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From: "Paul.B.Andersen" <relativity@paulba.no>
Newsgroups: sci.physics.relativity
Subject: Re: Relativity is a pseudoscience II. The Hafele-Keating HOAX,
Date: Fri, 20 Sep 2024 20:36:14 +0200
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Den 20.09.2024 03:08, skrev rhertz:
> ***************************************************************
> If τ and τ₀ are the respective times recorded by the flying and ground
> reference clocks during a complete circumnavigation, their time
> difference, to a first approximation, is given by
> 
> (τ - τ₀)/τ₀ = -(2RΩv + v²)/2c²
> 
> **************************************************************

This is the kinematic term, of course.

But note:
As clearly stated in the paper, this equation is only
valid for flights in the equatorial plane.
But H&K knew that, so I am sure they compensated for this
when the flights were at different latitudes.
> 
> Just a curiosity with this Hafele formula for SR:
> 
> R = 6,361,000 m
> Ω = 0.000072921159 rad/sec
> v = 900 Kmph = 250 m/sec


Duration of the trip in either direction:
τ₀ = 2⋅π⋅R/v = 159869 s ≈ 44.4 hours

This is the time measured by a clock on Earth,
so it is a proper time.

> 
> It gives to me a value
> 
> 
> (τ - τ₀)/τ₀ = -1.638E-12

So for the East going clock:
(τ - τ₀) = -1.638E-12⋅159869 s = -240 ns


West going clock (v negative):
(τ - τ₀)/τ₀ = +9.0257E-13
(τ - τ₀) = +9.0257E-13⋅159869 s = 144 ns

> 
> Accumulating 65 hours flying eastward, it gives

Your aircraft was flying at 900 km/h non stop for 44 hours.

H&K had several flight with many take offs and landing.
during 65 hours for the Eastwards trip, and during 80 hours
for the Westward trip. So of course the kinematic term would
be smaller in H&K.
As you can see:
H&K prediction for kinematic term East  -184 ns
Your prediction for kinematic term East -240 ns
H&K prediction for kinematic term West    96 ns
Your prediction for kinematic term West  144 ns

> 
> 
> (τ - τ₀) = -383.2 nanoseconds for a full eastward flight around the
> globe.

This is if your aircraft had flown at 900 km/h for 65 hours.
And then it would  have flown more than once around the world.


> 
> But Hafele published a theoretical SR value of -184 ± 18 nsec, which is
> almost half the value I calculated using his formula for SR.
> 
> Can anyone spot my error?

You know of course what the error is.

BTW, what was your point?

-- 
Paul

https://paulba.no/