.no>
Newsgroups: sci.physics.relativity
Subject: Re: "The Truth about GPS. Co-inventor of GPS says Relativity Not
 Required." by Brent Shadbolt
Date: Thu, 6 Feb 2025 22:03:14 +0100
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Den 06.02.2025 01:25, skrev LaurenceClarkCrossen:
> Source:
> https://brentshadbolt.substack.com/p/the-truth-about-gps-relativity-not
> 
> "Mar 18, 2024
> 
> GPS is used to pinpoint locations on the Earth’s surface and relies on
> radio signals sent from satellites in space. The signals carry coded
> information about the satellite’s location and the signal's time. A GPS
> receiver on Earth collects this information from three or four
> satellites simultaneously and calculates the distance to each satellite.
> The receiver then calculates where these distances intersect to
> determine its location in three-dimensional space. The coordinates of
> longitude, latitude and altitude are given in reference to a
> three-dimensional mathematical model of the Earth's ellipsoid shape (a
> slightly squashed sphere) called the ‘Conventional Inertial Frame’ or
> ‘World Geodetic System 1984’ (WGS 84)1 (figure 12).
> 
> The positioning system's success relies on radio signals' ability to
> transmit extremely precise information. To this end, GPS satellites
> carry caesium atomic clocks that are correct to less than 5 parts in
> 1014, or about 4 billionths of a second per day.2 As the satellites are
> orbiting 20,184 km above the Earth, they are in a much weaker
> gravitational field than clocks on the Earth, and general relativity
> predicts that the satellite clocks will tick more quickly by 45
> microseconds per day.3
> 
> Since the satellite clocks are moving relative to receivers on Earth,
> special relativity predicts the satellite clocks will tick more slowly
> by some amount compared to ground-based clocks. Satellite orbital speeds
> are cited as 3,874 m/s; thus, satellite atomic clocks are reported to
> experience a time dilation of about 7 microseconds per day.3
> 
> When the slowing effect of special relativity on a GPS satellite clock
> rate is subtracted from the speeding-up effect of general relativity,
> the result is about 38 microseconds of increase per day (45-7). GPS
> engineers adjust the clock rates before they are placed into orbit to
> correct this time increase in satellite atomic clocks. The clocks are
> given a rate offset of 4.465 parts in 1010 from their nominal frequency
> of 10.23 MHz so that, on average, they appear to run at the same rate as
> a clock on the ground. The actual frequency of the satellite clocks
> before launch is thus 10.22999999543 MHz.3 In other words, the clocks
> are pre-tuned to count a different number of caesium oscillations per
> second compared to the standard on Earth so that in space, they measure
> the same duration of time for one second as on Earth.

So the clocks are tuned to run slow by the factor -4.4647e-10 ,
or -38 μs/day because that's what the General Theory of Relativity
say must be done to make the GPS work.

And then the GPS does work.

GPS without relativity? :-D


https://paulba.no/pdf/Clock_rate.pdf

-- 
Paul

https://paulba.no/