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From: hertz778@gmail.com (rhertz)
Newsgroups: sci.physics.relativity
Subject: Re: Relativity is a pseudoscience II. The Hafele-Keating HOAX,
Date: Thu, 12 Sep 2024 04:08:59 +0000
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You have to download this paper, from 2017, in order to understand what
these "specimens" wrote in 1971:

Relativistic Corrections in the European GNSS Galileo
Dr. A. Mudraka, Dr. P. De Simonea, Dr. ing. M. Lisi a
a European Space Agency - ESTEC, Noordwijk, The Netherlands


https://www.academia.edu/112529110/Relativistic_Corrections_in_the_European_GNSS_Galileo


In this paper Mudrak and his team calculated the corrections to be
applied to ground receivers of the European GPS-like network: Galileo.

To do so, Mudrak used the basic Schwarzschild's solution (from 1915),
over which it was added a couple of minor corrections that can be
dismissed for the purpose of this test.

Considering the average height at which Galileo satellites orbit, Mudrak
separated the effects of GR and SR.

The GR influence on the difference that he calculated between atomic
clocks on orbit and a reference clock located at the surface of the
Earth was:

Δf/f = -GMe/c² (1/r - 1/a) , where a=radius of Earth ; r=distance of
satellite to the center of Earth.

As you can see, this is a better equation than using only h=average
height of the flights, but is not relevant. So, this part is EQUAL to
what Hafele-Keating used.

Now, Mudrak calculated that the influence of SR in the frequency
difference was:

Δf/f = vsat²/2c²

In these formulae, I dismissed the values of J2 (Earth quadrupole
moment) and Ωe (mean Earth angular rotation rate). This because of the
high speed and altitude involved.

So, for any practical purpose, there are no major differences between
Hafele-Keating and Mudrak formulae, WITH THE EXCEPTION THAT the speed of
the plane IS RELEVANT when compared with the rotational speed of Earth.

The remaining concept is that Δf/f (frequencies of atomic clocks in
orbit and at ground stations) is related to the TIME that these clocks
count. So, you can interpret, without any conceptual error, that f, f₀,
τ and τ₀ ARE DIRECTLY RELATED.

Finally, to reach to some values close to those of Hafele-Keating, you
HAVE TO COMPUTE the time lapses over which these formulae were applied
(flight time).

Thinking about the HUGE AMOUNT of anomalies not considered in the 1971
experiment, nor you or ANYBODY can seriously take such crappy experiment
as something CLOSE TO REAL VALUES. THEY WERE COOKED TO THE MAXIMUM.

One last thing concerning the two flights in opposite directions, is
that the angular speed of Earth is added or subtracted from the speed of
the planes.

As you can analyze, relativity was used discretionally by these two
guys, as the "differential velocity" between both frames of reference
(planes and Earth) is ARBITRARILY COMPUTED.

These two crooks took ONE YEAR to publish the cooked data in the Science
Magazine. The original article, in 1971, contain a funny and confusing
graphic where they, allegedly, showed the "results" of that farce.

Obviously, somebody in the gov. pushed them to make a new presentation
with tables and numerical values, PLUS a lot of explanations about the
SIMPLIFICATIONS that they made. But it only takes to watch the tables
(which I presented before) to see and smell the ROTTEN FISH that such
1971 experiment was.